WO2007085275A1 - Efficient filtering with a complex modulated filterbank - Google Patents

Efficient filtering with a complex modulated filterbank Download PDF

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Publication number
WO2007085275A1
WO2007085275A1 PCT/EP2006/008565 EP2006008565W WO2007085275A1 WO 2007085275 A1 WO2007085275 A1 WO 2007085275A1 EP 2006008565 W EP2006008565 W EP 2006008565W WO 2007085275 A1 WO2007085275 A1 WO 2007085275A1
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WO
WIPO (PCT)
Prior art keywords
filter
complex
signal
impulse response
subband
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PCT/EP2006/008565
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French (fr)
Inventor
Lars Villemoes
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Coding Technologies Ab
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Priority to DE602006020930T priority Critical patent/DE602006020930D1/en
Priority to BRPI0621207-7A priority patent/BRPI0621207B1/en
Application filed by Coding Technologies Ab filed Critical Coding Technologies Ab
Priority to BR122018017208-8A priority patent/BR122018017208B1/en
Priority to EP22214715.9A priority patent/EP4178110B1/en
Priority to JP2008551652A priority patent/JP5452936B2/en
Priority to EP21204932.4A priority patent/EP3979497B1/en
Priority to EP24168191.5A priority patent/EP4372743A3/en
Priority to AT06777144T priority patent/ATE503300T1/en
Priority to CA2640431A priority patent/CA2640431C/en
Priority to EP20184765.4A priority patent/EP3754846B1/en
Priority to AU2006336954A priority patent/AU2006336954B2/en
Priority to CN2006800538412A priority patent/CN101401305B/en
Priority to EP06777144A priority patent/EP1977510B1/en
Priority to EP18171733.1A priority patent/EP3454471B1/en
Priority to EP18153681.4A priority patent/EP3334043B1/en
Publication of WO2007085275A1 publication Critical patent/WO2007085275A1/en
Priority to NO20083675A priority patent/NO339847B1/en
Priority to HK09100077.7A priority patent/HK1120938A1/en
Priority to AU2010257205A priority patent/AU2010257205B2/en
Priority to NO20161716A priority patent/NO342163B1/en
Priority to NO20161718A priority patent/NO342467B1/en
Priority to NO20180322A priority patent/NO343578B1/en

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Classifications

    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
    • G10L19/00—Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis
    • G10L19/02—Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis using spectral analysis, e.g. transform vocoders or subband vocoders
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
    • G10L19/00—Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis
    • G10L19/02—Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis using spectral analysis, e.g. transform vocoders or subband vocoders
    • G10L19/0204—Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis using spectral analysis, e.g. transform vocoders or subband vocoders using subband decomposition
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0248—Filters characterised by a particular frequency response or filtering method
    • H03H17/0264—Filter sets with mutual related characteristics
    • H03H17/0266—Filter banks
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0294—Variable filters; Programmable filters
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H2218/00—Indexing scheme relating to details of digital filters
    • H03H2218/04—In-phase and quadrature [I/Q] signals

Definitions

  • the present invention relates to a filter apparatus and a method for filtering a time domain input signal, a filter generator and a method for generating an intermediate filter definition signal, especially for the field of encoding, decoding, manipulating and filtering of audio signals, e.g. in the field of HRTF (head related transfer function) .
  • HRTF head related transfer function
  • the resolution of the filter bank is still insufficient, in the sense that simple gain modifications in each subband do not suffice to truthfully model the action of a given filter.
  • HRTF head related transfer function
  • the intricate phase characteristics of the filters are important for the perceived audio quality. It is of course possible to apply fast convolution methods based on the DFT (Discrete Fourier Transform) as a post-process to the multi-channel rendering, but if the rendering device already contains the signals in the subband domain of complex exponential modulated filter bank, there are significant advantages in terms of computational complexity and algorithmic integration in performing the HRTF derived filtering in the subband domain, which will be outlined in more detail later.
  • HRTF's are different for each individual and the derived filters depend on virtual source and/or listener positions which can for instance be changed by control signals, user interfaces or by other description signals, it is also important to be able to efficiently convert a given HRTF related filter into subband domain filters.
  • a filter apparatus according to claim 1, by a method for filtering a time domain input signal according to claim 41, a filter generator according to claim 25, a method for providing an intermediate filter definition according to claim 42, a system according to claim 40 or by a computer program according to claim 43.
  • An embodiment of the present invention relates to a filter apparatus for filtering a time domain input signal to obtain a time domain output signal, which is a representation of the time domain input signal filtered using a filter characteristic having a non-uniform amplitude/frequency characteristic
  • a filter apparatus for filtering a time domain input signal to obtain a time domain output signal, which is a representation of the time domain input signal filtered using a filter characteristic having a non-uniform amplitude/frequency characteristic
  • a complex analysis filter bank for generating a plurality of complex subband signals from the time domain input signal, a plurality of intermediate filters, wherein one intermediate filter is provided for each complex subband signal, wherein at least one of the intermediate filters of the plurality of intermediate filters has a non-uniform amplitude/frequency characteristic, wherein the plurality of intermediate filters have a shorter impulse response compared to an impulse response of a filter having the filter characteristic, and wherein the non-uniform amplitude/frequency characteristic of the plurality of intermediate filters together represent the non
  • a further embodiment of the present invention is a filter generator for providing an intermediate filter definition signal comprising a complex modulated filter bank for filtering an impulse response signal indicative of an amplitude/frequency filter characteristic in a time domain to obtain a plurality of complex valued subband signals as the intermediate filter definition signal, wherein each complex valued subband signal of the complex modulated filter bank corresponds to an impulse response for an intermediate filter for a subband signal, wherein at least one of the complex valued subband signals comprises at least two different non- vanishing values, and wherein each complex valued subband signal is shorter than the impulse response signal.
  • Embodiments of the first aspect of the present invention are based on the finding that a more efficient and/or a more flexible filtering (or manipulation) of a time domain input signal can be achieved in the subband domain, which is sometimes also referred to as QMF domain (quadrature mirror filter) , with a better quality compared to other manipulation schemes.
  • the gain with respect to efficiency, especially computational efficiency is a consequence of the shorter impulse responses of the intermediate filters compared to the impulse response of a filter having the non-uniform filter characteristic in the time domain and the fact that the subband signals can be processed independently from one another. Due to the shorter impulse responses an embodiment of a filter apparatus can process each complex subband signals output by the complex analysis filter bank individually. Hence, the filtering can be carried out parallely, which speeds up the processing of the time domain input signal dramatically compared to manipulating the time domain input signal directly due to the shorter impulse responses.
  • Embodiments according the first aspect of the present invention are especially favorable when it comes to balancing computational efficiency on the one hand and quality on the other hand.
  • a direct processing of the time domain input signal in the time domain can be achieved by a convolution with the impulse response of a filter having the non-uniform amplitude/frequency characteristic, which usually leads to a very good quality
  • the convolution requires a high computational effort because of the length of the impulse response of the filter in the time domain.
  • transforming an audio signal into the frequency domain by performing a Fourier transformation represents the tremendous drawback that other manipulations, which are necessary in modern acoustical systems, cannot be efficiently performed in the Fourier domain with a high quality.
  • inventive filter apparatuses represent an excellent compromise between a direct processing of the time domain input signal for instance by means of convoluting the time domain input signal with the longer impulse response indicative of the non-uniform filter characteristic, which leads to an enormous computational effort, and employing a Fourier transform, which leads to more problems in the further course of processing the signals.
  • the complex analysis filter bank and the complex synthesis filter bank for generating the plurality of complex subband signals from the time domain input signal and for synthesizing the time domain output signal are already present.
  • embodiments of the present invention are based on the finding that a more flexible and more efficient filtering of the time domain input signal with a better quality can be achieved by providing an intermediate filter definition signal, which can for instance be provided to a filter apparatus according to the first aspect to define its intermediate filters .
  • an intermediate filter definition signal for a set of intermediate filters is obtained by providing an embodiment of the inventive filter generator with a filter defining signal, such as an impulse response signal indicative of an amplitude/frequency filter characteristic of a filter in the time domain or other filter definition signals.
  • a filter defining signal such as an impulse response signal indicative of an amplitude/frequency filter characteristic of a filter in the time domain or other filter definition signals.
  • an embodiment of a filter generator provides a filter definition signal for a set of intermediate filters to effectively the same filtering as a filter in the time domain defined by the filter definition signal virtually without introducing aliasing effects.
  • embodiments of an inventive filter generator enable a virtually alias free performance of an arbitrary filter in the subband domain.
  • arbitrary filter characteristics can be transferred from the time domain to the subband signal domain, like virtually alias free equalization, low- pass filter characteristics, high-pass filter characteristics, band-pass filter characteristics, band- rejection filter characteristics, resonance filter characteristics, notch filter characteristics or more complex filter characteristics.
  • a combination of several characteristics as well as HRTF-related filter characteristics are important to mention.
  • embodiments of the inventive filter generator enable to truthfully model an action of a given filter in the time domain in the subband domain.
  • the virtually alias free performance, which is especially important in HRTF-related applications, is made possible as the phase characteristics of a filter in the time domain is (almost) perfectly transferred into the subband domain. Examples illustrating this will be outlined in the further course of the present application.
  • the complex modulated filter banks of embodiments of the inventive filter generator produce a plurality of complex valued subband signals as the intermediate filter definition signal, wherein each of the complex valued subband signal is shorter than the impulse response signal indicative of the amplitude/frequency filter characteristic in the time domain.
  • the filter generator hence, produces an intermediate filter definition signal comprising the output of the complex modulated filter bank with its plurality of short complex valued subband signals, which does not only enable a fast, efficient and parallel computation with respect to filtering a time domain input signal to obtain a time domain output signal in the frame work of an embodiment of a filter apparatus, but does also enable a fast, efficient and parallel computation of the intermediate filter definition signal itself.
  • the application of an embodiment of an inventive filter generator according to the second aspect of the present invention enables a simplified, faster and more efficient computation, which leads to an audibly indistinguishable result compared to the more complex convolution method.
  • an embodiment of the inventive filter generator also offers the advantage of a significantly enhanced flexibility with respect to the possible filter characteristics applied in the subband domain.
  • an enormous flexibility is introduced to audio signal processing and manipulation.
  • an embodiment of an inventive filter generator is capable of providing an intermediate filter definition signal corresponding to an individually altered filter characteristic of an HRTF-related filter. In the field of HRTF this offers the opportunity to individually modify the HRTF filters according to the needs and hearing capabilities of an individual.
  • the source position as well as the listener position with respect to each other and with respect to a (simulated or calculated) environment e.g. a concert hall, an open space, a stadium
  • a (simulated or calculated) environment e.g. a concert hall, an open space, a stadium
  • An embodiment of the inventive filter generator hence, provides the possibility to virtually switch from a stadium to a concert hall or an open field, without employing the necessity to transfer the audio signals between the time domain, the subband domain and/or the frequency domain.
  • all these manipulations of the audio signal can be performed inside the subband domain with a very high quality, which is perceptually indistinguishable from a signal processing in the time domain, but which offers an enormous computational efficiency improvement.
  • An embodiment of an inventive filter generator offers the possibility to alter the filter characteristics of the plurality of the intermediate filters in a quasi-continuous fashion.
  • An application in the field of HRTF is an application of an embodiment of the filter generator and/or of the filter apparatus in a head tracking application, in which for instance the position of the listener with respect to different audio sources varies
  • Possible applications comprise, for instance, simulations and computer games with a very high quality.
  • Another advantage of an embodiment of a filter generator is that the application of an embodiment of a filter generator is more efficient with respect to the memory usage, as an impulse response signal provided to the complex modulated filter bank of the filter generator is typically a real valued signal, whereas the intermediate filter definition signal is a complex valued signal of approximately the same over-all length.
  • storing the impulse response signals compared to the intermediate filter definition signals (or the filter taps of the intermediate filters) saves memory, roughly speaking, of an order of 2. Due to the possibility of a fast and efficient parallel computation, especially in the field of memory-sensitive
  • the filter generator is provided with a filter definition signal, which can comprise for instance the filter taps of a digital filter in the time domain or by a transfer function in the frequency domain, which can comprise the amplitude/frequency characteristic and/or the phase/frequency characteristic of a filter.
  • a filter definition signal can comprise for instance the filter taps of a digital filter in the time domain or by a transfer function in the frequency domain, which can comprise the amplitude/frequency characteristic and/or the phase/frequency characteristic of a filter.
  • an embodiment of the filter generator furthermore comprises an impulse response signal generator, which provides the appropriate impulse response signal indicative of the resulting amplitude/frequency filter characteristic in the time domain to the complex modulated filter bank of the filter generator.
  • an impulse response signal generator in some embodiments of an inventive filter generator offers an even more flexibility with respect to providing the intermediate filter definition signal, as not only the impulse response signals in the form of discrete time signals can be provided to an embodiment of the filter generator but also the filter taps or the frequency domain description of a filter in the time domain can be transferred into the subband domain by an appropriate embodiment of a filter generator.
  • Fig. Ia illustrates the processing of a digital audio signal by means of subband filtering in a system comprising a filter generator and a filter apparatus;
  • Fig. Ib illustrates a possible solution for a complex analysis bank
  • Fig. Ic illustrates a possible solution for a complex synthesis filter bank
  • Fig. Id illustrates a further possible solution for a complex synthesis filter bank
  • Fig. Ie illustrates an interplay of an embodiment of a filter generator with a plurality of intermediate filters of an embodiment of a filter apparatus
  • Fig. 2 illustrates the processing of a digital audio signal by means of direct form filtering
  • Fig. 3 illustrates a preferred embodiment of a system with a filter converter
  • Fig. 4 illustrates a given filter impulse response
  • Fig. 5 illustrates an impulse response obtained by complex gain adjustment of subbands
  • Fig. 6 illustrates the magnitude response of a given filter
  • Fig. 7 illustrates the magnitude response of a filter obtained by complex gain adjustment of subbands
  • Fig. 8 compares the performance of the present invention with complex gain adjustment of subbands
  • Fig. 9 illustrates a preferred embodiment of a filter apparatus comprising an optional embodiment of a filter generator and further components
  • Fig. 10 illustrates a filter characteristic along with several frequency bands for different subbands.
  • Fig. 11 illustrates a preferred embodiment of a filter generator.
  • Figure Ia illustrates in the form of a system comprising embodiments of both a filter apparatus and a filter generator the processing of a digital audio signal by means of subband filtering according to the present invention.
  • This signal path can for instance represent a part of a spatial audio rendering system where the input is a received audio channel and the output is a component of a signal to be played back at the right ear.
  • the input signal (Digital audio signal or time domain input signal) is analyzed by the complex analysis bank 101 by means of filtering with a set of L analysis filters followed by downsampling of a factor L , wherein L is a positive integer, preferably larger than 1.
  • the analysis filters are usually obtained by a complex modulation of a prototype filter p(y) , wherein v is a positive integer indicating an index in an array of data or an index of a value in a signal not downsampled by factor L.
  • the output of the filter bank consists of L subband signals that are processed by a subband filtering 102.
  • This subband filtering consists of a combination of manipulations such as subband gain adjustment according to received control data and application of finite impulse response filters applied separately in each subband.
  • the filter taps of the subband filters are obtained from an (inventive) filter converter 104 as an embodiment of a filter generator which takes as input a filter described by direct form filter
  • the complex synthesis bank 103 reconstructs an output signal by means of upsampling by a factor L , filtering by L synthesis filters, summation of all the results, and extraction of the real part.
  • the summation of all the results and the extraction of the real part can also be switched with respect to their order, as will be outlined more closely with respect to Figs. Ic and Id.
  • Fig. Ib shows a complex analysis bank 101 in more detail.
  • the complex analysis bank 101 comprises a plurality of L intermediate analysis filters 120 for each subband to be output by complex analysis bank 101.
  • each of the L intermediate analysis filters 120 is connected in parallel to a node 130 to which the time domain input signal to be processed is provided.
  • Each of the intermediate analysis filters 120 is adapted for filtering the input signal of the complex analysis bank 101 with respect to a center frequency of each subband.
  • each subband is labeled by a subband index or index n, wherein n is a non-negative integer, typically in the range from 0 to L-I.
  • the intermediate analysis filters 120 of the complex analysis bank 101 can be derived from a prototype filter p(v) by a complex modulation according to the subband index n of the subband to which the intermediate analysis filter 120 is applied. More details concerning the complex modulation of a prototype filter are explained below.
  • the sampling frequency of the signal output by the intermediate analysis filter bank 120 is reduced by a factor L.
  • the downsamplers 140 supplied to each subband signal output by the corresponding intermediate analysis filters 120 are optional as, depending on the concrete implementation, the downsampling
  • the intermediate analysis filters 120 can also be carried out in the frame work of the intermediate analysis filters 120.
  • downsampling the signal output by the intermediate analysis filters 120 is not required. Nevertheless, the presence of the explicit or implicit downsamplers 140 is a preferred option as the amount of data provided by the complex analysis bank 101 would alternatively be raised by a factor of L, leading to a significant redundancy of data.
  • Fig. Ic illustrates a possible solution for a complex synthesis bank 103.
  • the complex synthesis bank 103 comprises L intermediate synthesis filters to which the L subband signals from the subband filtering 102 are provided to.
  • the subband signals are upsampled by L upsampler 160, which reconstruct the sampled frequency of the subband signals by increasing the sampling frequency by a factor of L.
  • the optional upsampler 160 reconstruct or reform the subband signals provided to the upsampler 160 in such a way that the information contained in each of the subband signals is retained while the sampling frequency is increased by a factor of L.
  • the upsamplers 160 are optional components, as the upsampling can also be carried out in the frame work of the intermediate synthesis filters 150. Hence, the step of upsampling the subband signals carried out by the upsampler 160 can be simultaneously processed in the frame work of the intermediate synthesis filers 150. If, however, the downsamplers 190 are neither explicitly nor implicitly implemented, the upsamplers 160 do not have to be implemented explicitly or implicitly.
  • the intermediate synthesis filters 150 are connected via an output to an adder 170 which sums up the filtered subband signals output by the L intermediate synthesis filters 150.
  • the adder 170 is further connected to a real part extractor
  • the real part extractor 180 can perform this task for instance by extracting the real part of a complex valued signal provided by the adder 170, by calculating the absolute value of the complex valued signal provided by the adder 170 or by another method that forms a real valued output signal based on a complex valued input signal.
  • the signal output by the real part extractor 180 is the time domain output signal output by the embodiment of the inventive filter apparatus.
  • the second possible solution for a complex synthesis bank 103 shown in Fig. Id differs from the first possible solution shown in Fig. Ic only concerning the real part extractors 180 and the adder 170.
  • the outputs of the intermediate synthesis filters 150 are connected separately from each subband to a real part extractor 180 extracting or forming a real valued signal based on the complex valued signal output by the intermediate synthesis filters 150.
  • the real part extractor 180 extracting or forming a real valued signal based on the complex valued signal output by the intermediate synthesis filters 150.
  • Fig. Ia is the time domain output signal.
  • Fig. Ie shows the subband filtering 102 and its interplay with the filter converter 104 in more details.
  • the subband filtering 102 comprises a plurality of intermediate filters
  • the subband filtering 102 comprises L intermediate filters 190.
  • the filter converter 104 is connected to each of the intermediate filters 190. As a consequence, the filter
  • 16 converter 104 is capable of providing the filter taps for each of the intermediate filters 190 of the subband filtering 102. More details concerning the filtering done by the intermediate filters 190 will be explained in the further course of the application. Hence, the filters taps provided to the different intermediate filters 190 and output by the filter converter 104 form the intermediate filter definition signal.
  • the embodiments, solutions and implementations can comprise additional and/or optional delays for delaying any of the signals or a subset of signals, which have been omitted in Fig. Ia to Ie for the sake of simplicity. Also in the Fig. 2 to 11 optional delays have been omitted for the sake of simplicity. Nevertheless, delays or delayers can be comprised in elements shown (e.g. filters) or added as optional elements in all embodiments depending on their concrete implementation.
  • Figure 2 illustrates the processing of a digital audio signal by means of direct form filtering 201. If the same filter is given as input to the filter converter 104 of Fig. 1 and the direct filtering 201, a design goal for the filter converter 104 is that the digital audio output of 103 should be perceptually (or audibly) indistinguishable from the digital audio output of the direct filtering 201, if the digital audio inputs to the complex analysis bank 101 and the direct filtering 201 are identical and the processing in the direct filtering 102 consists of pure stationary subband filtering.
  • the filter input to the filter converter 104 is given as a filter definition signal, which can for instance comprise the filter taps of a corresponding time domain filter, a frequency domain description (amplitude/frequency characteristic and/or phase/frequency
  • the same filter definition signal can in principle be used.
  • the filtering can be carried out by direct application of the filter taps in the frame work a digital filter, by a discrete Fourier transform along with a transfer function or another frequency domain description or by means of convolution with the impulse response signal.
  • Figure 3 illustrates a preferred embodiment of a filter converter 104 according to the present invention as an embodiment of a filter generator.
  • the filter is assumed to be given by its impulse response. Viewing this impulse response as a discrete time signal, it is analyzed by an L -band complex analysis (filter) bank 301.
  • the resulting subband signal outputs are then exactly the impulse responses of filters to be applied separately in each subband in the subband filtering 102.
  • the filter definition signal provided to the filter converter 104 and its complex analysis bank or complex analysis filter bank 301 is the impulse response signal indicative of the amplitude/frequency characteristic of a filter, which is to be transferred into the subband domain.
  • the output of the complex analysis (filter) bank 301 of each of the L subbands represents the impulse response of the intermediate filters comprised in the subband filtering 102.
  • the complex analysis bank 301 is in principle derived from the analysis bank 101 but it has a different prototype filter and a slightly different modulation structure, the details of which will be outlined in the following description.
  • the length of the prototype filter q(y) can be designed to be only a fraction of the length of the prototype filter p(v) . Due to the downsampling by a factor L 1 the length of subband filters are also a factor of L smaller than the sum of the lengths of the given time domain filter and the prototype filter q(y) .
  • the computational effort is thus reduced in comparison to the direct form filtering 201 by approximately a factor of LIA .
  • the offset factor of 4 is due to the replacement of real filtering with complex filtering.
  • Another offset is the computational cost of the complex analysis and synthesis banks 101 and 103. For efficient implementations this cost is comparable to the cost of rather short FIR filters, and hence negligible, as outlined before. Moreover, this offset of the reduction in computational cost does not exist for systems that already employs these two filter banks 101 and 103.
  • a non-vanishing tap or value is a tap or a value which is ideally not equal to zero.
  • a non-vanishing value or tap is a real valued or complex valued tap or value with an absolute value which is larger than a predetermined threshold, e.g. 10 "s or 2 ⁇ s , wherein s is a positive integer depending on the requirements of a concrete- implementation.
  • a predetermined threshold e.g. 10 "s or 2 ⁇ s
  • this threshold is preferably defined in the binary system (basis 2), wherein the integer s has a predetermined value depending on the
  • the value s is 4, 5, 6, 7, 8, 10, 12, 14, 16 or 32.
  • Figure 5 illustrates the impulse response 410 of the system of Figure 1 with a 64 band filterbank, in a special case corresponding to prior art usage for envelope adjustment and equalization.
  • the subband filters or rather intermediate filters 190 are all of one tap only, so a constant complex gain is applied to each subband.
  • the corresponding gain is chosen to be equal to the complex frequency response of the filter of Figure 4 evaluated at the center frequency of the particular subband.
  • Figure 6 illustrates the magnitude response 420 of the filter of Figure 4.
  • Figure 7 illustrates the magnitude response 430 of the filter underlying the impulse response 410 shown in Figure 5.
  • the usage of only one gain per subband results in a poor approximation to the desired frequency response.
  • the main reason for this is the fast variation of the target phase spectrum. In fact, this
  • Figure 8 finally compares the performance of an embodiment of the present invention and of the prior art method of complex gain adjustment of subbands.
  • the dotted curve is a redrawing of the target magnitude response 420 of Figure 6.
  • the dashed curve 440 is the magnitude response of the difference between the complex frequency responses of the target filter and its approximation by the prior art method.
  • the solid curve 450 is the magnitude response of the difference between the complex frequency responses of the target filter and its approximation by the method taught by the present invention with the parameters as discussed during the description of Figure 4.
  • the error of the prior art method is small only at the 64 midpoints of filter bank subbands whereas the inventive method leads to an approximation quality in the 50 dB range. It should be pointed out that this is also the level of performance one measures when comparing the output of the inventive system to the output of the reference system for an arbitrary input signal.
  • an embodiment of an inventive filter apparatus, an embodiment of a filter generator and a system comprising both embodiments offer a significant advantage concerning the quality of the manipulation of an input signal.
  • the significant difference concerning the quality of filtering (or manipulation) of the input signal outlined above is a consequence of the fact that at least one of the intermediate filters 190 has an impulse response with two or more non-vanishing values. In other words, at least one of the intermediate filters 190 comprises at least two non- vanishing filter taps.
  • the number of subbands L processed by an embodiment of a filter apparatus is larger or at least equal to 2. Nevertheless, the number of subbands L is significantly
  • both an embodiment of the filter apparatus as well as an embodiment of the filter generator 104 can process the respective input signals highly efficiently in a fast and a parallel manner.
  • the processing of both a digital audio input as an input signal as well as an impulse response indicative of a filter characteristic can be carried out highly efficiently in a parallel fashion.
  • an embodiment of an inventive filter apparatus as well as an embodiment of an inventive filter generator combine the advantages of both a direct processing of audio signals in the time domain leading to a very high quality and using a combination of a Fourier transform along with a transfer function in the frequency domain offering a high efficiency as each frequency band is only multiplied with a (complex or real valued) tap in the process of filtering the signal.
  • an embodiment of an inventive filter apparatus comprising a complex analysis filter bank 101, a plurality of intermediate filters 190 in the subband filtering 102 and a complex synthesis filter bank 103 offers especially in the field of HRTF-related applications significant computational advantages due to the possible parallel processing of subband signals.
  • Embodiments of a filter generator and embodiments of systems comprising both a filter apparatus and a filter generator offer furthermore the advantage that filters can easily be adapted to specific environments, parameters or other specific needs of the application at hand.
  • an embodiment of such a system can be used in head-tracking applications, in which several sources of sounds and noises as well as the position of the listener vary over time.
  • Such an embodiment of a system comprising a filter apparatus and a filter generator therefore offer a highly efficient and flexible way to present an audio impression of a three dimensional arrangement of sound sources with respect to a varying position and orientation of a hypothetical listener via headphones or other head-related sound systems (stereo sound systems) .
  • an embodiment of an inventive filter apparatus along with an inventive filter generator offers not only a highly efficient system for audio manipulation with an excellent quality but also a very flexible way to introduce altering audio impressions in an efficient way.
  • v is an integer indicating an index or a time index of a time signal
  • ⁇ 2 ⁇ • f is the circular frequency associated to the frequency f
  • the complex exponential modulated £ -band filterbank is defined from a real valued prototype filter p(v) of finite length. For the computations below it will be assumed by extension with zeros that the prototype filter is defined for all integers v . Given a real valued discrete time signal x(v) the analysis filter bank 101 applies, as already explained, the complex modulated prototype filters followed by downsampling by a factor L in order to output the subband signals,
  • time index k differs from the time index v with respect to the fact that k refers to the downsampled signals, whereas the integer v withers to signals with the full sample frequency.
  • the synthesis filter bank 103 Given complex valued subband signals d n (k) , the synthesis filter bank 103 applies filtering followed by upsampling by a factor of L and a real value extraction in order to output the real valued signals, as already explained, to obtain the output signal
  • the present invention is applicable to the pseudo QMF type of design as taught by PCT/SE02/00626 "Aliasing reduction using complex exponential modulated filter banks".
  • the perfect reconstruction is also replaced by a near-perfect reconstruction property.
  • P( ⁇ ) 0 for ⁇ lL ⁇ .
  • the phase factors are assumed to satisfy the condition that ⁇ - ⁇ xs equal to an integer multiple of AL.
  • G n ( ⁇ ) ⁇ k g n (k)exp(-ik ⁇ ) is the discrete time Fourier transform of the filter applied in subband «for «>0and
  • G K (a>) G_ l _ m (-a>y for « ⁇ 0. (6)
  • H( ⁇ ) be a given filter (e.g. transfer function) with real valued impulse response h ⁇ v) . This data is considered as input to the filter converter 104.
  • H( ⁇ ) be a given filter (e.g. transfer function) with real valued impulse response h ⁇ v) . This data is considered as input to the filter converter 104.
  • a filter generator or a filter converter 104 is used to teach to convert the filter (defined by its impulse response) /z(v)into intermediate subband filters 190 by means of the second analysis filter bank 301 which employs real valued prototype filter q(y) ,
  • any given filter h(v) can be efficiently transformed into intermediate subband filter responses.
  • q(v) has A ⁇ -Z taps
  • a time domain filter h(v) of K N -L taps is converted into subband domain filters (12) with K H +K Q -l taps, wherein K n and K Q are positive integers.
  • This prototype filter corresponds to the choice (8) and has the disadvantage of having an infinite and slowly decaying impulse response q(y) . Instead, the present
  • a multi-slot QMF representation (subband domain) of the HRTF filters is described.
  • the filter conversion from the time domain into the complex QMF subband domain is performed by an FIR filter in the filter converter 104 of Fig. Ia.
  • the following description outlines a method for implementing a given FIR filter h (v) of length N h in the complex QMF subband domain.
  • the principle of the operation is illustrated in Fig. Ia in the case of a system also comprising an embodiment of an inventive filter apparatus.
  • the subband filtering itself is carried out by a set of or a plurality of intermediate filters 190 inside the subband filtering 102.
  • the subband filtering consist of the separate application of one complex valued FIR intermediate filter g n (l) for each QMF subband with an
  • the filter converter 104 converts the given time domain FIR filter h (v) into the complex subband domain filters g n (l) .
  • the filter converter 104 comprises a complex analysis bank 301 similar to the QMF analysis bank 101.
  • J 0 and v 0 are delays
  • 1 is an integer indicating an index of the filter taps
  • N h is the length of the impulse response h(v) of the filter characteristics to be transferred into the subband domain.
  • the filter coefficients qr(v) can be expressed by the following equations for the integer v in the range between 0 and 191, wherein according to the requirements and specifications of special implementations, the prototype filter coefficients may deviate from the following equations either individually or from the maximum absolute value typically by 10%, 5% or 2% and preferably by 1% or 0.1%:
  • the present invention relates to the application of an arbitrary filter to a signal which is available in the transform domain of a complex exponential modulated filter bank, when this filter bank is designed to give virtually alias free performance of operations like equalization, spectral envelope adjustment, frequency selective panning, or frequency selective spatialization of audio signals.
  • the present invention permits to efficiently transform a given finite impulse response (FIR) filter in the time domain into a set of shorter FIR filters, to be applied with one filter for each subband of the filter bank.
  • FIR finite impulse response
  • the present invention also teaches how to convert a given discrete time domain filter into to a set of subband domain filters.
  • the result is that any given filter can be implemented with a high degree of accuracy in the subband domain of a complex exponential modulated filter bank.
  • the filter converter consists of a second complex exponential modulated analysis filter bank.
  • the methods of the present invention coincides with that of PCT/EP2004/004607 "Advanced processing based on a complex-exponential modulated filterbank and adaptive time framing" .
  • the present invention comprises the following features:
  • a method for obtaining a high quality approximation to the filtering of a discrete-time input signal with a given filter comprising the steps of - analyzing the input signal with a downsampled complex analysis filter bank in order to obtain a multitude of subband signals,
  • the filter converter consists of a downsampled complex analysis filter bank.
  • a computer program having instructions for performing, when running on a computer, a method for obtaining a high quality approximation to the filtering of a discrete-time input signal with a given filter, the method comprising the steps of analyzing the input signal with a downsampled complex analysis filter bank in order to obtain a multitude of subband signals,
  • each subband signal with a subband filter, where the multitude of subband filters are obtained from the given filter by means of a filter converter, synthesizing an output signal from the filtered subband signals with a downsampled complex synthesis filter bank.
  • Fig. 9 illustrates an embodiment of an inventive filter apparatus for filtering a time domain input signal of an inventive filter apparatus to obtain a time domain output signal.
  • the filter apparatus of Fig. 9 comprises a complex analysis filter bank 101, a subband filtering 102 and a complex
  • Fig. 1 shows a system comprising an embodiment of an inventive filter apparatus along with an embodiment of a filter generator 104
  • the filter apparatus shown in Fig. 9 comprises only as an option a filter converter 104, which provides the subband filtering 102 with the intermediate filter definition signal, for instance in the form of the filter taps or the impulse response for each of the intermediate filters 190 of the subband filtering 102.
  • the filter apparatus shown in Fig. 9, comprises additional optional components, which can provide the subband filtering 102 with the filter taps for the plurality of intermediate filters 190 of the subband filtering 102.
  • the filter taps can also be taken from an optional data base 500, which is connected to the subband filtering 102.
  • the data base 500 comprises the complex valued filter taps of the intermediate filters 190.
  • the data base can be implemented as a memory system, for instance in the form of a nonvolatile memory system or volatile memory system depending on the concrete implementation.
  • such an embodiment comprises a data base 500 from which the filter taps for the subband filtering 102 can be taken.
  • the CPU 510 is capable of on-line calculating the filter taps.
  • the CPU 510 accesses the data base 500 according to a set of parameters provided by the user and/or according to a set of parameters, which are based on further circumstances, reads one or more sets of filter taps for the intermediate filters of the subband filtering 102 and calculates, optionally accompanied by an interpolation scheme or another estimation scheme, the desired intermediate filter taps and provides them to the subband filtering 102.
  • the CPU 510 or another processor or computer system provides the filter taps of the intermediate filters 190 to the subband filtering 102 without accessing a data base 500.
  • the CPU 510 or another processor calculates the filter taps and provides them to the subband filtering 102. Examples for such an embodiment will be explained more closely with respect to Fig. 10.
  • the CPU 510 accesses a further data base 520, reads one or more filter definition signals (e.g. in the form of impulse response signals corresponding to filter characteristic in the time domain) , calculates an effective filter definition signal, for instance an appropriate impulse response, and provides the results of this computation to the filter converter 104.
  • the filter converter 104 then provides the subband filtering 102 with the appropriate filter taps for the intermediate filters 190.
  • the filter converter 104 generates the effective subband filters or intermediate filters applied to each individual subband filters of each individual subband signal inside the subband filtering 102 leading to a filtering effect audibly indistinguishable from a corresponding filter applied to the time domain input signal (input signal) .
  • this embodiment is
  • An example might for instance be a device, which calculates the taps of the intermediate filters 190 of the subband filtering 102 according to a set of parameters for instance provided by the user, wherein the parameter basis is so large, that an effective predetermination of the filter taps, optionally accompanied by some sort of interpolation scheme, would not lead to the desired results.
  • a more concrete application comes for instance of the field of dynamic chance of HRTF filters in one domain to be converted to the subband or QMF domain.
  • the data base 520 is an HRTF data base comprising the time impulse responses of the HRTF filters.
  • the use of such a scheme is especially interesting, as the taps for the intermediate filters 190 or the QMF taps are complex. Storing the data base in this domain would roughly double the memory requirements compared to the memory requirement of storing the impulse responses in the time domain.
  • the advantage of the reduced memory requirement can also be employed without having a CPU 510 which calculates the impulse response provided to the filter converter 504. Instead, the data base 520 can be simply be prompted to output the corresponding definition signal, which might be an impulse response in the time domain to the filter converter 104.
  • the filter coefficients or filter taps are the intermediate filters 190 of the subband filtering 102 can be stored in the data base like the data base 500 of Fig. 9. Alternatively or additionally, for some applications, the filter taps of the intermediate filters
  • the filter taps of the intermediate filters 190 after subband filtering 102 can be estimated without a filter converter 104 or another embodiment of a filter generator.
  • Possible applications especially comprise voice transmission over low quality lines, like telephones or small band radio communications.
  • a determination of the filter taps corresponding the transfer function 550 of Fig. 10 or another amplitude/frequency characteristic into several subbands 560 with different subband frequencies can be carried out without employing an inventive filter converter.
  • Fig. 11 shows an embodiment of an inventive filter converter 104.
  • the filter converter 104 comprises a complex analysis filter bank 301 to which a (real valued) impulse response signal indicative of an amplitude/frequency filter characteristic can be supplied via an input 104a and via an optional switch 600.
  • the complex analysis filter bank 301 converts the impulse response signal into a plurality of complex valued subband signals and the intermediate filter definition signal output at an output 104b of the filter converter.
  • the output 104b of the filter converter 104 can be connected to a subband filtering 102.
  • each of the complex valued subband signals of the complex modulated filter bank 301 corresponds to an impulse response for one of the intermediate filters 190 for a subband signal in the subband filtering 102 shown in Fig. Ia and 9.
  • the complex valued subband signals are significantly shorter than the impulse response signal of the filter characteristic provided at the input 104a in the time
  • At least one of the complex valued subband signals output at the output 104b comprises at least two different non-vanishing values.
  • the last feature distinguishes the output of the filter converter 104 from a simple gain adjustment in the frame work of filtering using a direct Fourier transform procedure .
  • the filter converter 104 comprises an impulse response generator 610 for converting the filter definition signal into the impulse response signal, which is then provided via the optional switch 600 to the complex analysis filter bank 301.
  • the impulse response generator 610 can for instance calculate the impulse response signal provided to the complex analysis filter bank 301 by superposition of real valued oscillations (Fourier synthesis) , wherein the amplitude characteristics and the phase characteristics of the intended filter to be transferred into the complex subband domain are regarded as defined by the definition signal provided to the input 104c.
  • real valued oscillations Frier synthesis
  • an impulse response signal can be computed by the impulse response generator 610 by supposition of (harmonic) oscillations considering the amplitude and phase relations as defined by the filter definition signal.
  • such a parametric multi-channel audio decoder e.g. MPEG Surround reconstructs ⁇ channels based on M transmitted channels, where N>M f anc j the additional control- data.
  • the additional control data represents a significantly lower data rate than that required for transmission of all N channels, making the coding very efficient while at the same time ensuring compatibility with both A/ channel devices and N channel devices.
  • These parametric surround coding methods usually comprise a parameterization of the surround signal based on Channel Level Difference (CLD) and Inter-channel coherence/cross- correlation (ICC) . These parameters describe power ratios and correlation between channel pairs in the up-mix process. Further Channel Prediction Coefficients (CPC) are also used in prior art to predict intermediate or output channels during the up-mix procedure.
  • CLD Channel Level Difference
  • ICC Inter-channel coherence/cross- correlation
  • CPC Channel Prediction Coefficients
  • inventive methods can be implemented
  • an embodiment of the present invention is, therefore, a computer program product with a program code stored on an machine-readable carrier, the program code being operative for performing the inventive methods when the computer program product runs on a computer or a processor.
  • embodiments of the inventive methods are, therefore, a computer program having a program code for performing at least one of the inventive methods when the computer program runs of a computer.

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Abstract

A filter apparatus for filtering a time domain input signal to obtain a time domain output signal, which is a representation of the time domain input signal filtered using a filter characteristic having an non-uniform amplitude/frequency characteristic, comprises a complex analysis filter bank (101) for generating a plurality of complex subband signals from the time domain input signals, a plurality of intermediate filters, wherein at least one of the intermediate filters (102) of the plurality of the intermediate filters has a non-uniform amplitude/frequency characteristic, wherein the plurality of intermediate filters have a shorter impulse response compared to an impulse response of a filter having the filter characteristic, and wherein the non-uniform amplitude/frequency characteristics of the plurality of intermediate filters together represent the non-uniform filter characteristic, and a complex synthesis filter bank (103) for synthesizing the output of the intermediate filters to obtain the time domain output signal.

Description

EFFICIENT FILTERING WITH A COMPLEX MODULATED FILTERBANK
TECHNICAL FIELD
The present invention relates to a filter apparatus and a method for filtering a time domain input signal, a filter generator and a method for generating an intermediate filter definition signal, especially for the field of encoding, decoding, manipulating and filtering of audio signals, e.g. in the field of HRTF (head related transfer function) .
BACKGROUND OF THE INVENTION
It has been shown in [P. Ekstrand, "Bandwidth extension of audio signals by spectral band replication", Proc. 1st IEEE Benelux Workshop on Model based Processing and Coding of Audio (MPCA-2002), pp. 53-58, Leuven, Belgium, 2002], that a complex-exponential modulated filter bank is an excellent tool for spectral envelope adjustment of audio signals. One application of this feature is audio coding based on Spectral Band Replication (SBR) . Other fruitful applications of a complex filter bank include frequency selective panning and spatialization for parametric stereo, see [E. Schuijers, J. Breebart, H. Purnhagen, J. Engdegard: "Low complexity parametric stereo coding", Proc. 116th AES convention, 2004, paper 6073] and parametric multichannel coding, see [J. Herre et al.: "The reference model architecture for MPEG spatial audio coding", Proc. 118th AES convention, 2005, paper 6447]. In those applications the frequency resolution of the complex filter bank is further enhanced at low frequencies by means of sub-subband filtering. The combined hybrid filter bank hereby achieves a frequency resolution that enables the processing of spatial cues at a spectral resolution which closely follows the spectral resolution of the binaural auditory system.
In some applications, however, the resolution of the filter bank is still insufficient, in the sense that simple gain modifications in each subband do not suffice to truthfully model the action of a given filter. For binaural rendering of multi-channel audio by means of HRTF (head related transfer function) related filtering, the intricate phase characteristics of the filters are important for the perceived audio quality. It is of course possible to apply fast convolution methods based on the DFT (Discrete Fourier Transform) as a post-process to the multi-channel rendering, but if the rendering device already contains the signals in the subband domain of complex exponential modulated filter bank, there are significant advantages in terms of computational complexity and algorithmic integration in performing the HRTF derived filtering in the subband domain, which will be outlined in more detail later. Since HRTF' s are different for each individual and the derived filters depend on virtual source and/or listener positions which can for instance be changed by control signals, user interfaces or by other description signals, it is also important to be able to efficiently convert a given HRTF related filter into subband domain filters.
It is therefore the object of the present invention to provide a filter apparatus for filtering a time domain input signal, a method for filtering a time domain input signal, a filter generator or a method for providing an intermediate filter definition signal, which allow a more efficient or a more flexible manipulation of a time domain input signal with a better quality.
This object is achieved by a filter apparatus according to claim 1, by a method for filtering a time domain input signal according to claim 41, a filter generator according to claim 25, a method for providing an intermediate filter definition according to claim 42, a system according to claim 40 or by a computer program according to claim 43.
SUMMARY OF THE INVENTION
An embodiment of the present invention relates to a filter apparatus for filtering a time domain input signal to obtain a time domain output signal, which is a representation of the time domain input signal filtered using a filter characteristic having a non-uniform amplitude/frequency characteristic comprising a complex analysis filter bank for generating a plurality of complex subband signals from the time domain input signal, a plurality of intermediate filters, wherein one intermediate filter is provided for each complex subband signal, wherein at least one of the intermediate filters of the plurality of intermediate filters has a non-uniform amplitude/frequency characteristic, wherein the plurality of intermediate filters have a shorter impulse response compared to an impulse response of a filter having the filter characteristic, and wherein the non-uniform amplitude/frequency characteristic of the plurality of intermediate filters together represent the non-uniform filter characteristic, and a complex synthesis filter bank for synthesizing the output of the intermediate filters to obtain the time domain output signal.
As a second aspect, a further embodiment of the present invention is a filter generator for providing an intermediate filter definition signal comprising a complex modulated filter bank for filtering an impulse response signal indicative of an amplitude/frequency filter characteristic in a time domain to obtain a plurality of complex valued subband signals as the intermediate filter definition signal, wherein each complex valued subband signal of the complex modulated filter bank corresponds to an impulse response for an intermediate filter for a subband signal, wherein at least one of the complex valued subband signals comprises at least two different non- vanishing values, and wherein each complex valued subband signal is shorter than the impulse response signal.
Embodiments of the first aspect of the present invention are based on the finding that a more efficient and/or a more flexible filtering (or manipulation) of a time domain input signal can be achieved in the subband domain, which is sometimes also referred to as QMF domain (quadrature mirror filter) , with a better quality compared to other manipulation schemes. The gain with respect to efficiency, especially computational efficiency, is a consequence of the shorter impulse responses of the intermediate filters compared to the impulse response of a filter having the non-uniform filter characteristic in the time domain and the fact that the subband signals can be processed independently from one another. Due to the shorter impulse responses an embodiment of a filter apparatus can process each complex subband signals output by the complex analysis filter bank individually. Hence, the filtering can be carried out parallely, which speeds up the processing of the time domain input signal dramatically compared to manipulating the time domain input signal directly due to the shorter impulse responses.
Embodiments according the first aspect of the present invention are especially favorable when it comes to balancing computational efficiency on the one hand and quality on the other hand. While a direct processing of the time domain input signal in the time domain can be achieved by a convolution with the impulse response of a filter having the non-uniform amplitude/frequency characteristic, which usually leads to a very good quality, the convolution requires a high computational effort because of the length of the impulse response of the filter in the time domain. On the other hand, transforming an audio signal into the frequency domain by performing a Fourier transformation represents the tremendous drawback that other manipulations, which are necessary in modern acoustical systems, cannot be efficiently performed in the Fourier domain with a high quality.
Hence, by employing a plurality of intermediate filters, each having a shorter impulse response compared to an impulse response of a filter having the filter characteristic of a corresponding filter in the time domain, of which at least one has an impulse response with at least two non-vanishing values represents a highly favorable compromise between computational efficiency on the one hand and quality on the other hand. As a consequence, embodiments of inventive filter apparatuses represent an excellent compromise between a direct processing of the time domain input signal for instance by means of convoluting the time domain input signal with the longer impulse response indicative of the non-uniform filter characteristic, which leads to an enormous computational effort, and employing a Fourier transform, which leads to more problems in the further course of processing the signals.
The advantages of the embodiments of the first aspect of the present invention unfold especially in the context of FIR-filters (final impulse response) , as each of the intermediate filters of the plurality of intermediate filters has a significantly shorter impulse response compared to the impulse response of the FIR-filter in the time domain. Hence, by parallely processing the different subband signals output by the complex analysis filter bank the computational efficiency can drastically be improved. This aspect is especially important in the field of filters having long impulse responses. One field of application, in which filters with very long impulse responses frequently occur, are HRTF-related applications (HRTF = head related transfer function) , like for instance down-mixing multiple channel audio signals for feeding to headphones, other head-related speaker systems or stereo sound systems.
In many concrete applications the computational efficiency is even more increased, as the audio signals are already present in the (complex) subband or QMF domain. Hence, in many concrete implementations, the complex analysis filter bank and the complex synthesis filter bank for generating the plurality of complex subband signals from the time domain input signal and for synthesizing the time domain output signal are already present.
With respect to the second aspect, embodiments of the present invention are based on the finding that a more flexible and more efficient filtering of the time domain input signal with a better quality can be achieved by providing an intermediate filter definition signal, which can for instance be provided to a filter apparatus according to the first aspect to define its intermediate filters .
A significant advantage of embodiments according to the second aspect of the present invention is that an intermediate filter definition signal for a set of intermediate filters is obtained by providing an embodiment of the inventive filter generator with a filter defining signal, such as an impulse response signal indicative of an amplitude/frequency filter characteristic of a filter in the time domain or other filter definition signals. Hence, an embodiment of a filter generator provides a filter definition signal for a set of intermediate filters to effectively the same filtering as a filter in the time domain defined by the filter definition signal virtually without introducing aliasing effects. As a consequence, embodiments of an inventive filter generator enable a virtually alias free performance of an arbitrary filter in the subband domain. By utilizing an embodiment of the inventive filter generator arbitrary filter characteristics can be transferred from the time domain to the subband signal domain, like virtually alias free equalization, low- pass filter characteristics, high-pass filter characteristics, band-pass filter characteristics, band- rejection filter characteristics, resonance filter characteristics, notch filter characteristics or more complex filter characteristics. Among the more complex filter characteristics, a combination of several characteristics as well as HRTF-related filter characteristics are important to mention.
Especially in the context of HRTF-related applications in the field of multi-channel audio systems and other high quality applications it is important to note that embodiments of the inventive filter generator enable to truthfully model an action of a given filter in the time domain in the subband domain. The virtually alias free performance, which is especially important in HRTF-related applications, is made possible as the phase characteristics of a filter in the time domain is (almost) perfectly transferred into the subband domain. Examples illustrating this will be outlined in the further course of the present application.
Among the advantages of embodiments of the second aspect of the present invention is especially the significant gain with respect to the achievable computational efficiency. The complex modulated filter banks of embodiments of the inventive filter generator produce a plurality of complex valued subband signals as the intermediate filter definition signal, wherein each of the complex valued subband signal is shorter than the impulse response signal indicative of the amplitude/frequency filter characteristic in the time domain. The filter generator, hence, produces an intermediate filter definition signal comprising the output of the complex modulated filter bank with its plurality of short complex valued subband signals, which does not only enable a fast, efficient and parallel computation with respect to filtering a time domain input signal to obtain a time domain output signal in the frame work of an embodiment of a filter apparatus, but does also enable a fast, efficient and parallel computation of the intermediate filter definition signal itself. Compared to a direct application of the impulse response signal indicative of the amplitude/frequency filter characteristic in the time domain by convoluting the impulse response signal with the time domain input signal, the application of an embodiment of an inventive filter generator according to the second aspect of the present invention enables a simplified, faster and more efficient computation, which leads to an audibly indistinguishable result compared to the more complex convolution method.
Furthermore, an embodiment of the inventive filter generator also offers the advantage of a significantly enhanced flexibility with respect to the possible filter characteristics applied in the subband domain. As arbitrary filter characteristics can be transferred from the time domain to the subband domain by an embodiment of an inventive filter generator, an enormous flexibility is introduced to audio signal processing and manipulation. For instance, an embodiment of an inventive filter generator is capable of providing an intermediate filter definition signal corresponding to an individually altered filter characteristic of an HRTF-related filter. In the field of HRTF this offers the opportunity to individually modify the HRTF filters according to the needs and hearing capabilities of an individual. Moreover, the source position as well as the listener position with respect to each other and with respect to a (simulated or calculated) environment (e.g. a concert hall, an open space, a stadium) can be adapted. This offers the great advantage of providing a listener with a great flexibility with respect to the acoustic conditions. An embodiment of the inventive filter generator, hence, provides the possibility to virtually switch from a stadium to a concert hall or an open field, without employing the necessity to transfer the audio signals between the time domain, the subband domain and/or the frequency domain. By employing an embodiment of an inventive filter generator all these manipulations of the audio signal can be performed inside the subband domain with a very high quality, which is perceptually indistinguishable from a signal processing in the time domain, but which offers an enormous computational efficiency improvement.
This flexibility is not only limited to switching from one environment to another, e.g. switching from a stadium to a concert hall and visa versa. An embodiment of an inventive filter generator offers the possibility to alter the filter characteristics of the plurality of the intermediate filters in a quasi-continuous fashion. An application in the field of HRTF is an application of an embodiment of the filter generator and/or of the filter apparatus in a head tracking application, in which for instance the position of the listener with respect to different audio sources varies
- in a quasi-continuous way. Possible applications comprise, for instance, simulations and computer games with a very high quality.
Another advantage of an embodiment of a filter generator is that the application of an embodiment of a filter generator is more efficient with respect to the memory usage, as an impulse response signal provided to the complex modulated filter bank of the filter generator is typically a real valued signal, whereas the intermediate filter definition signal is a complex valued signal of approximately the same over-all length. As a consequence, storing the impulse response signals compared to the intermediate filter definition signals (or the filter taps of the intermediate filters) saves memory, roughly speaking, of an order of 2. Due to the possibility of a fast and efficient parallel computation, especially in the field of memory-sensitive
10 applications comprising a great parameter space with respect to the possible impulse response signals, this represents a significant advantage.
In one embodiment of in an inventive filter generator the filter generator is provided with a filter definition signal, which can comprise for instance the filter taps of a digital filter in the time domain or by a transfer function in the frequency domain, which can comprise the amplitude/frequency characteristic and/or the phase/frequency characteristic of a filter. In these cases, an embodiment of the filter generator furthermore comprises an impulse response signal generator, which provides the appropriate impulse response signal indicative of the resulting amplitude/frequency filter characteristic in the time domain to the complex modulated filter bank of the filter generator. Hence, the inclusion of an impulse response signal generator in some embodiments of an inventive filter generator offers an even more flexibility with respect to providing the intermediate filter definition signal, as not only the impulse response signals in the form of discrete time signals can be provided to an embodiment of the filter generator but also the filter taps or the frequency domain description of a filter in the time domain can be transferred into the subband domain by an appropriate embodiment of a filter generator.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will now be described by way of illustrative examples, not limiting the scope or spirit of the invention, with reference to the accompanying drawings, in which:
Fig. Ia illustrates the processing of a digital audio signal by means of subband filtering in a system comprising a filter generator and a filter apparatus;
11 Fig. Ib illustrates a possible solution for a complex analysis bank;
Fig. Ic illustrates a possible solution for a complex synthesis filter bank; Fig. Id illustrates a further possible solution for a complex synthesis filter bank;
Fig. Ie illustrates an interplay of an embodiment of a filter generator with a plurality of intermediate filters of an embodiment of a filter apparatus; Fig. 2 illustrates the processing of a digital audio signal by means of direct form filtering;
Fig. 3 illustrates a preferred embodiment of a system with a filter converter;
Fig. 4 illustrates a given filter impulse response; Fig. 5 illustrates an impulse response obtained by complex gain adjustment of subbands;
Fig. 6 illustrates the magnitude response of a given filter;
Fig. 7 illustrates the magnitude response of a filter obtained by complex gain adjustment of subbands;
Fig. 8 compares the performance of the present invention with complex gain adjustment of subbands;
Fig. 9 illustrates a preferred embodiment of a filter apparatus comprising an optional embodiment of a filter generator and further components;
Fig. 10 illustrates a filter characteristic along with several frequency bands for different subbands; and
Fig. 11 illustrates a preferred embodiment of a filter generator.
DESCRIPTION OF PREFERRED EMBODIMENTS
The below-described embodiments are merely illustrative for the principles of the present invention of efficient filtering with a complex modulated filterbank. It is understood that modifications and variations of the arrangements and the details described herein will be apparent to others skilled in the art. It is the intent,
12 therefore, to be limited only by the scope of the impending patent claims and not by the specific details presented by way of description and explanation of the embodiments herein.
In the following, objects with the same or similar functional properties are denoted with the same reference signs. Unless explicitly noted otherwise, the description with respect to objects with similar or equal functional properties can be exchanged with respect to each other.
Figure Ia illustrates in the form of a system comprising embodiments of both a filter apparatus and a filter generator the processing of a digital audio signal by means of subband filtering according to the present invention. This signal path can for instance represent a part of a spatial audio rendering system where the input is a received audio channel and the output is a component of a signal to be played back at the right ear. The input signal (Digital audio signal or time domain input signal) is analyzed by the complex analysis bank 101 by means of filtering with a set of L analysis filters followed by downsampling of a factor L , wherein L is a positive integer, preferably larger than 1. Typically the factor L is a power of 2, preferably L = 64. The analysis filters are usually obtained by a complex modulation of a prototype filter p(y) , wherein v is a positive integer indicating an index in an array of data or an index of a value in a signal not downsampled by factor L. The output of the filter bank consists of L subband signals that are processed by a subband filtering 102. This subband filtering consists of a combination of manipulations such as subband gain adjustment according to received control data and application of finite impulse response filters applied separately in each subband. The filter taps of the subband filters are obtained from an (inventive) filter converter 104 as an embodiment of a filter generator which takes as input a filter described by direct form filter
13 taps, a frequency domain description or an impulse response (signal) . The complex synthesis bank 103 reconstructs an output signal by means of upsampling by a factor L , filtering by L synthesis filters, summation of all the results, and extraction of the real part. The summation of all the results and the extraction of the real part can also be switched with respect to their order, as will be outlined more closely with respect to Figs. Ic and Id.
Fig. Ib shows a complex analysis bank 101 in more detail. The complex analysis bank 101 comprises a plurality of L intermediate analysis filters 120 for each subband to be output by complex analysis bank 101. To be more precise, each of the L intermediate analysis filters 120 is connected in parallel to a node 130 to which the time domain input signal to be processed is provided. Each of the intermediate analysis filters 120 is adapted for filtering the input signal of the complex analysis bank 101 with respect to a center frequency of each subband. According to the center frequencies of the different subbands, each subband is labeled by a subband index or index n, wherein n is a non-negative integer, typically in the range from 0 to L-I. The intermediate analysis filters 120 of the complex analysis bank 101 can be derived from a prototype filter p(v) by a complex modulation according to the subband index n of the subband to which the intermediate analysis filter 120 is applied. More details concerning the complex modulation of a prototype filter are explained below.
Either directly by the intermediate analysis filters 120 or by an optional downsampler 140 (denoted by doted line in Fig. Ib) the sampling frequency of the signal output by the intermediate analysis filter bank 120 is reduced by a factor L. As mentioned before, the downsamplers 140 supplied to each subband signal output by the corresponding intermediate analysis filters 120 are optional as, depending on the concrete implementation, the downsampling
14 can also be carried out in the frame work of the intermediate analysis filters 120. In principle, downsampling the signal output by the intermediate analysis filters 120 is not required. Nevertheless, the presence of the explicit or implicit downsamplers 140 is a preferred option as the amount of data provided by the complex analysis bank 101 would alternatively be raised by a factor of L, leading to a significant redundancy of data.
Fig. Ic illustrates a possible solution for a complex synthesis bank 103. The complex synthesis bank 103 comprises L intermediate synthesis filters to which the L subband signals from the subband filtering 102 are provided to. Depending on the concrete implementation of the complex synthesis bank 103 prior to the filtering in the frame work of the intermediate synthesis filters 150, the subband signals are upsampled by L upsampler 160, which reconstruct the sampled frequency of the subband signals by increasing the sampling frequency by a factor of L. In other words, the optional upsampler 160 reconstruct or reform the subband signals provided to the upsampler 160 in such a way that the information contained in each of the subband signals is retained while the sampling frequency is increased by a factor of L. Nevertheless, as already explained in the context of Fig. Ib, the upsamplers 160 are optional components, as the upsampling can also be carried out in the frame work of the intermediate synthesis filters 150. Hence, the step of upsampling the subband signals carried out by the upsampler 160 can be simultaneously processed in the frame work of the intermediate synthesis filers 150. If, however, the downsamplers 190 are neither explicitly nor implicitly implemented, the upsamplers 160 do not have to be implemented explicitly or implicitly.
The intermediate synthesis filters 150 are connected via an output to an adder 170 which sums up the filtered subband signals output by the L intermediate synthesis filters 150. The adder 170 is further connected to a real part extractor
15 180, which extracts or forms a real valued signal or rather a (real valued) time domain output signal based on the complex valued signal provided by the adder 170. The real part extractor 180 can perform this task for instance by extracting the real part of a complex valued signal provided by the adder 170, by calculating the absolute value of the complex valued signal provided by the adder 170 or by another method that forms a real valued output signal based on a complex valued input signal. In the case of the system shown in Fig. Ia, the signal output by the real part extractor 180 is the time domain output signal output by the embodiment of the inventive filter apparatus.
The second possible solution for a complex synthesis bank 103 shown in Fig. Id differs from the first possible solution shown in Fig. Ic only concerning the real part extractors 180 and the adder 170. To be more precise, the outputs of the intermediate synthesis filters 150 are connected separately from each subband to a real part extractor 180 extracting or forming a real valued signal based on the complex valued signal output by the intermediate synthesis filters 150. The real part extractor
180 are then connected to the adder 170, which sums up the
L real valued signals derived from the L filtered subband signals to form the real valued output signal provided by the adder 170, which in the case of the system shown in
Fig. Ia is the time domain output signal.
Fig. Ie shows the subband filtering 102 and its interplay with the filter converter 104 in more details. The subband filtering 102 comprises a plurality of intermediate filters
190, wherein one intermediate filter 190 is provided for each complex valued subband signal provided to the subband filtering 102. Hence, the subband filtering 102 comprises L intermediate filters 190.
The filter converter 104 is connected to each of the intermediate filters 190. As a consequence, the filter
16 converter 104 is capable of providing the filter taps for each of the intermediate filters 190 of the subband filtering 102. More details concerning the filtering done by the intermediate filters 190 will be explained in the further course of the application. Hence, the filters taps provided to the different intermediate filters 190 and output by the filter converter 104 form the intermediate filter definition signal.
Furthermore, it should be noted that the embodiments, solutions and implementations can comprise additional and/or optional delays for delaying any of the signals or a subset of signals, which have been omitted in Fig. Ia to Ie for the sake of simplicity. Also in the Fig. 2 to 11 optional delays have been omitted for the sake of simplicity. Nevertheless, delays or delayers can be comprised in elements shown (e.g. filters) or added as optional elements in all embodiments depending on their concrete implementation.
Figure 2 illustrates the processing of a digital audio signal by means of direct form filtering 201. If the same filter is given as input to the filter converter 104 of Fig. 1 and the direct filtering 201, a design goal for the filter converter 104 is that the digital audio output of 103 should be perceptually (or audibly) indistinguishable from the digital audio output of the direct filtering 201, if the digital audio inputs to the complex analysis bank 101 and the direct filtering 201 are identical and the processing in the direct filtering 102 consists of pure stationary subband filtering.
In the embodiment of the system shown in Fig. Ia to Fig. Ie the filter input to the filter converter 104 is given as a filter definition signal, which can for instance comprise the filter taps of a corresponding time domain filter, a frequency domain description (amplitude/frequency characteristic and/or phase/frequency
17 characteristic) or an impulse response signal of the appropriate filter.
In the case of the direct filtering 201 the same filter definition signal can in principle be used. Depending on the concrete implementation and the filter definition signal, the filtering can be carried out by direct application of the filter taps in the frame work a digital filter, by a discrete Fourier transform along with a transfer function or another frequency domain description or by means of convolution with the impulse response signal.
Figure 3 illustrates a preferred embodiment of a filter converter 104 according to the present invention as an embodiment of a filter generator. The filter is assumed to be given by its impulse response. Viewing this impulse response as a discrete time signal, it is analyzed by an L -band complex analysis (filter) bank 301. The resulting subband signal outputs are then exactly the impulse responses of filters to be applied separately in each subband in the subband filtering 102. In the preferred embodiment shown in Fig. 3, the filter definition signal provided to the filter converter 104 and its complex analysis bank or complex analysis filter bank 301 is the impulse response signal indicative of the amplitude/frequency characteristic of a filter, which is to be transferred into the subband domain. Hence, the output of the complex analysis (filter) bank 301 of each of the L subbands represents the impulse response of the intermediate filters comprised in the subband filtering 102.
The complex analysis bank 301 is in principle derived from the analysis bank 101 but it has a different prototype filter and a slightly different modulation structure, the details of which will be outlined in the following description. The same fast algorithms that are used for an
18 implementation of the complex analysis bank 101 can be reused for complex analysis bank 301, leading to a very fast and very efficient conversion process.
Moreover, the length of the prototype filter q(y) can be designed to be only a fraction of the length of the prototype filter p(v) . Due to the downsampling by a factor L1 the length of subband filters are also a factor of L smaller than the sum of the lengths of the given time domain filter and the prototype filter q(y) . The computational effort is thus reduced in comparison to the direct form filtering 201 by approximately a factor of LIA . The offset factor of 4 is due to the replacement of real filtering with complex filtering. Another offset is the computational cost of the complex analysis and synthesis banks 101 and 103. For efficient implementations this cost is comparable to the cost of rather short FIR filters, and hence negligible, as outlined before. Moreover, this offset of the reduction in computational cost does not exist for systems that already employs these two filter banks 101 and 103.
Figure 4 illustrates an example of a given filter impulse response 400. It consists of 192 (= 64*3) nonzero taps. In other words, the impulse response 400 shown in Fig. 4 comprises 192 non-vanishing values.
In the present application, a non-vanishing tap or value is a tap or a value which is ideally not equal to zero. Nevertheless, due to implementation restraints in the frame work of this application a non-vanishing value or tap is a real valued or complex valued tap or value with an absolute value which is larger than a predetermined threshold, e.g. 10"s or 2~s, wherein s is a positive integer depending on the requirements of a concrete- implementation. In digital systems this threshold is preferably defined in the binary system (basis 2), wherein the integer s has a predetermined value depending on the
19 specifics of the implementation. Typically, the value s is 4, 5, 6, 7, 8, 10, 12, 14, 16 or 32.
The impulse response 400 of the system of Figure 1 is indistinguishable from this given impulse response at the resolution of the image, in a case where a L = 64 band filterbank with a prototype filter of length 640 (= 64*10) is applied and a prototype filter of length 192 (= 64-3) is used for the filter converter 104 of Figure 3. The corresponding intermediate subband filters have only 5 (= 3+3-1) taps each, as will be explained later.
Figure 5 illustrates the impulse response 410 of the system of Figure 1 with a 64 band filterbank, in a special case corresponding to prior art usage for envelope adjustment and equalization. In this case, the subband filters or rather intermediate filters 190 are all of one tap only, so a constant complex gain is applied to each subband. For each subband, the corresponding gain is chosen to be equal to the complex frequency response of the filter of Figure 4 evaluated at the center frequency of the particular subband. As it can be seen from the result, there are severe pre-echo artefact and there will be a significant perceptual difference between the application of this filter response compared to the target impulse response 400 of figure 4.
Figure 6 illustrates the magnitude response 420 of the filter of Figure 4. The frequency scale of Fig. 6 is adjusted to the resolution of a 64 band filter bank ( L = 64) .
Figure 7 illustrates the magnitude response 430 of the filter underlying the impulse response 410 shown in Figure 5. As it can be seen, the usage of only one gain per subband results in a poor approximation to the desired frequency response. The main reason for this is the fast variation of the target phase spectrum. In fact, this
20 prior art method is better suited at modeling linear phase responses .
Figure 8 finally compares the performance of an embodiment of the present invention and of the prior art method of complex gain adjustment of subbands. The dotted curve is a redrawing of the target magnitude response 420 of Figure 6. The dashed curve 440 is the magnitude response of the difference between the complex frequency responses of the target filter and its approximation by the prior art method. The solid curve 450 is the magnitude response of the difference between the complex frequency responses of the target filter and its approximation by the method taught by the present invention with the parameters as discussed during the description of Figure 4. As it can be seen, the error of the prior art method is small only at the 64 midpoints of filter bank subbands whereas the inventive method leads to an approximation quality in the 50 dB range. It should be pointed out that this is also the level of performance one measures when comparing the output of the inventive system to the output of the reference system for an arbitrary input signal.
As the comparison of the two curves 440 and 450 in Fig. 8 shows, an embodiment of an inventive filter apparatus, an embodiment of a filter generator and a system comprising both embodiments offer a significant advantage concerning the quality of the manipulation of an input signal. The significant difference concerning the quality of filtering (or manipulation) of the input signal outlined above is a consequence of the fact that at least one of the intermediate filters 190 has an impulse response with two or more non-vanishing values. In other words, at least one of the intermediate filters 190 comprises at least two non- vanishing filter taps. Furthermore, it is important to note that the number of subbands L processed by an embodiment of a filter apparatus is larger or at least equal to 2. Nevertheless, the number of subbands L is significantly
21 smaller than the number of frequency bands required for a comparable quality in the case of a Fourier transform-based filtering combined with a filter mainly described by an amplitude/frequency characteristic and/or a phase/frequency characteristic as the transfer function of the filter.
Due to the fact that the impulse response of the intermediate filters 190 are significantly shorter than the impulse response of the underlying filter characteristic in the time domain, the computations with respect to each subband can be carried out significantly faster. Furthermore, as the different subband signals can be processed independently, both an embodiment of the filter apparatus as well as an embodiment of the filter generator 104 can process the respective input signals highly efficiently in a fast and a parallel manner. Hence, the processing of both a digital audio input as an input signal as well as an impulse response indicative of a filter characteristic can be carried out highly efficiently in a parallel fashion. As outlined earlier, an embodiment of an inventive filter apparatus as well as an embodiment of an inventive filter generator combine the advantages of both a direct processing of audio signals in the time domain leading to a very high quality and using a combination of a Fourier transform along with a transfer function in the frequency domain offering a high efficiency as each frequency band is only multiplied with a (complex or real valued) tap in the process of filtering the signal.
On the other hand, the disadvantages of both, purely processing the input signals in the time domain, which leads to an enormous computation effort, and those of a Fourier transform, can be significantly reduced and suppressed to a level that the output of an embodiment of a filter apparatus is perceptually indistinguishable from the quality of a direct processing in the time domain.
22 These two advantages offer a great flexibility for filtering digital signals with varying filtering characteristics. This is especially important in the field of HRTF, as HRTF-related filters usually have a very long impulse response. Hence, an embodiment of an inventive filter apparatus comprising a complex analysis filter bank 101, a plurality of intermediate filters 190 in the subband filtering 102 and a complex synthesis filter bank 103 offers especially in the field of HRTF-related applications significant computational advantages due to the possible parallel processing of subband signals.
Embodiments of a filter generator and embodiments of systems comprising both a filter apparatus and a filter generator offer furthermore the advantage that filters can easily be adapted to specific environments, parameters or other specific needs of the application at hand. Especially in terms of HRTF-related applications, an embodiment of such a system can be used in head-tracking applications, in which several sources of sounds and noises as well as the position of the listener vary over time. Such an embodiment of a system comprising a filter apparatus and a filter generator therefore offer a highly efficient and flexible way to present an audio impression of a three dimensional arrangement of sound sources with respect to a varying position and orientation of a hypothetical listener via headphones or other head-related sound systems (stereo sound systems) .
As this last example illustrates, an embodiment of an inventive filter apparatus along with an inventive filter generator offers not only a highly efficient system for audio manipulation with an excellent quality but also a very flexible way to introduce altering audio impressions in an efficient way.
23 Complex modulated filter banks
In the following, let Z(ώ)=^^z(v)exp(-ivώ) be the discrete time Fourier transform of a discrete time signal z(v) . As before, v is an integer indicating an index or a time index of a time signal, while ω = 2 π • f is the circular frequency associated to the frequency f, π is the circular number (π = 3.1415926...) and i = j = V-T is the imaginary unit .
The complex exponential modulated £ -band filterbank is defined from a real valued prototype filter p(v) of finite length. For the computations below it will be assumed by extension with zeros that the prototype filter is defined for all integers v . Given a real valued discrete time signal x(v) the analysis filter bank 101 applies, as already explained, the complex modulated prototype filters followed by downsampling by a factor L in order to output the subband signals,
cn(k)=∑x(v +kL)p(y)exp\-ij(r,+±)(v +θ) (D
for each subband index n = 0,1,...,L-I , and integer time index k . The time index k differs from the time index v with respect to the fact that k refers to the downsampled signals, whereas the integer v withers to signals with the full sample frequency.
Given complex valued subband signals dn(k) , the synthesis filter bank 103 applies filtering followed by upsampling by a factor of L and a real value extraction in order to output the real valued signals, as already explained, to obtain the output signal
Figure imgf000024_0001
In the equations (1) and (2) 0and ψ represent (constant) phase factors for filtering the real valued discrete time
24 signal x (v) into complex valued subband signal and for reconstructing real valued output samples y (v) from complex valued subband signals dn(k). It is well known that a prototype filter and fixed phase factors #and ψ can be chosen to give perfect reconstruction, y(v) = x(v) , in the case where dn(k) = cn(k) , that is when the subband signals are unaltered. In practice, the perfect reconstruction property will hold true up to a delay (and/or a sign change) , but in the computations that follow, this detail will be ignored by allowing the use of an acausal prototype filter. The present invention is applicable to the pseudo QMF type of design as taught by PCT/SE02/00626 "Aliasing reduction using complex exponential modulated filter banks". Here the prototype filter is symmetric p(-v) = p(y) i and its discrete time Fourier transform P(βi) essentially vanishes outside the interval |<y|≤7r/Z,. The perfect reconstruction is also replaced by a near-perfect reconstruction property. For the derivation that follows it will be assumed for simplicity that both perfect reconstruction holds and that P(ω) = 0 for πlL<\ω\≤π . Moreover, the phase factors are assumed to satisfy the condition that ψ-θxs equal to an integer multiple of AL.
In a critically sampled filter bank, the alteration of subband signals prior to synthesis usually leads to the introduction of aliasing artifacts. This is overcome here due to the fact that an oversampling by a factor two is introduced by using complex valued signals. Although the total sampling rate of the subband samples is identical to the sampling rate of the discrete time input signal, the input signal is real valued and the subband samples are complex valued. As it will be outlined below, the absence of alias opens the door for efficient time invariant signal processing.
Subband filtering in a complex modulated filter bank
25 Consider the modification of subband filtering 102 of each subband signal obtained by filtering the analysis samples cn(k) from the complex analysis bank 101 with a filter with impulse response gn{k) prior to the synthesis (2) performed by the complex synthesis (filter) bank 103
dn(k)=∑gπ(i)cn(k-l). O)
Elementary computations show that given the assumptions on the frequency response of the prototype filter, the resulting effect on the reconstructed time signal is that of a discrete time filtering
Y(ω) =G(ω)X(ω)r (4)
where
Figure imgf000026_0001
Here, Gn(ω) =∑kgn(k)exp(-ikω) is the discrete time Fourier transform of the filter applied in subband «for «>0and
GK(a>) = G_l_m(-a>y for «<0. (6)
where * denotes complex conjugation. Observe here that the special case Gn(ω) =\ leads to G(ω) = \ in (5) due to the assumed special design of the prototype p(y) , which implies
Figure imgf000026_0002
Another case of interest is Gn(ω) =exp(-iω) which leads to
Figure imgf000026_0003
Approximating a given filter response by subband filtering
Let H(ω) be a given filter (e.g. transfer function) with real valued impulse response h{v) . This data is considered as input to the filter converter 104. In view of (5) and
26 (7), a trivial choice for the subband filters which result in the desired response G(ω) = H(ω) is given by
Figure imgf000027_0001
The drawback of this formula is that although H(ώ) is a smooth function of ω , the periodized segment of it defined by (8) will exhibit jumps and the impulse response of the subband filters will be unnecessarily long. The prior art usage of the complex pseudo QMF bank for equalization or envelope adjustment consists of applying a single gain gn in each subband, which results in the transfer function
Figure imgf000027_0002
with the extension £„
Figure imgf000027_0003
«<0 defined in accordance with (6). In view of (7), one achieves
Figure imgf000027_0004
and the transfer function is interpolated between those frequencies. For target filter responses H{ώ) that vary slowly as a function of the frequency ω , a first method of approximating the filter is therefore obtained by choosing
Figure imgf000027_0005
An example of the resulting quality of this procedure is given in figures 5 and 7.
According to an embodiment of the present invention a filter generator or a filter converter 104 is used to teach to convert the filter (defined by its impulse response) /z(v)into intermediate subband filters 190 by means of the second analysis filter bank 301 which employs real valued prototype filter q(y) ,
27
Figure imgf000028_0001
In terms of Fourier transforms this reads
Figure imgf000028_0002
The advantage of this procedure is that any given filter h(v) can be efficiently transformed into intermediate subband filter responses. If q(v) has A^-Z taps, a time domain filter h(v) of KN-L taps is converted into subband domain filters (12) with KH +KQ-l taps, wherein Kn and KQ are positive integers. With respect to the exemplary numbers given in the context of the description of Fig. 4, KH and KQ are equal to 3 and with a prototype filter length and an impulse response corresponding to a length of 3 • 64 = 192 (L = 64) each. Hence, each intermediate subband filter 190 has an impulse response length of only 3 + 3 - 1 = 5 taps each.
Design of the prototype filter for the filter converter
Insertion of (13) into (5) yields
Figure imgf000028_0003
Hence, the condition for G(ω) = H(ω) to hold is that
Figure imgf000028_0004
whereδ[l] =\ for / =0and £[/] = 0 for /≠O. A simple solution to (15) is given by the brick wall filter
Figure imgf000028_0005
This prototype filter corresponds to the choice (8) and has the disadvantage of having an infinite and slowly decaying impulse response q(y) . Instead, the present
28 invention teaches to solve (15) approximately (e.g. in the least-square sense) with a finite impulse response filter q(v) . The time domain equivalent of (15) is the system of linear equations for n = 0,1,...,Z-I and for all integers k ,
∑p2(n+vL-2kL)q(n+vL)=z}-δ[k], (16)
where
p2(v)= ∑p(l)p(l+v) (17)
is the autocorrelation of p(v) . For any given support length the system of linear equations (16) can be solved in the least squares sense for a prototype filter q(y) . It is desirable to use a support significantly shorter than that of the original filter bank prototype filter p(y) , and in that case the linear system (16) is over-determined. A given quality of approximation can also be traded for other desirable properties via joint optimization. One example of such a property is a low pass type of frequency response Q(ω) .
In the following the determination of a multi-slot QMF representation (subband domain) of the HRTF filters is described. The filter conversion from the time domain into the complex QMF subband domain is performed by an FIR filter in the filter converter 104 of Fig. Ia. To be more precise, the following description outlines a method for implementing a given FIR filter h (v) of length Nh in the complex QMF subband domain. The principle of the operation is illustrated in Fig. Ia in the case of a system also comprising an embodiment of an inventive filter apparatus.
The subband filtering itself is carried out by a set of or a plurality of intermediate filters 190 inside the subband filtering 102. To be more precise, the subband filtering consist of the separate application of one complex valued FIR intermediate filter gn(l) for each QMF subband with an
29 index n = 0,1,..., 63. In other words, in the following description special references will be made to embodiments with L = 64 different subband signals. Nevertheless, this specific number of subband signals is not essential and the appropriate equations will also be given in a more general form.
One of the key components of the system shown in Fig. Ia is the filter converter 104, which converts the given time domain FIR filter h (v) into the complex subband domain filters gn(l) . The filter converter 104 comprises a complex analysis bank 301 similar to the QMF analysis bank 101. The prototype filter of the complex analysis filter bank 301 of the filter converter 104 q(v) of length 192 (= 3-64) for the specific case of L = 64 subband signals are created by solving in the least square sense the over determined system of the equation (16) . The filter coefficients q(v) or rather the relations they fulfill will be described in more detail for the case of L = 64 subbands signals later on.
To be more accurate in terms of mathematical description, an extension with zeros in the time domain FIR filter is defined by
Figure imgf000030_0001
The resulting intermediate subband domain filters are based on equation (12) and can be expressed in the general case as
&W= fΛ(u+I.(/-/o))-^).exp-/^»+0υ-uo) (19)
30 wherein J0 and v0 are delays, 1 is an integer indicating an index of the filter taps and Nq (= NQ) is the length of the impulse response of the prototype filter ςr(v) .
It should be noted, that in the frame work of the present application under an equation being based on an equation an introduction of additional delays (cf. I0 and v0) factors, additional coefficients and an introduction of a window function or another simple function is understood.
In the case L = 64, the expression for the subband domain filters or intermediate filters 190 becomes
Figure imgf000031_0001
These subdomain filters have a length Lq = Kh + 2 , where
Figure imgf000031_0002
and Nh is the length of the impulse response h(v) of the filter characteristics to be transferred into the subband domain.
In this case, the integer n = 0, 1, ..., 63 is once again the index of a subband and 1 = 0, 1, ..., (Kh+1) is an integer indicating taps of the resulting intermediate filters 190.
The extra addend of (-2) in equation (20) as compared to equation (12) is there, because equation (12) was developed without any regard to casualty of filters. Real implementations will cause always introduce delays. Hence, depending on the concrete implementation, additional delayers or delays can be implemented in the embodiments shown in Figs. Ia to Ie and Figs. 2 to 11, which have been omitted for the sake of simplicity in Figures mentioned.
31 As outlined earlier, in many cases the system of linear equations (16) is over determined. Nevertheless, it can be solved or approximated in the least square sense with respect to the prototype filter coefficients ςr(v) . Solving the system of linear equations (16) in the least square sense, leads to the filter taps of the prototype filter g(v) to fulfill the following relations for integers v from 0 to 191:
-0.204 < q[0] < -0.202
-0.199 < q[l] < -0.197
-0.194 < q[2] < -0.192
-0.189 < q[3] < -0.187 -0.183 < q[4] < -0.181
-0.178 < q[5] < -0.176
-0.172 < q[6] < -0.170
-0.166 < q[7] < -0.164
-0.160 < q[8] < -0.158 -0.154 < q[9] < -0.152
-0.148 < q[10] < -0.146
-0.142 < q[ll] < -0.140
-0.135 < q[12] < -0.133
-0.129 < q[13] < -0.127 -0.122 < q[14] < -0.120
-0.116 < q[15] < -0.114
-0.109 < q[16] < -0.107
-0.102 < q[17] < -0.100
-0.096 < q[18] < -0.094 -0.089 < q[19] < -0.087
-0.082 < q[20] < -0.080
-0.075 < q[21] < -0.073
-0.068 < q[22] < -0.066
-0.061 < q[23] < -0.059 -0.054 < q[24] < -0.052
-0.046 < q[25] < -0.044
-0.039 < q[26] < -0.037
-0.032 < q[27] < -0.030
32 -0.024 < q[28] < -0.022 -0.017 < q[29] < -0.015 -0.009 < q[30] < -0.007 -0.002 < q[31] < 0.000 0.006 < q[32] < 0.008 0.014 < q[33] < 0.016 0.021 < q[34] < 0.023 0.029 < q[35] < 0.031 0.037 < q[36] < 0.039
10 0.045 < q[37] < 0.047 0.054 < q[38] < 0.056 0.062 < q[39] < 0.064 0.070 < q[40] < 0.072 0.079 < q[41] < 0.081
15 0.087 < q[42] < 0.089 0.096 < q[43] < 0.098 0.105 < q[44] < 0.107 0.113 < q[45] < 0.115 0.122 < q[46] < 0.124
20 0.132 < q[47] < 0.134 0.141 < q[48] < 0.143 0.150 < q[49] < 0.152 0.160 < q[50] < 0.162 0.170 < qt51] < 0.172
25 0.180 < q[52] < 0.182 0.190 < q[53] < 0.192 0.200 < q[54] < 0.202 0.210 < q[55] < 0.212 0.221 < q[56] < 0.223
30 0.232 < q[57] < 0.234 0.243 < q[58] < 0.245 0.254 < q[59] < 0.256 0.266 < q[60] < 0.268 0.278 < q[61] < 0.280
35 0.290 < q[62] < 0.292 0.303 < q[63] < 0.305 0.902 < q[64] < 0.904 0.909 < q[65] < 0.911
33 0.917 < q[66] < 0.919
0.924 < q[67] < 0.926
0.930 < q[68] < 0.932
0.936 < q[69] < 0.938
5 0.942 < q[70] < 0.944
0.947 < q[71] < 0.949
0.952 < q[72] < 0.954
0.957 < q[73] < 0.959
0.961 < q[74] < 0.963
10 0.965 < q[75] < 0.967
0.969 < q[76] < 0.971
0.972 < q[77] < 0.974
0.975 < q[78] < 0.977
0.978 < q[79] < 0.980
15 0.981 < q[80] < 0.983
0.984 < q[81] < 0.986
0.986 < q[82] < 0.988
0.988 < q[83] < 0.990
0.990 < q[84] < 0.992
20 0.992 < q[85] < 0.994
0.993 < q[86] < 0.995
0.995 < q[87] < 0.997
0.996 < q[88] < 0.998
0.997 < q[89] < 0.999
25 0.998 < q[90] < 1.000
0.999 < q[91] < 1.001
0.999 < q[92] < 1.001
1.000 < q[93] < 1.002
1.000 < q[94] < 1.002
30 1.000 < q[95] < 1.002
1.000 < q[96] < 1.002
1.000 < q[97] < 1.002
0.999 < q[98] < 1.001
0.999 < q[99] < 1.001
35 0.998 < q[100] < 1.000
0.997 < q[101] < 0.999
0.996 < q[102] < 0.998
0.995 < q[103] < 0.997
34 0.993 < q[104] < 0.995
0.992 < q[105] < 0.994
0.990 < q[106] < 0.992
0.988 < q[107] < 0.990
5 0.986 < q[108] < 0.988
0.984 < q[109] < 0.986
0.981 < q[110] < 0.983
0.978 < q[lll] < 0.980
0.975 < q[112] < 0.977
10 0.972 < q[113] < 0.974
0.969 < q[114] < 0.971
0.965 < q[115] < 0.967
0.961 < q[116] < 0.963
0.957 < q[117] < 0.959
15 0.952 < q[118] < 0.954
0.947 < q[119] < 0.949
0.942 < q[120] < 0.944
0.936 < q[121] < 0.938
0.930 < q[122] < 0.932
20 0.924 < q[123] < 0.926
0.917 < q[124] < 0.919
0.909 < q[125] < 0.911
0.902 < q[126] < 0.904
0.893 < q[127] < 0.895
25 0.290 < q[128] < 0.292
0.278 < q[129] < 0.280
0.266 < q[130] < 0.268
0.254 < q[131] < 0.256
0.243 < q[132] < 0.245
30 0.232 < q[133] < 0.234
0.221 < q[134] < 0.223
0.210 < q[135] < 0.212
0.200 < q[136] < 0.202
0.190 < q[137] < 0.192
35 0.180 < q[138] < 0.182
0.170 < q[139] < 0.172
0.160 < q[140] < 0.162
0.150 < q[141] < 0.152
35 0.141 < q[142] < 0.143
0.132 < q[143] < 0.134
0.122 < q[144] < 0.124
0.113 < q[145] < 0.115
5 0.105 < q[146] < 0.107
0.096 < q[147] < 0.098
0.087 < q[148] < 0.089
0.079 < q[149] < 0.081
0.070 < q[150] < 0.072
10 0.062 < q[151] < 0.064
0.054 < q[152] < 0.056
0.045 < q[153] < 0.047
0.037 < q[154] < 0.039
0.029 < q[155] < 0.031
15 0.021 < q[156] < 0.023
0.014 < q[157] < 0.016
0.006 < q[158] < 0.008
-0.002 < q[159] < 0.000
-0.009 < q[160] < -0.007
20 -0.017 < q[161] < -0.015
-0.024 < q[162] < -0.022
-0.032 < q[163] ≤ -0.030
-0.039 < q[164] < -0.037
-0.046 < q[165] < -0.044
25 -0.054 < q[166] < -0.052
-0.061 < q[167] < -0.059
-0.068 < q[168] < -0.066
-0.075 < q[169] < -0.073
-0.082 < q[170] < -0.080
30 -0.089 < q[171] < -0.087
-0.096 < q[172] < -0.094
-0.102 < q[173] < -0.100
-0.109 < q[174] < -0.107
-0.116 < q[175] < -0.114
35 -0.122 < q[176] < -0.120
-0.129 < q[177] < -0.127
-0.135 < q[178] < -0.133
-0.142 < q[179] < -0.140
36 -0.148 < q[180] < -0.146 -0.154 < q[181] < -0.152 -0.160 ≤ q[182] < -0.158 -0.166 < q[183] < -0.164 -0.172 < q[184] < -0.170 -0.178 < q[185] < -0.176 -0.183 < q[186] < -0.181 -0.189 < q[187] < -0.187 -0.194 < q[188] < -0.192 -0.199 < q[189] < -0.197 -0.204 < q[190] < -0.202 -0.209 < q[191] < -0.207
To be more precise, the filter coefficients ςr(v) obey the following relations:
-0.20294 < q[0] < -0. 20292 -0.19804 < q[l] < -0. 19802 -0.19295 < q[2] < -0. 19293 -0.18768 < q[3] < -0. 18766 -0.18226 < q[4] < -0. 18224 -0.17668 < q[5] < -0. 17666 -0.17097 < q[6] < -0. 17095 -0.16514 < q[7] < -0. 16512 -0.15919 < q[8] < -0. 15917 -0.15313 < q[9] < -0. 15311 -0.14697 < q[10] < -0 .14695 -0.14071 < q[H] < -0 .14069 -0.13437 < q[12] < -0 .13435 -0.12794 < q[13] < -0 .12792 -0.12144 < q[14] < -0 .12142 -0.11486 < q[15] < -0 .11484 -0.10821 < q[16] < -0 .10819 -0.10149 < q[17] < -0 .10147 -0.09471 < q[18] < -0 .09469 -0.08786 < q[19] < -0 .08784 -0.08095 < q[20] < -0 .08093 -0.07397 < q[21] < -0 .07395
37 -0.06694 < q[22] < -0.06692
-0.05984 < q[23] < -0.05982
-0.05269 < q[24] < -0.05267
-0.04547 < q[25] < -0.04545
-0.03819 < q[26] < -0.03817
-0.03085 < q[27] < -0.03083
-0.02345 < q[28] < -0.02343
-0.01598 < q[29] < -0.01596
-0.00845 < q[30] < -0.00843
10 -0.00084 < q[31] < -0.00082
0.00683 < q[32] < 0.00685
0.01458 < q[33] < 0.01460
0.02240 < q[34] < 0.02242
0.03030 < q[35] < 0.03032
15 0.03828 < q[36] < 0.03830
0.04635 < q[37] < 0.04637
0.05451 < q[38] < 0.05453
0.06275 < q[39] < 0.06277
0.07110 < q[40] < 0.07112
20 0.07954 < q[41] < 0.07956
0.08809 < q[42] < 0.08811
0.09675 < q[43] < 0.09677
0.10552 < q[44] < 0.10554
0.11442 < q[45] < 0.11444
25 0.12344 < q[46] < 0.12346
0.13259 < q[47] < 0.13261
0.14189 < q[48] < 0.14191
0.15132 < q[49] < 0.15134
0.16091 < q[50] < 0.16093
30 0.17066 < q[51] < 0.17068
0.18058 < q[52] < 0.18060
0.19067 < q[53] < 0.19069
0.20095 < q[54] < 0.20097
0.21143 < q[55] < 0.21145
35 0.22211 < q[56] < 0.22213
0.23300 ≤ q[57] < 0.23302
0.24412 < q[58] < 0.24414
0.25549 < q[59] < 0.25551
38 0.26711 ≤ q[60] < 0.26713 0.27899 < q[61] < 0.27901 0.29117 < q[62] < 0.29119 0.30364 < q[63] < 0.30366 0.90252 < q[64] < 0..90254 0.91035 ≤ q[65] < 0..91037 0.91769 ≤ q[66] < 0..91771 0.92457 < q[67] < 0..92459 0.93101 < q[68] < 0..93103
10 0.93705 < q[69] < 0..93707 0.94270 < q[70] < 0..94272 0.94800 < q[71] < 0..94802 0.95295 < q[72] < 0..95297 0.95758 ≤ q[73] < 0..95760
15 0.96190 < q[74] < 0..96192 0.96593 < q[75] < 0..96595 0.96968 < q[76] < 0..96970 0.97317 < q[77] < 0..97319 0.97641 < q[78] < 0..97643
20 0.97940 < q[79] < 0..97942 0.98217 < q[80] < 0..98219 0.98472 ≤ q[81] < 0..98474 0.98706 < q[82] < 0..98708 0.98919 < q[83] < 0..98921
25 0.99113 ≤ q[84] < 0..99115 0.99288 < q[85] < 0..99290 0.99444 < q[86] < 0..99446 0.99583 < q[87] < 0..99585 0.99704 < q[88] < 0..99706
30 0.99809 < q[89] < 0..99811 0.99896 < q[90] < 0..99898 0.99967 < q[91] < 0..99969
00023 < q[92] < 1.00025 00062 < q[93] < 1.00064
35 00086 < q[94] < 1.00088 00093 < q[95] < 1.00095 00086 < q[96] < 1.00088
1.00062 < q[97] < 1.00064
39 1.00023 ≤ q[98] < 1.00025 0.99967 < q[99] < O. 99969 0.99896 < q[100] < O .99898 0.99809 < q[101] < O .99811 0.99704 ≤ q[102] < O .99706 0.99583 < q[103] < O .99585 0.99444 < q[104] < O .99446 0.99288 < q[105] < O .99290 0.99113 < q[106] < O .99115
10 0.98919 < q[107] < O .98921 0.98706 < q[108] < O .98708 0.98472 < q[109] < O .98474 0.98217 < qCllO] < O .98219 0.97940 < q[Hl]- < O .97942
15 0.97641 < q[H2] < O .97643 0.97317 < q[113] < O .97319 0.96968 < q[H4] < O .96970 0.96593 < q[H5] < O .96595 0.96190 < q[116] < O .96192
20 0.95758 < q[117] < O .95760 0.95295 < q[H8] < O .95297 0.94800 < q[H9] < O .94802 0.94270 < q[120] < O .94272 0.93705 < q[121] < O .93707
25 0.93101 < q[122] < O .93103 0.92457 < q[123] < O .92459 0.91769 < q[124] < O .91771 0.91035 < q[125] < O .91037 0.90252 < q[126] < O .90254
30 0.89416 < q[127] < O .89418 0.29117 < q[128] < O .29119 0.27899 < q[129] < O .27901 0.26711 < q[130] < O .26713 0.25549 < q[131] < O .25551
35 0.24412 < q[132] < O .24414 0.23300 < q[133] < O .23302 0.22211 < q[134] < O .22213 0.21143 < q[135] < O .21145
40 0.20095 ≤ q[136] < 0.20097
0.19067 < q[137] < 0.19069
0.18058 < q[138] < 0.18060
0.17066 < q[139] < 0.17068
0.16091 < q[140] < 0.16093
0.15132 < q[141] < 0.15134
0.14189 < q[142] < 0.14191
0.13259 < q[143] < 0.13261
0.12344 < q[144] < 0.12346
10 0.11442 < q[145] < 0.11444
0.10552 < q[146] < 0.10554
0.09675 < q[147] < 0.09677
0.08809 < q[148] < 0.08811
0.07954 < q[149] < 0.07956
15 0.07110 < q[150] < 0.07112
0.06275 < q[151] < 0.06277
0.05451 < q[152] < 0.05453
0.04635 < q[153] < 0.04637
0.03828 < q[154] < 0.03830
20 0.03030 < q[155] < 0.03032
0.02240 < q[156] < 0.02242
0.01458 < q[157] < 0.01460
0.00683 < q[158] < 0.00685
-0.00084 < q[159] < -0.00082
25 -0.00845 < q[160] < -0.00843
-0.01598 < q[161] < -0.01596
-0.02345 < q[162] < -0.02343
-0.03085 < q[163] < -0.03083
-0.03819 < q[164] < -0.03817
30 -0.04547 < q[165] < -0.04545
-0.05269 < q[166] < -0.05267
-0.05984 < q[167] < -0.05982
-0.06694 < q[168] < -0.06692
-0.07397 < q[169] < -0.07395
35 -0.08095 < q[170] < -0.08093
-0.08786 < q[171] < -0.08784
■0.09471 < q[172] < -0.09469
-0.10149 < q[173] < -0.10147
41 -0.10821 < q[174] < -0.10819 -0.11486 < q[175] < -0.11484 -0.12144 < q[176] < -0.12142 -0.12794 < q[177] < -0.12792 -0.13437 < q[178] < -0.13435 ■0.14071 < q[179] < -0.14069 -0.14697 < q[180] < -0.14695 -0.15313 < q[181] < -0.15311 -0.15919 < q[182] < -0.15917 -0.16514 < q[183] < -0.16512 -0.17097 < q[184] < -0.17095 -0.17668 < q[185] < -0.17666 -0.18226 < q[186] < -0.18224 -0.18768 < q[187] < -0.18766 -0.19295 < q[188] < -0.19293 -0.19804 < q[189] < -0.19802 -0.20294 < q[190] < -0.20292 ■0.20764 < q[191] < -0.20762
Even more accurately, the filter coefficients qr(v) can be expressed by the following equations for the integer v in the range between 0 and 191, wherein according to the requirements and specifications of special implementations, the prototype filter coefficients may deviate from the following equations either individually or from the maximum absolute value typically by 10%, 5% or 2% and preferably by 1% or 0.1%:
q[0] = -0.2029343380 q[l] = -0.1980331588 q[2] = -0.1929411519 q[3] = -0.1876744222 q[4] = -0.1822474011 q[5] = -0.1766730202 q[6] = -0.1709628636 q[7] = -0.1651273005 q[8] = -0.1591756024 q[9] = -0.1531160455
42 q[10] = -0.1469560005 q[ll] = -0.1407020132 q[12] = -0.1343598738 q[13] = -0.1279346790
5 q[14] = -0.1214308876 q[15] = -0.1148523686 q[16] = -0.1082024454 q[17] = -0.1014839341 q[18] = -0.0946991783
10 q[19] = -0.0878500799 q[20] = -0.0809381268 q[21] = -0.0739644174 q[22] = -0.0669296831 q[23] = -0.0598343081
15 q[24] = -0.0526783466 q[25] = -0.0454615388 q[26] = -0.0381833249 q[27] = -0.0308428572 q[28] = -0.0234390115
20 q [ 29] = -0 . 0159703957 q[30] = -0.0084353584 q[31] = -0.0008319956 q[32] = 0.0068418435 q[33] = 0.0145885527
25 q[34] = 0.0224107648 q[35] = 0.0303113495 q[36] = 0.0382934126 q[37] = 0.0463602959 q[38] = 0.0545155789
30 q[39] = 0.0627630810 q[40] = 0.0711068657 q[41] = 0.0795512453 q[42] = 0.0881007879 q[43] = 0.0967603259
35 q[44] = 0.1055349658 q[45] = 0.1144301000 q[46] = 0.1234514222 q[47] = 0.1326049434
43 q[48] = 0.1418970123 q[49] = 0.1513343370 q[50] = 0.1609240126 q[51] = 0.1706735517 q[52] = 0.1805909194 q[53] = 0.1906845753 q[54] = 0.2009635191 q[55] = 0.2114373458 q[56] = 0.2221163080
10 q[57] = 0.2330113868 q[58] = 0.2441343742 q[59] = 0.2554979664 q[60] = 0.2671158700 q[61] = 0.2790029236
15 q[62] = 0.2911752349 q[63] = 0.3036503350 q[64] = 0.9025275713 q[65] = 0.9103585196 q[66] = 0.9176977825
20 q[67] = 0.9245760683 q[68] = 0.9310214581 q[69] = 0.9370596739 q[70] = 0.9427143143 q[71] = 0.9480070606
25 q[72] = 0.9529578566 q[73] = 0.9575850672 q[74] = 0.9619056158 q[75} = 0.9659351065 q[76] = 0.9696879297
30 q[77] = 0.9731773547 q[78] = 0.9764156119 q[79] = 0.9794139640 q[80] = 0.9821827692 q[81] = 0.9847315377
35 q[82] = 0.9870689790 q[83] = 0.9892030462 q[84] = 0.9911409728 q[85] = 0.9928893067
44 q[86] = 0.9944539395 q[87] = 0.9958401318 q[88] = 0.9970525352 q[89] = 0.9980952118
5 q[90] = 0.9989716504 q[91] = 0.9996847806 q[92] = 1.0002369837 q[93] = 1.0006301028 q[94] = 1.0008654482
10 q[95] = 1.0009438063 q[96] = 1.0008654482 q[97] = 1.0006301028 q[98] = 1.0002369837 q[99] = 0.9996847806
15 q[100] = 0.9989716504 qtlOl] = 0.9980952118 q[102] = 0.9970525352 q[103] = 0.9958401318 q[104] = 0.9944539395
20 q[105] = 0.9928893067 q[106] = 0.9911409728 q[107] = 0.9892030462 q[108] = 0.9870689790 q[109] = 0.9847315377
25 qtllO] = 0.9821827692 q[lll] = 0.9794139640 q[112] = 0.9764156119 q[113] = 0.9731773547 q[114] = 0.9696879297
30 q[115] = 0.9659351065 q[116] = 0.9619056158 q[117] = 0.9575850672 q[118] = 0.9529578566 q[119] = 0.9480070606
35 q[120] = 0.9427143143 q[121] = 0.9370596739 q[122] = 0.9310214581 q[123] = 0.9245760683
45 q[124] = 0.9176977825 q[125] = 0.9103585196 q[126] = 0.9025275713 q[127] = 0.8941712974
5 q[128] = 0.2911752349 q[129] = 0.2790029236 q[130] = 0.2671158700 q[131] = 0.2554979664 q[132] = 0.2441343742
10 q[133] = 0.2330113868 q[134] = 0.2221163080 q[135] = 0.2114373458 q[136] = 0.2009635191 q[137] = 0.1906845753
15 q[138] = 0.1805909194 q[139] = 0.1706735517 q[140] = 0.1609240126 q[141] = 0.1513343370 q[142] = 0.1418970123
20 q[143] = 0.1326049434 q[144] = 0.1234514222 q[145] = 0.1144301000 q[146] = 0.1055349658 q[147] = 0.0967603259
25 q[148] = 0.0881007879 q[149] = 0.0795512453 q[150] = 0.0711068657 q[151] = 0.0627630810 q[152] = 0.0545155789
30 q[153] = 0.0463602959 q[154] = 0.0382934126 q[155] = 0.0303113495 q[156] = 0.0224107648 q[157] = 0.0145885527
35 q[158] = 0.0068418435 q[159] = -0.0008319956 q[160] = -0.0084353584 q[161] = -0.0159703957
46 q[162] = -0.0234390115 q[163] = -0.0308428572 q[164] = -0.0381833249 q[165] = -0.0454615388 q[166] = -0.0526783466 q[167] = -0.0598343081 q[168] = -0.0669296831 q[169] = -0.0739644174 q[170] = -0.0809381268 q[171] = -0.0878500799 q[172] = -0.0946991783 q[173] = -0.1014839341 q[174] = -0.1082024454 q[175] = -0.1148523686 q[176] = -0.1214308876 q[177] = -0.1279346790 q[178] = -0.1343598738 q[179] = -0.1407020132 q[180] = -0.1469560005 q[181] = -0.1531160455 q[182] = -0.1591756024 q[183] = -0.1651273005 q[184] = -0.1709628636 q[185] = -0.1766730202 q[186] = -0.1822474011 q[187] = -0.1876744222 q[188] = -0.1929411519 q[189] = -0.1980331588 q[190] = -0.2029343380 q[191] = -0.2076267137
Hence, the present invention relates to the application of an arbitrary filter to a signal which is available in the transform domain of a complex exponential modulated filter bank, when this filter bank is designed to give virtually alias free performance of operations like equalization, spectral envelope adjustment, frequency selective panning, or frequency selective spatialization of audio signals.
47 The present invention permits to efficiently transform a given finite impulse response (FIR) filter in the time domain into a set of shorter FIR filters, to be applied with one filter for each subband of the filter bank.
The present invention also teaches how to convert a given discrete time domain filter into to a set of subband domain filters. The result is that any given filter can be implemented with a high degree of accuracy in the subband domain of a complex exponential modulated filter bank. In a preferred embodiment, the filter converter consists of a second complex exponential modulated analysis filter bank. For the special case of filters that implement a pure delay, the methods of the present invention coincides with that of PCT/EP2004/004607 "Advanced processing based on a complex-exponential modulated filterbank and adaptive time framing" .
Furthermore, the present invention comprises the following features:
- A method for obtaining a high quality approximation to the filtering of a discrete-time input signal with a given filter, comprising the steps of - analyzing the input signal with a downsampled complex analysis filter bank in order to obtain a multitude of subband signals,
- filtering each subband signal with a subband filter, where the multitude of subband filters are obtained from the given filter by means of a filter converter,
- synthesizing an output signal from the filtered subband signals with a downsampled complex synthesis filter bank.
- A method according to the above where the filter converter consists of a downsampled complex analysis filter bank.
48 - An apparatus for performing a method for obtaining a high quality approximation to the filtering of a discrete-time input signal with a given filter, the method comprising the steps of - analyzing the input signal with a downsampled complex analysis filter bank in order to obtain a multitude of subband signals,
- filtering each subband signal with a subband filter, where the multitude of subband filters are obtained from the given filter by means of a filter converter,
- synthesizing an output signal from the filtered subband signals with a downsampled complex synthesis filter bank.
- A computer program having instructions for performing, when running on a computer, a method for obtaining a high quality approximation to the filtering of a discrete-time input signal with a given filter, the method comprising the steps of analyzing the input signal with a downsampled complex analysis filter bank in order to obtain a multitude of subband signals,
- filtering each subband signal with a subband filter, where the multitude of subband filters are obtained from the given filter by means of a filter converter, synthesizing an output signal from the filtered subband signals with a downsampled complex synthesis filter bank.
Adaptation for real cosine modulated filter banks
Whereas the above derivation is based on complex modulated filter banks, a note can be made here for the critically sampled real representation obtained by a cosine modulated filter bank defined by taking the real part of the subband
49 samples (1) for an appropriate phase factor θ. In this case it is no longer feasible to use the in-band subband filtering method (3) to obtain a good approximation to a given filter. However, due to the assumptions made on the prototype filter response, a generalization to a multiband filter of the type
Figure imgf000050_0001
will be applicable, (with obvious modifications for the first and last subbands) . Due to the critical sampling there is much less freedom in the construction of the filter mask gπ r(l) . One has to do the following, which is obvious for those skilled in the art. For each m = 0,1,...,L-I , use the elementary subband signal dn{k) = δ[n—m]δ[k] as input to the real synthesis bank, and filter the resulting output y(y) with the filter h(y) to get the filtered synthesis waveform z(y) . Now use this filtered waveform as input to the real analysis bank. The resulting subband signal carries the coefficients of the masks gn r(I) for n+r = m. Some reduction in work necessary for the filter is obtained by observing that the three cases m = 3κ+ε for £• = 0,1,2 can be processed in parallel by feeding the first synthesis bank with all the corresponding elementary subband signals for each case. Thus the real valued filter converter comprises three real synthesis and three real analysis bank operations. This parallel computation represents an implementation short cut for real valued filter converter for the case of a QMF band with good side lope suppression.
Fig. 9 illustrates an embodiment of an inventive filter apparatus for filtering a time domain input signal of an inventive filter apparatus to obtain a time domain output signal. As already mentioned in the context of Fig. Ia, the filter apparatus of Fig. 9 comprises a complex analysis filter bank 101, a subband filtering 102 and a complex
50 synthesis filter bank 103, which outputs the time domain output signal.
While Fig. 1 shows a system comprising an embodiment of an inventive filter apparatus along with an embodiment of a filter generator 104, the filter apparatus shown in Fig. 9 comprises only as an option a filter converter 104, which provides the subband filtering 102 with the intermediate filter definition signal, for instance in the form of the filter taps or the impulse response for each of the intermediate filters 190 of the subband filtering 102. The filter apparatus shown in Fig. 9, comprises additional optional components, which can provide the subband filtering 102 with the filter taps for the plurality of intermediate filters 190 of the subband filtering 102.
As an example, the filter taps can also be taken from an optional data base 500, which is connected to the subband filtering 102. In one embodiment, the data base 500 comprises the complex valued filter taps of the intermediate filters 190. The data base can be implemented as a memory system, for instance in the form of a nonvolatile memory system or volatile memory system depending on the concrete implementation. Hence, memory solutions for the data base 500 comprise ROM (ROM = read only memory) , RAM (RAM = random access memory) , flash memory, magnetical memory, optical memory or other memory systems.
Depending on the concrete implementation, a processor or a CPU (CPU = central processing unit) 510 can access the data base and provide the filter taps to the subband filtering
102 or can also access the data base to provide the corresponding filter taps to the intermediate filters of the subband filtering 102. Hence, such an embodiment comprises a data base 500 from which the filter taps for the subband filtering 102 can be taken.
51 In a further embodiment of an inventive filter apparatus, which is also depicted as an option in Fig. 9, the CPU 510 is capable of on-line calculating the filter taps. In such an embodiment, the CPU 510 accesses the data base 500 according to a set of parameters provided by the user and/or according to a set of parameters, which are based on further circumstances, reads one or more sets of filter taps for the intermediate filters of the subband filtering 102 and calculates, optionally accompanied by an interpolation scheme or another estimation scheme, the desired intermediate filter taps and provides them to the subband filtering 102. In a further embodiment, the CPU 510 or another processor or computer system provides the filter taps of the intermediate filters 190 to the subband filtering 102 without accessing a data base 500. In such an embodiment, the CPU 510 or another processor calculates the filter taps and provides them to the subband filtering 102. Examples for such an embodiment will be explained more closely with respect to Fig. 10.
In a further embodiment depicted in Fig. 9, the CPU 510 accesses a further data base 520, reads one or more filter definition signals (e.g. in the form of impulse response signals corresponding to filter characteristic in the time domain) , calculates an effective filter definition signal, for instance an appropriate impulse response, and provides the results of this computation to the filter converter 104. In this embodiment, the filter converter 104 then provides the subband filtering 102 with the appropriate filter taps for the intermediate filters 190. Hence, in this embodiment, the filter converter 104 generates the effective subband filters or intermediate filters applied to each individual subband filters of each individual subband signal inside the subband filtering 102 leading to a filtering effect audibly indistinguishable from a corresponding filter applied to the time domain input signal (input signal) . As consequence, this embodiment is
52 also capable of on-line calculating the filter taps via the filter converter 104.
An example might for instance be a device, which calculates the taps of the intermediate filters 190 of the subband filtering 102 according to a set of parameters for instance provided by the user, wherein the parameter basis is so large, that an effective predetermination of the filter taps, optionally accompanied by some sort of interpolation scheme, would not lead to the desired results.
A more concrete application comes for instance of the field of dynamic chance of HRTF filters in one domain to be converted to the subband or QMF domain. As mentioned before, this is for instance relevant in applications involving a head-tracker in which the data base 520 is an HRTF data base comprising the time impulse responses of the HRTF filters. As the HRTF filters usually have very long impulse responses, the use of such a scheme is especially interesting, as the taps for the intermediate filters 190 or the QMF taps are complex. Storing the data base in this domain would roughly double the memory requirements compared to the memory requirement of storing the impulse responses in the time domain. However, the advantage of the reduced memory requirement can also be employed without having a CPU 510 which calculates the impulse response provided to the filter converter 504. Instead, the data base 520 can be simply be prompted to output the corresponding definition signal, which might be an impulse response in the time domain to the filter converter 104.
In Fig. 10, an amplitude/frequency characteristic 550 is illustrated in the frequency domain. In some applications, as explained before, the filter coefficients or filter taps are the intermediate filters 190 of the subband filtering 102 can be stored in the data base like the data base 500 of Fig. 9. Alternatively or additionally, for some applications, the filter taps of the intermediate filters
53 can also be calculated by the CPU 510 of Fig. 9. In the case of a special effect filtering or a lower quality signal processing, in which aliasing effects might become tolerable (at least to some extend) , the filter taps of the intermediate filters 190 after subband filtering 102 can be estimated without a filter converter 104 or another embodiment of a filter generator. Possible applications especially comprise voice transmission over low quality lines, like telephones or small band radio communications. Hence, in these applications a determination of the filter taps corresponding the transfer function 550 of Fig. 10 or another amplitude/frequency characteristic into several subbands 560 with different subband frequencies can be carried out without employing an inventive filter converter.
Fig. 11 shows an embodiment of an inventive filter converter 104. As previously outlined in the context of Fig. 3, the filter converter 104 comprises a complex analysis filter bank 301 to which a (real valued) impulse response signal indicative of an amplitude/frequency filter characteristic can be supplied via an input 104a and via an optional switch 600. As outlined before, the complex analysis filter bank 301 converts the impulse response signal into a plurality of complex valued subband signals and the intermediate filter definition signal output at an output 104b of the filter converter. As indicated in Fig. Ia and Fig. 9, the output 104b of the filter converter 104 can be connected to a subband filtering 102.
As already mentioned earlier, each of the complex valued subband signals of the complex modulated filter bank 301 corresponds to an impulse response for one of the intermediate filters 190 for a subband signal in the subband filtering 102 shown in Fig. Ia and 9. Typically, the complex valued subband signals are significantly shorter than the impulse response signal of the filter characteristic provided at the input 104a in the time
54 domain. Furthermore, typically at least one of the complex valued subband signals output at the output 104b comprises at least two different non-vanishing values. Especially the last feature distinguishes the output of the filter converter 104 from a simple gain adjustment in the frame work of filtering using a direct Fourier transform procedure .
If, however, the filter converter 104 is not provided with an impulse response signal indicative of an amplitude/frequency filter characteristic, but a filter definition signal, which comprises at least one of an amplitude/frequency filter characteristic, a phase/frequency filter characteristic or the filter taps in the time domain or another domain of a filter, the filter converter 104 comprises an impulse response generator 610 for converting the filter definition signal into the impulse response signal, which is then provided via the optional switch 600 to the complex analysis filter bank 301. In a concrete implementation, the impulse response generator 610 can for instance calculate the impulse response signal provided to the complex analysis filter bank 301 by superposition of real valued oscillations (Fourier synthesis) , wherein the amplitude characteristics and the phase characteristics of the intended filter to be transferred into the complex subband domain are regarded as defined by the definition signal provided to the input 104c. In other words, if at least one of an amplitude/frequency characteristic and a phase/frequency characteristic is applied to the impulse response generator 610, an impulse response signal can be computed by the impulse response generator 610 by supposition of (harmonic) oscillations considering the amplitude and phase relations as defined by the filter definition signal.
Possible applications of both embodiments of the filter apparatus and the filter generator and especially in the field of high quality audio coding and decoding.
55 Recent developments in audio coding have provided means to obtain a multi-channel signal impression over stereo headphones. This is commonly done by downmixing a multi- channel signal to stereo using the original multi-channel signal and HRTF filters. It has been shown in prior art that the parametric multi-channel audio decoder can be combined with a binaural downmix algorithm making it possible to render a multi-channel signal over headphones without the need for first re-creating the multi-channel signal from the transmitted downmix signal, and subsequently downmixing it again by means of the HRTF filters. However, this requires that the parameters for recreating the multi-channel signal (e.g. HD, CLD parameters) are combined with the HRTF filters, which in turn requires a parameterization of the HRTF filters. This requirement for a parameterization of the HRTF filters imposes high limitation on the system, since HRTF filters can be long and thus very hard to correctly model with a parametric approach. This limitation makes it impossible to use long HRTF filters for combined parametric multi-channel and binaural downmix decoders. The crucial algorithmic component required to obtain a proper combination of multichannel parameters and HRTF filters is to have access to a representation of the given HRTF filters in the subband domain assumed by the spatial parameters. This is exactly what is offered by the embodiments of the present invention. Once this representation is available, the HRTF filters can be combined into 2JV filters as a function of the parametric multi-channel representation. This gives a significant advantage in terms of computational complexity over the method that first recreates the -^channels and then applies 2M filtering operations.
An example of a different application of the method employed by embodiments of the current invention is the efficient compensation for non-perfect audio rendering devices for audio content coded in the MPEG HE-AAC format
56 [ISO/IEC 14496-3:2001/AMDl:2003]. Such advanced filtering steps, possibly including cross talk cancellation, can be applied directly in the subband domain prior to the time domain synthesis.
Other developments in audio coding has made methods available to recreate a multi-channel representation of an audio signal based on a stereo (or mono) signal and corresponding control data. These methods differ substantially from older matrix based solution such as Dolby® Prologic, since additional control data is transmitted to control the re-creation, also referred to as up-mix, of the surround channels based on the transmitted mono or stereo channels.
Hence, such a parametric multi-channel audio decoder, e.g. MPEG Surround reconstructs ^ channels based on M transmitted channels, where N>M f ancj the additional control- data. The additional control data represents a significantly lower data rate than that required for transmission of all N channels, making the coding very efficient while at the same time ensuring compatibility with both A/ channel devices and N channel devices. [J. Breebaart et al. "MPEG spatial audio coding / MPEG Surround: overview and current status", Proc. 119th AES convention, New York, USA, October 2005, Preprint 6447] .
These parametric surround coding methods usually comprise a parameterization of the surround signal based on Channel Level Difference (CLD) and Inter-channel coherence/cross- correlation (ICC) . These parameters describe power ratios and correlation between channel pairs in the up-mix process. Further Channel Prediction Coefficients (CPC) are also used in prior art to predict intermediate or output channels during the up-mix procedure.
Depending on certain implementation requirements of the inventive methods, the inventive methods can be implemented
57 in hardware or in software. The implementation can be performed using a digital storage medium, in particular a disc, CD or a DVD having an electronically readable control signal stop thereon, which cooperates with a programmable computer system in such that an embodiment of the inventive methods is performed. Generally, an embodiment of the present invention is, therefore, a computer program product with a program code stored on an machine-readable carrier, the program code being operative for performing the inventive methods when the computer program product runs on a computer or a processor. In other words, embodiments of the inventive methods are, therefore, a computer program having a program code for performing at least one of the inventive methods when the computer program runs of a computer.
While the foregoing has been particularly shown and described with references to particular embodiments thereof, it will be understood by those skilled in the art that various other changes in the form and details maybe made without departing from the spiritual scope thereof. It is to be understood that various changes may be made in adapting to different embodiments without departing from the broader concept disclosed herein and comprehend by the claims that follows.
58

Claims

1. Filter apparatus for filtering a time domain input signal to obtain a time domain output signal, which is a representation of the time domain input signal filtered using a filter characteristic having an nonuniform amplitude/frequency characteristic,
comprising:
a complex analysis filter bank (101) for generating a plurality of complex subband signals from the time domain input signals;
a plurality of intermediate filters (190) , wherein at least one of the intermediate filters (190) of the plurality of the intermediate filters (190) has a nonuniform amplitude/frequency characteristic, wherein the plurality of intermediate filters (190) have a shorter impulse response compared to an impulse response of a filter having the filter characteristic, and wherein the non-uniform amplitude/frequency characteristics of the plurality of intermediate filters together represent the non-uniform filter characteristic; and
a complex synthesis filter bank (103) for synthesizing the output of the intermediate filters (190) to obtain the time domain output signal.
2. Filter apparatus according to claim 1, wherein at least one of the immediate filters (190) has a low pass filter characteristic, a high pass filter characteristic, a band pass filter characteristic, a band rejection filter characteristic or a notch filter characteristic.
59
3. Filter apparatus according to any of the preceding claims, wherein the intermediate filters (190) of the plurality of intermediate filters (190) are finite impulse response filters.
4. Filter apparatus according to any of the preceding claims, wherein each intermediate filter (190) is operative to have an impulse response depending on an intermediate filter definition signal.
5. Filter apparatus according to claim 4, wherein the plurality of intermediate filter (190) is operative to receive the intermediate filter definition signal from a data base (500) or from a processor (510) .
6. Filter apparatus according to any of the claims 4 or 5, wherein the plurality of intermediate filters is operative to receive the intermediate filter definition signal from a filter generator (104) comprising a complex modulated filter bank (301) for filtering an impulse response signal indicative of an amplitude/frequency filter characteristic in a time domain to obtain a plurality of complex valued subband signals as the intermediate filter definition signal, wherein each complex valued subband signal of the complex modulated filter bank corresponds to an impulse response for one intermediate filter (190) , wherein at least one of the complex valued subband signals comprises at least two different non-vanishing values, and wherein each complex valued subband signal is shorter than the impulse response signal.
7. Filter apparatus according to any of the preceding claims, wherein the complex analysis filter bank (101) is operative to output L complex subband signals, wherein the plurality of intermediate filters (190) comprises L intermediate filters (190) , wherein the complex synthesis filter bank (103) is operative to
60 synthesize the output of the L intermediate filters (190) , and wherein L is a positive integer greater than 1.
8. Filter apparatus according to claim 7, wherein the complex analysis filter bank (101) , the plurality of intermediate filters (190) and the complex synthesis filter bank (103) is operative to have L = 64.
9. Filter apparatus according to any of the claims 7 or
8, wherein the plurality of intermediate filters (190) is operative to filter the complex subband signals based on the equation
dn(k) = ∑gn(l)cn(k-l) (3)
wherein n is an integer in the range from 0 to (L-I) indicating an index of the subband signals, wherein L and k are integers, wherein dn{k) is the output of the intermediate filter (190) of the subband signal with the index n, wherein cn{k) is the subband signal with the index n, and wherein gn\l) is the impulse response of the intermediate filter (190) for the subband signal with the index n.
10. Filter apparatus according to any of the claims 7 to
9, wherein the intermediate filter (190) with an index n has an impulse response gn(k) , which is based on the equation
*„(*)= ∑ Kv+kL)q(y)exp(-ij(n+±)v] (12) v=-∞ V -" / wherein n is an integer in the range from 0 to (L-I) indicating the index of the subband signal, wherein k and v are integers, wherein h(v) is the response of a filter having the filter characteristic, wherein π = 3.1415926... is the circular number, wherein i = V-T is
61 the complex unit, and wherein q{v) are filter taps of a real valued prototype filter.
11. Filter apparatus according to any of the claims 7 to 9, wherein at least one of the intermediate filters
(190) with an index n has an impulse response gn{k) , which is based on the equation
Figure imgf000062_0001
wherein
Figure imgf000062_0002
wherein Nj, is the length of the impulse response h ( υ ) of a filter having the filter characteristic, wherein π = 3.1415926... is the circular number, wherein i = V-I is the complex unit, and wherein q(υ) are filter taps of a real valued prototype filter.
12. Filter apparatus according to any of the claims 10 or 11, wherein the intermediate filters (190) are adapted so that the prototype filter taps q{v) fulfil for integers υ from 0 to 191 the relations:
-0.204 < q[0] < -0.202
-0.199 < q[l] < -0.197
-0.194 < q[2] < -0.192
-0.189 < q[3] < -0.187 -0.183 < q[4] < -0.181
-0.178 < q[5] < -0.176
-0.172 < q[6] < -0.170
-0.166 < q[7] < -0.164
-0.160 < q[8] < -0.158 -0.154 < q[9] < -0.152
-0.148 < q[10] < -0.146
-0.142 < q[ll] < -0.140
-0.135 < q[12] < -0.133
62 -0.129 < q[13] < -0.127
-0.122 < q[14] < -0.120
-0.116 < q[15] < -0.114
-0.109 < q[16] < -0.107
5 -0.102 < q[17] < -0.100
-0.096 < q[18] ≤ -0.094
-0.089 < q[19] < -0.087
-0.082 < q[20] < -0.080
-0.075 < q[21] < -0.073
10 -0.068 < q[22] < -0.066
-0.061 < q[23] < -0.059
-0.054 < q[24] < -0.052
-0.046 < q[25] < -0.044
-0.039 < q[26] < -0.037
15 -0.032 < q[27] < -0.030
-0.024 < q[28] < -0.022
-0.017 < q[29] < -0.015
-0.009 < q[30] < -0.007
-0.002 < q[31] < 0.000
20 0.006 < q[32] < 0.008
0.014 < q[33] < 0.016
0.021 < q[34] < 0.023
0.029 < q[35] < 0.031
0.037 < q[36] < 0.039
25 0.045 < q[37] < 0.047
0.054 < q[38] < 0.056
0.062 < q[39] < 0.064
0.070 < q[40] < 0.072
0.079 < q[41] < 0.081
30 0.087 < q[42] < 0.089
0.096 < q[43] < 0.098
0.105 < q[44] < 0.107
0.113 < q[45] < 0.115
0.122 < q[46] < 0.124
35 0.132 < q[47] < 0.134
0.141 < q[48] < 0.143
0.150 < q[49] < 0.152
0.160 < q[50] < 0.162
63
0.170 < q[51] < 0.172 0.180 < q[52] < 0, 182 0.190 < q[53] < 0.192 0.200 < q[54] < 0 202 0.210 < q[55] < 0, 212 0.221 < q[56] < 0, 223 0.232 < q[57] < 0, 234 0.243 < q[58] < 0, 245 0.254 < q[59] < 0.256
10 0.266 < q[60] < 0, 268 0.278 < q[61] < 0.280 0.290 < q[62] < 0, 292 0.303 < q[63] < 0.305 0.902 < q[64] < 0.904
15 0.909 < q[65] < 0.911 0.917 < q[66] < 0.919 0.924 < q[67] < 0.926 0.930 < q[68] < 0.932 0.936 < q[69] < 0.938
20 0.942 ≤ q[70] < 0.944 0.947 < q[71] < 0.949 0.952 < q[72] < 0.954 0.957 < q[73] < 0.959 0.961 < q[74] < 0.963
25 0.965 < q[75] < 0.967 0.969 < q[76] < 0.971 0.972 < q[77] < 0.974 0.975 < q[78] < 0.977 0.978 < q[79] < 0.980
30 0.981 < q[80] < 0.983 0.984 < q[81] < 0.986 0.986 < q[82] < 0.988 0.988 < q[83] < 0.990 0.990 < q[84] < 0.992
35 0.992 < q[85] < 0.994 0.993 < q[86] < 0.995 0.995 < q[87] < 0.997 0.996 ≤ q[88] < 0.998
64
0.997 < q[89] < 0.999
0.998 < q[90] < 1.000
0.999 < q[91] < 1.001
0.999 < q[92] < 1.001
5 1.000 < q[93] < 1.002
1.000 < q[94] < 1.002
1.000 < q[95] < 1.002
1.000 < q[96] < 1.002
1.000 < q[97] < 1.002
10 0.999 < q[98] < 1.001
0.999 < q[99] < 1.001
0.998 < q[100] < 1.000
0.997 < q[101] < 0.999
0.996 < q[102] < 0.998
15 0.995 < q[103] < 0.997
0.993 < q[104] < 0.995
0.992 < q[105] < 0.994
0.990 < q[106] < 0.992
0.988 < q[107] < 0.990
20 0.986 < q[108] < 0.988
0.984 < q[109] < 0.986
0.981 < q[110] < 0.983
0.978 < q[lll] < 0.980
0.975 < q[112] < 0.977
25 0.972 < q[113] < 0.974
0.969 < q[114] < 0.971
0.965 < q[115] < 0.967
0.961 < q[116] < 0.963
0.957 < q[117] < 0.959
30 0.952 < q[118] < 0.954
0.947 < q[119] < 0.949
0.942 < q[120] < 0.944
0.936 < q[121] < 0.938
0.930 < q[122] < 0.932
35 0.924 < q[123] < 0.926
0.917 < q[124] < 0.919
0.909 < q[125] < 0.911
0.902 < q[126] < 0.904
65
0.893 < q[127] < 0.895
0.290 < q[128] < 0.292
0.278 < q[129] < 0.280
0.266 < q[130] < 0.268
5 0.254 < q[131] < 0.256
0.243 < q[132] < 0.245
0.232 < q[133] < 0.234
0.221 < q[134] < 0.223
0.210 < q[135] < 0.212
10 0.200 < q[136] < 0.202
0.190 < q[137] < 0.192
0.180 < q[138] < 0.182
0.170 < q[139] < 0.172
0.160 < q[140] < 0.162
15 0.150 < q[141] < 0.152
0.141 < q[142] < 0.143
0.132 < q[143] < 0.134
0.122 < q[144] < 0.124
0.113 < q[145] < 0.115
20 0.105 < q[146] < 0.107
0.096 < q[147] < 0.098
0.087 < q[148] < 0.089
0.079 < q[149] < 0.081
0.070 < q[150] < 0.072
25 0.062 < q[151] < 0.064
0.054 < q[152] < 0.056
0.045 < q[153] < 0.047
0.037 < q[154] < 0.039
0.029 < q[155] < 0.031
30 0.021 < q[156] < 0.023
0.014 < q[157] < 0.016
0.006 < q[158] < 0.008
-0.002 < q[159] < 0.000
-0.009 < q[160] < -0.007
35 -0.017 < q[161] < -0.015
-0.024 < q[162] < -0.022
-0.032 < q[163] < -0.030
-0.039 < q[164] < -0.037
66 -0.046 < q[165] < -0.044
-0.054 < q[166] < -0.052
-0.061 < q[167] < -0.059
-0.068 < q[168] < -0.066 -0.075 < q[169] < -0.073
-0.082 < q[170] < -0.080
-0.089 < q[171] < -0.087
-0.096 < q[172] < -0.094
-0.102 < q[173] < -0.100 -0.109 < q[174] < -0.107
-0.116 < q[175] < -0.114
-0.122 < q[176] < -0.120
-0.129 < q[177] < -0.127
-0.135 < q[178] < -0.133 -0.142 < q[179] < -0.140
-0.148 < q[180] < -0.146
-0.154 < q[181] < -0.152
-0.160 < q[182] < -0.158
-0.166 < q[183] < -0.164 -0.172 < q[184] < -0.170
-0.178 < q[185] < -0.176
-0.183 < q[186] < -0.181
-0.189 < q[187] < -0.187
-0.194 < q[188] < -0.192 -0.199 < q[189] < -0.197
-0.204 < q[190] < -0.202
-0.209 < q[191] < -0.207.
13. Filter apparatus according to any of the claims 10 to 12, wherein the intermediate filters (190) are adapted so that the prototype filter taps q(υ) fulfil for integers υ from 0 to 191 the relations:
-0.20294 < q[0] < -0.20292 -0.19804 < q[l] < -0.19802
-0.19295 < q[2] < -0.19293
-0.18768 < q[3] < -0.18766
-0.18226 < q[4] < -0.18224
67 -0.17668 < q[5] < -0.17666
-0.17097 < q[6] < -0.17095
-0.16514 < q[7] < -0.16512
-0.15919 < q[8] < -0.15917
-0.15313 < q[9] < -0.15311
-0.14697 < q[10] < -0.14695
-0.14071 < q[H] < -0.14069
-0.13437 ≤ q[12] < -0.13435
-0.12794 < q[13] < -0.12792
10 -0.12144 < q[14] < -0.12142
-0.11486 < q[15] < -0.11484
-0.10821 < q[16] < -0.10819
-0.10149 < q[17] < -0.10147
-0.09471 < q[18] < -0.09469
15 -0.08786 < q[19] < -0.08784
-0.08095 < q[20] < -0.08093
-0.07397 < q[21] < -0.07395
-0.06694 < q[22] < -0.06692
-0.05984 < q[23] < -0.05982
20 -0.05269 < q[24] < -0.05267
-0.04547 < q[25] < -0.04545
-0.03819 < q[26] < -0.03817
-0.03085 < q[27] < -0.03083
-0.02345 < q[28] < -0.02343
25 -0.01598 < q[29] < -0.01596
-0.00845 < q[30] < -0.00843
-0.00084 < q[31] < -0.00082
0.00683 < q[32] < 0.00685
0.01458 < q[33] < 0.01460
30 0.02240 < q[34] < 0.02242
0.03030 < q[35] < 0.03032
0.03828 < q[36] < 0.03830
0.04635 < q[37] < 0.04637
0.05451 < q[38] < 0.05453
35 0.06275 ≤ q[39] < 0.06277
0.07110 < q[40] < 0.07112
0.07954 < q[41] < 0.07956
0.08809 < q[42] < 0.08811
68
0.09675 < q[43] < 0.09677 0.10552 < q[44] < 0.10554 0.11442 < q[45] < 0.11444 0.12344 < q[46] < 0.12346 0.13259 < q[47] < 0.13261 0.14189 ≤ q[48] < 0.14191 0.15132 < q[49] < 0.15134 0.16091 < q[50] < 0.16093 0.17066 < q[51] < 0.17068
10 0.18058 < q[52] < 0.18060 0.19067 < q[53] < 0.19069 0.20095 ≤ q[54] < 0.20097 0.21143 < q[55] < 0.21145 0.22211 ≤ q[56] < 0.22213
15 0.23300 < q[57] < 0.23302 0.24412 < q[58] < 0.24414 0.25549 < q[59] < 0.25551 0.26711 < q[60] < 0.26713 0.27899 < q[61] < 0.27901
20 0.29117 < q[62] < 0.29119 0.30364 < q[63] < 0.30366 0.90252 < q[64] < 0.90254 0.91035 < q[65] < 0.91037 0.91769 < q[66] < 0.91771
25 0.92457 < q[67] < 0.92459 0.93101 < q[68] < 0.93103 0.93705 < q[69] < 0.93707 0.94270 < q[70] < 0.94272 0.94800 < q[71] < 0.94802
30 0.95295 < q[72] < 0.95297 0.95758 < q[73] < 0.95760 0.96190 < q[74] < 0.96192 0.96593 < q[75] < 0.96595 0.96968 < q[76] < 0.96970
35 0.97317 < q[77] < 0.97319 0.97641 < q[78] < 0.97643 0.97940 < q[79] < 0.97942 0.98217 ≤ q[80] < 0.98219
69
0.98472 < q[81] < 0.98474
0 .98706 < q[82] < 0.98708
0 .98919 < q[83] < 0.98921
0 .99113 < q[84] < 0.99115
0 .99288 < q[85] < 0.99290
0 .99444 < q[86] < 0.99446
0 .99583 < q[87] < 0.99585
0 .99704 < q[88] < 0.99706
0 .99809 < q[89] < 0.99811
10 0 .99896 < q[90] < 0.99898
0 .99967 < q[91] < 0.99969
1 .00023 < q[92] < 1.00025
1 .00062 < q[93] < 1.00064
1 .00086 < q[94] < 1.00088
15 1 .00093 < q[95] < 1.00095
1 .00086 < q[96] < 1.00088
1 .00062 < q[97] < 1.00064
1 .00023 < q[98] < 1.00025
0 .99967 < q[99] < 0.99969
20 0. 99896 < q[100] < 0.99898
0. 99809 < q[101] < 0.99811
0. 99704 < q[102] < 0.99706
0. 99583 < q[103] < 0.99585
0. 99444 < q[104] < 0.99446
25 0. 99288 < q[105] < 0.99290
0. 99113 < q[106] < 0.99115
0. 98919 < q[107] < 0.98921
0. 98706 < q[108] < 0.98708
0. 98472 < q[109] < 0.98474
30 0. 98217 < q[110] < 0.98219
0. 97940 < q[lll] < 0.97942
0. 97641 < q[112] < 0.97643
0. 97317 < q[H3] < 0.97319
0. 96968 < q[114] < 0.96970
35 0. 96593 < q[H5] < 0.96595
0. 96190 < q[116] < 0.96192
0. 95758 < q[H7] < 0.95760
0. 95295 < q[118] < 0.95297
70
0.94800 < q[119] < 0.94802 0.94270 < q[120] < 0.94272 0.93705 < q[121] < 0.93707 0.93101 < q[122] < 0.93103 0.92457 < q[123] < 0..92459 0.91769 < q[124] < 0..91771 0.91035 < q[125] < 0..91037 0.90252 < q[126] < 0..90254 0.89416 < q[127] < 0..89418
10 0.29117 < q[128] < 0..29119 0.27899 < q[129] < 0..27901 0.26711 < q[130] < 0..26713 0.25549 < q[131] < 0..25551 0.24412 < q[132] < 0..24414
15 0.23300 < q[133] < 0..23302 0.22211 < q[134] < 0..22213 0.21143 < q[135] < 0..21145 0.20095 < q[136] < 0..20097 0.19067 < q[137] < 0..19069
20 0.18058 < q[138] < 0..18060 0.17066 < q[139] < 0..17068 0.16091 < q[140] < 0..16093 0.15132 < q[141] < 0..15134 0.14189 < q[142] < 0..14191
25 0.13259 < q[143] < 0..13261 0.12344 < q[144] < 0..12346 0.11442 < q[145] < 0..11444 0.10552 < q[146] < 0..10554 0.09675 < q[147] < 0.09677
30 0.08809 < q[148] < 0.08811 0.07954 < q[149] < 0.07956 0.07110 < q[150] < 0.07112 0.06275 < qfl51] < 0.06277 0.05451 < q[152] < 0.05453
35 0.04635 < q[153] < 0.04637 0.03828 < q[154] < 0.03830 0.03030 < q[155] < 0.03032 0.02240 < q[156] < 0.02242
71
0.01458 < q[157] < 0.01460 0.00683 < q[158] < 0.00685 -0.00084 < q[159] < -0.00082 -0.00845 < q[160] < -0.00843 -0.01598 < q[161] < -0.01596 -0.02345 < q[162] < -0.02343 -0.03085 < q[163] < -0.03083 -0.03819 < q[164] < -0.03817 -0.04547 < q[165] < -0.04545 -0.05269 < q[166] < -0.05267 -0.05984 < q[167] < -0.05982 -0.06694 < q[168] < -0.06692 -0.07397 < q[169] < -0.07395 -0.08095 < q[170] < -0.08093 -0.08786 < q[171] < -0.08784 -0.09471 < q[172] < -0.09469 -0.10149 < q[173] < -0.10147 -0.10821 < q[174] < -0.10819 -0.11486 < q[175] < -0.11484 -0.12144 < q[176] < -0.12142 -0.12794 < q[177] < -0.12792 -0.13437 < q[178] < -0.13435 -0.14071 < q[179] < -0.14069 -0.14697 < q[180] < -0.14695 -0.15313 < q[181] < -0.15311 -0.15919 < q[182] < -0.15917 -0.16514 < q[183] < -0.16512 -0.17097 < q[184] < -0.17095 -0.17668 < q[185] < -0.17666 -0.18226 < q[186] < -0.18224 -0.18768 < q[187] < -0.18766 -0.19295 < q[188] < -0.19293 -0.19804 < q[189] < -0.19802 -0.20294 < q[190] < -0.20292 -0.20764 < q[191] < -0.20762
14. Filter apparatus according to any of the claims 10 to 14, wherein the intermediate filters (190) are adapted, so that the real valued prototype filter
72 coefficients q(υ) for integer υ in the range from 0 to 191 are given by
q[0] = -0.2029343380 q[l] = -0.1980331588 q[2] = -0.1929411519 q[3] = -0.1876744222 q[4] = -0.1822474011 q[5] = -0.1766730202 q[6] = -0.1709628636 q[7] = -0.1651273005 q[8] = -0.1591756024 q[9] = -0.1531160455 qtlO] = -0.1469560005 q[ll] = -0.1407020132 q[12] = -0.1343598738 q[13] = -0.1279346790 q[14] = -0.1214308876 q[15] = -0.1148523686 q[16] = -0.1082024454 q[17] = -0.1014839341 q[18] = -0.0946991783 q[19] = -0.0878500799 q[20] = -0.0809381268 q[21] = -0.0739644174 q[22] = -0.0669296831 q[23] = -0.0598343081 q[24] = -0.0526783466 q[25] = -0.0454615388 q[26] = -0.0381833249 q[27] = -0.0308428572 q[28] = -0.0234390115 q[29] = -0.0159703957 q[30] = -0.0084353584 q[31] = -0.0008319956 q[32] = 0.0068418435 q[33] = 0.0145885527 q [ 34 ] = 0. 0224107648
73 q[35] = 0.0303113495 q[36] = 0.0382934126 q[37] = 0.0463602959 q[38] = 0.0545155789
5 q[39] = 0.0627630810 q[40] = 0.0711068657 q[41] = 0.0795512453 q[42] = 0.0881007879 q[43] = 0.0967603259
10 q[44] = 0.1055349658 q[45] = 0.1144301000 q[46] = 0.1234514222 q[47] = 0.1326049434 q[48] = 0.1418970123
15 q[49] = 0.1513343370 q[50] = 0.1609240126 q[51] = 0.1706735517 q[52] = 0.1805909194 q[53] = 0.1906845753
20 q[54] = 0.2009635191 q[55] = 0.2114373458 q[56] = 0.2221163080 q[57] = 0.2330113868 q[58] = 0.2441343742
25 q[59] = 0.2554979664 q[60] = 0.2671158700 q[61] = 0.2790029236 q[62] = 0.2911752349 q[63] = 0.3036503350
30 q[64] = 0.9025275713 q[65] = 0.9103585196 q[66] = 0.9176977825 q[67] = 0.9245760683 q[68] = 0.9310214581
35 q[69] = 0.9370596739 q[70] = 0.9427143143 q[71] = 0.9480070606 q[72] = 0.9529578566
74 q[73] = 0.9575850672 q[74] = 0.9619056158 q[75] = 0.9659351065 q[76] = 0.9696879297 q[77] = 0.9731773547 q[78] = 0.9764156119 q[79] = 0.9794139640 q[80] = 0.9821827692 q[81] = 0.9847315377
10 q[82] = 0.9870689790 q[83] = 0.9892030462 q[84] = 0.9911409728 q[85] = 0.9928893067 q[86] = 0.9944539395
15 q[87] = 0.9958401318 q[88] = 0.9970525352 q[89] = 0.9980952118 q[90] = 0.9989716504 q[91] = 0.9996847806
20 q[92] = 1.0002369837 q[93] = 1.0006301028 q[94] = 1.0008654482 q[95] = 1.0009438063 q[96] = 1.0008654482
25 q[97] = 1.0006301028 q[98] = 1.0002369837 q[99] = 0.9996847806 q[100] = 0.9989716504 q[101] = 0.9980952118
30 q[102] = 0.9970525352 q[103] = 0.9958401318 q[104] = 0.9944539395 q[105] = 0.9928893067 q[106] = 0.9911409728
35 q[107] = 0.9892030462 q[108] = 0.9870689790 q[109] = 0.9847315377 q[H0] = 0.9821827692
75 q[lll] = 0.9794139640 q[112] = 0.9764156119 q[113] = 0.9731773547 q[114] = 0.9696879297
5 q[H5] = 0.9659351065 q[116] = 0.9619056158 q[117] = 0.9575850672 q[118] = 0.9529578566 q[119] = 0.9480070606
10 q[120] = 0.9427143143 q[121] = 0.9370596739 q[122] = 0.9310214581 q[123] = 0.9245760683 q[124] = 0.9176977825
15 q[125] = 0.9103585196 q[126] = 0.9025275713 q[127] = 0.8941712974 q[128] = 0.2911752349 q[129] = 0.2790029236
20 q[130] = 0.2671158700 q[131] = 0.2554979664 q[132] = 0.2441343742 q[133] = 0.2330113868 q[134] = 0.2221163080
25 q[135] = 0.2114373458 q[136] = 0.2009635191 q[137] = 0.1906845753 q[138] = 0.1805909194 q[139] = 0.1706735517
30 q[140] = 0.1609240126 q[141] = 0.1513343370 q[142] = 0.1418970123 q[143] = 0.1326049434 q[144] = 0.1234514222
35 q[145] = 0.1144301000 q[146] = 0.1055349658 q[147] = 0.0967603259 q[148] = 0.0881007879
76 q[149] = 0.0795512453 q[150] = 0.0711068657 q[151] = 0.0627630810 q[152] = 0.0545155789
5 q[153] = 0.0463602959 q[154] = 0.0382934126 q[155] = 0.0303113495 q[156] = 0.0224107648 q[157] = 0.0145885527
10 q[158] = 0.0068418435 q[159] = -0.0008319956 q[160] = -0.0084353584 q[161] = -0.0159703957 q[162] = -0.0234390115
15 q[163] = -0.0308428572 q[164] = -0.0381833249 q[165] = -0.0454615388 q[166] = -0.0526783466 q[167] = -0.0598343081
20 q[168] = -0.0669296831 q[169] = -0.0739644174 q[170] = -0.0809381268 q[171] = -0.0878500799 q[172] = -0.0946991783
25 q[173] = -0.1014839341 q[174] = -0.1082024454 q[175] = -0.1148523686 q[176] = -0.1214308876 q[177] = -0.1279346790
30 q[178] = -0.1343598738 q[179] = -0.1407020132 q[180] = -0.1469560005 q[181] = -0.1531160455 q[182] = -0.1591756024
35 q[183] = -0.1651273005 q[184] = -0.1709628636 q[185] = -0.1766730202 q[186] = -0.1822474011
77 q[187] = -0.1876744222 q[188] = -0.1929411519 q[189] = -0.1980331588 q[190] = -0.2029343380 q[191] = -0.2076267137
15. Filter apparatus according to any of preceding, wherein the filter characteristic is based on an HRTF filter characteristic.
16. Filter apparatus according to any of the preceding claims, wherein the complex analysis filter bank (101) comprises a downsampler (140) for each subband signal output by the complex analysis filter bank (101) .
17. Filter apparatus according to claim 16, wherein the complex analysis filter bank (101) is adapted to output L complex subband signals, wherein L is a positive integer greater than 1, and wherein each of the downsampler (140) is adapted to downsample the subband signals by a factor of L.
18. Filter apparatus according to any of the preceding claims, wherein the complex analysis filter bank (101) comprises a complex modulated filter for each complex subband signal based on a prototype filter.
19. Filter apparatus according to any of the preceding claims, wherein the complex synthesis filter bank (103) comprises an upsampler (160) for each of the subband signals.
20. Filter apparatus according to claim 19, wherein the complex synthesis filter bank (103) is operative to synthesize L signals of the intermediate filters to obtain the time domain output signal, wherein L is a positive integer greater than 1, wherein the complex synthesis filter bank (103) comprises L upsampler
78 (160) and wherein each of the upsampler (160) is adapted for upsampling the output of the intermediate filters (190) by a factor of L.
21. Filter apparatus according to any of the preceding claims, wherein the complex synthesis filter bank (103) comprises for each subband signal an intermediate synthesis filter, wherein the complex synthesis filter bank (103) comprises a real part extractor (180) for each signal output by intermediate synthesis filters (150) , and wherein the complex synthesis filter bank (103) further comprises an adder (170) for adding the output of each of a the real part extractor (180) to obtain the time domain output signal.
22. Filter apparatus according to any of the claims 1 to 20, wherein the complex synthesis filter bank (103) comprises an intermediate synthesis filter (150) for each of the subband signals output by the intermediate filters (190) , wherein the complex synthesis filter bank (103) further comprises an adder (170) for summing up the ouputs of each intermediate synthesis filters (150) and wherein the complex synthesis filter bank (103) further comprises a real part extractor (180) for extracting a real valued signal as the time domain output signal from the output of the adder (170) .
23. Filter apparatus according to any of the preceding claims, wherein the filter apparatus further comprises a gain adjuster for at least one subband signal or for at least one signal output by intermediate filter (190) for adjusting the gain.
24. Filtering apparatus according to any of the preceding claims, wherein the filtering apparatus further comprises a further intermediate filter for filtering
79 at least one of the complex valued subband signals or for filtering at least one of the signals output by one of the intermediate filters (190) .
25. Filter generator (104) for providing an intermediate filter definition signal,
comprising:
a complex modulated filter bank (301) for filtering an impulse response signal indicative of an amplitude/frequency filter characteristic in a time domain to obtain a plurality of complex valued subband signals as the intermediate filter definition signal,
wherein each complex valued subband signal of the complex modulated filter bank (301) corresponds to an impulse response for an intermediate filter for a subband signal;
wherein at least one of the complex valued subband signals comprises at least two different non-vanishing values; and
wherein each complex valued subband signal is shorter than the impulse response signal.
26. Filter generator (104) according to claim 25, wherein the complex modulated filter bank (301) is adapted for outputting at least one complex valued subband signal as a linear combination of at least two values of the impulse response signal.
27. Filter generator (104) according to any of the claims 25 to 26, wherein the complex modulated filter bank
(301) is adapted for filtering an impulse response signal of a non-uniform amplitude/frequency filter characteristic.
80
28. Filter generator (104) according to any of the claims 25 to 27, wherein the complex modulated filter bank (301) is operative to filter the impulse response signal, and wherein the impulse response signal is based on a HRTF-related impulse response.
29. Filter generator (104) according to any of the claims 25 to 28, wherein the complex modulated filter bank (301) is adapted to output L complex valued subband signals, wherein L is a positive integer greater than 1.
30. Filter generator (104) according to claim 29, wherein the complex modulated filter bank (301) is adapted for providing the L complex valued subband signals downsampled by a factor L.
31. Filter generator (104) according to any of the claims 29 to 30, wherein the complex modulated filter bank
(301) is adapted to output L = 64 complex valued subband signals.
32. Filter generator (104) according to any of the claims 29 to 31, wherein the complex modulated filter bank
(301) is adapted to provide complex valued subband signals having values gn (k) based on the equation
&,(*)= ∑ h(y+kL)q(y)exp(-ij(n+±)v) (12) "~ y L J
, wherein n is an integer in the range from Fig. 0 to
[L-I) indicating an index of the complex valued subband signal, wherein k and v are integers, wherein h(v) is the response of a filter having the filter characteristic, wherein π = 3.1415926... is the circular number, wherein i = V-I is the complex unit, and wherein g{υ) are filter taps of a real valued prototype filter.
81
33. Filter generator (104) according to any of the claims 29 to 32, wherein the complex modulated filter bank (301) is adapted to provide complex valued subband signals having a value of gn (k) based on the equation
Figure imgf000082_0001
wherein
[0 , otherwise wherein Nh is the length of the impulse response h(υ) of a filter having the filter characteristic, wherein π = 3.1415926... is the circular number, wherein i = v-1 is the complex unit, and wherein q{v) are filter taps of a real valued prototype filter.
34. Filter generator (104) according to one of the claims 32 to 33, wherein the complex modulated filter bank (301) is adapted so that the prototype filter taps q(υ) fulfil for integers υ from 0 to 191 the relations :
-0.204 < q[0] < -0.202 -0.199 < q[l] < -0.197
-0.194 < q[2] < -0.192
-0.189 < q[3] < -0.187
-0.183 < q[4] < -0.181
-0.178 < q[5] < -0.176 -0.172 < q[6] < -0.170
-0.166 < q[7] < -0.164
-0.160 < q[8] < -0.158
-0.154 < q[9] < -0.152
-0.148 < q[10] < -0.146 -0.142 < q[ll] < -0.140
-0.135 < q[12] < -0.133
-0.129 < q[13] < -0.127
-0.122 < q[14] < -0.120
82 -0.116 < q[15] < -0.114
-0.109 ≤ q[16] < -0.107
-0.102 < q[17] < -0.100
-0.096 < q[18] < -0.094
-0.089 < qtl9] < -0.087
-0.082 < q[20] < -0.080
-0.075 < q[21] < -0.073
-0.068 < q[22] < -0.066
-0.061 < q[23] < -0.059
10 -0.054 < q[24] < -0.052
-0.046 < q[25] < -0.044
-0.039 < q[26] < -0.037
-0.032 < q[27] < -0.030
-0.024 < q[28] < -0.022
15 -0.017 < q[29] < -0.015
-0.009 < q[30] < -0.007
-0.002 < q[31] < 0.000
0.006 < q[32] < 0.008
0.014 < q[33] < 0.016
20 0.021 < q[34] < 0.023
0.029 < q[35] < 0.031
0.037 < q[36] < 0.039
0.045 < q[37] < 0.047
0.054 < q[38] < 0.056
25 0.062 < q[39] < 0.064
0.070 < q[40] < 0.072
0.079 < q[41] < 0.081
0.087 < q[42] < 0.089
0.096 < q[43] < 0.098
30 0.105 < q[44] < 0.107
0.113 < q[45] < 0.115
0.122 < q[46] < 0.124
0.132 < q[47] < 0.134
0.141 < q[48] < 0.143
35 0.150 < q[49] < 0.152
0.160 < q[50] < 0.162
0.170 < q[51] < 0.172
0.180 < q[52] < 0.182
83
0.190 < q[53] < 0.192 0.200 < q[54] < 0.202 0.210 < q[55] < 0.212 0.221 < q[56] < 0.223 0.232 < q[57] < 0.234 0.243 < q[58] < 0.245 0.254 < q[59] < 0.256 0.266 < q[60] < 0.268 0.278 < q[61] < 0..280
10 0.290 < q[62] < 0..292 0.303 < q[63] < 0..305 0.902 < q[64] < 0..904 0.909 < q[65] < 0..911 0.917 ≤ q[66] < 0..919
15 0.924 < q[67] < 0..926 0.930 < q[68] < 0..932 0.936 < q[69] < 0..938 0.942 < q[70] < 0..944 0.947 < q[71] < 0..949
20 0.952 < q[72] < 0..954 0.957 < q[73] < 0..959 0.961 < q[74] < 0..963 0.965 < q[75] < 0..967 0.969 < q[76] < 0..971
25 0.972 < q[77] < 0..974 0.975 < q[78] < 0..977 0.978 ≤ q[79] < 0..980 0.981 < q[80] < 0..983 0.984 < q[81] < 0.986
30 0.986 < q[82] < 0.988 0.988 < q[83] < 0.990 0.990 < q[84] < 0.992 0.992 < q[85] < 0.994 0.993 < q[86] < 0.995
35 0.995 < q[87] < 0.997 0.996 < q[88] < 0.998 0.997 < q[89] < 0.999 0.998 < q[90] < 1.000
84
0.999 < q[91] < 1.001
0.999 < q[92] < 1.001
1.000 < q[93] < 1.002
1.000 < q[94] < 1.002
5 1.000 < q[95] < 1.002
1.000 < q[96] < 1.002
1.000 < q[97] < 1.002
0.999 < q[98] < 1.001
0.999 < q[99] < 1.001
10 0.998 < q[100] < 1.000
0.997 < q[101] < 0.999
0.996 < q[102] < 0.998
0.995 < q[103] < 0.997
0.993 < q[104] < 0.995
15 0.992 < q[105] < 0.994
0.990 < q[106] < 0.992
0.988 < q[107] < 0.990
0.986 < q[108] < 0.988
0.984 < q[109] < 0.986
20 0.981 < q[110] < 0.983
0.978 < q[lll] < 0.980
0.975 < q[112] < 0.977
0.972 < q[113] < 0.974
0;969 < q[114] < 0.971
25 0.965 < q[115] < 0.967
0.961 < q[116] < 0.963
0.957 < q[117] < 0.959
0.952 < q[118] < 0.954
0.947 < q[119] < 0.949
30 0.942 < q[120] < 0.944
0.936 < q[121] < 0.938
0.930 < q[122] < 0.932
0.924 < q[123] < 0.926
0.917 < q[124] < 0.919
35 0.909 < q[125] < 0.911
0.902 < q[126] < 0.904
0.893 < q[127] < 0.895
0.290 < q[128] < 0.292
85
0.278 < q[129] < 0.280
0.266 < q[130] < 0.268
0.254 < q[131] < 0.256
0.243 < q[132] < 0.245
5 0.232 < q[133] < 0.234
0.221 < q[134] < 0.223
0.210 < q[135] < 0.212
0.200 < q[136] < 0.202
0.190 < q[137] < 0.192
10 0.180 < q[138] < 0.182
0.170 < q[139] < 0.172
0.160 < q[140] < 0.162
0.150 < q[141] < 0.152
0.141 < q[142] < 0.143
15 0.132 < q[143] < 0.134
0.122 < q[144] < 0.124
0.113 < q[145] < 0.115
0.105 < q[146] < 0.107
0.096 < q[147] < 0.098
20 0.087 < q[148] < 0.089
0.079 < q[149] < 0.081
0.070 < q[150] < 0.072
0.062 < q[151] < 0.064
0.054 < q[152] < 0.056
25 0.045 < q[153] < 0.047
0.037 < q[154] < 0.039
0.029 < q[155] < 0.031
0.021 < q[156] < 0.023
0.014 < q[157] < 0.016
30 0.006 < q[158] < 0.008
-0.002 < q[159] < 0.000
-0.009 < q[160] < -0.007
-0.017 < q[161] < -0.015
-0.024 < q[162] < -0.022
35 -0.032 < q[163] < -0.030
-0. 039 < q [ 164 ] < -0. 037
-0 . 046 < q [ 165 ] < -0. 044
-0 . 054 < q [ 166] < -0. 052
86 -0.061 < q[167] < -0 059 -0.068 < q[168] < -0 066 -0.075 < q[169] < -0 073 -0.082 < q[170] < -0 080 -0.089 ≤ q[171] < -0 087 -0.096 < q[172] < -0 094 -0.102 < q[173] < -0 100 -0.109 < q[174] < -0 .107 -0.116 < q[175] < -0 .114 -0.122 < q[176] < -0 .120 -0.129 ≤ q[177] < -0 .127 -0.135 < q[178] < -0 .133 -0.142 < q[179] < -0 .140 -0.148 < q[180] < -0 .146 -0.154 < q[181] < -0 .152 -0.160 < q[182] < -0 .158 -0.166 ≤ q[183] < -0 .164 -0.172 < q[184] < -0 .170 -0.178 < q[185] < -0 .176 -0.183 < q[186] < -0 .181 -0.189 < q[187] < -0 .187 -0.194 < q[188] < -0 .192 -0.199 < q[189] < -0 .197 -0.204 < q[190] < -0 .202 -0.209 < q[191] < -0. 207.
35. Filter generator (104) according to any of the claims 32 to 33, wherein the complex modulated filter bank (301) is adapted so that the prototype filter g(υ) fulfils for integers υ from 0 to 191 the relations:
-0.20294 < q[0] < -0.20292 ■0.19804 < q[l] < -0.19802 -0.19295 < q[2] < -0.19293 -0.18768 < q[3] < -0.18766 •0.18226 < q[4] < -0.18224 ■0.17668 < q[5] < -0.17666
-0.17097 < q[6] < -0.17095
87 -0.16514 < q[7] < -0.16512
-0.15919 < q[8] < -0.15917
-0.15313 ≤ q[9] < -0.15311
-0.14697 < q[10] < -0.14695
-0.14071 < q[H] < -0.14069
-0.13437 < q[12] < -0.13435
-0.12794 < q[13] < -0.12792
-0.12144 ≤ q[14] < -0.12142
-0.11486 < q[15] < -0.11484
10 -0.10821 < q[16] < -0.10819
-0.10149 < q[17] < -0.10147
-0.09471 < q[18] < -0.09469
-0.08786 < q[19] < -0.08784
-0.08095 ≤ q[20] < -0.08093
15 -0.07397 < q[21] < -0.07395
-0.06694 < q[22] < -0.06692
-0.05984 < q[23] < -0.05982
-0.05269 < q[24] < -0.05267
-0.04547 < q[25] < -0.04545
20 -0.03819 < q[26] < -0.03817
-0.03085 < q[27] < -0.03083
-0.02345 < q[28] < -0.02343
-0.01598 < q[29] < -0.01596
-0.00845 < q[30] < -0.00843
25 -0.00084 < q[31] < -0.00082
0.00683 < q[32] < 0.00685
0.01458 < q[33] < 0.01460
0.02240 < q[34] < 0.02242
0.03030 < q[35] < 0.03032
30 0.03828 < q[36] < 0.03830
0.04635 < q[37] < 0.04637
0.05451 < q[38] < 0.05453
0.06275 < q[39] < 0.06277
0.07110 < q[40] < 0.07112
35 0.07954 < q[41] < 0.07956
0.08809 < q[42] < 0.08811
0.09675 < q[43] < 0.09677
0.10552 < q[44] < 0.10554
88
0.11442 < q[45] < 0.11444 0.12344 < q[46] < 0.12346 0.13259 < q[47] < 0, 13261 0.14189 < q[48] < 0, 14191 0.15132 < q[49] < 0, 15134 0.16091 < q[50] < 0.16093 0.17066 < q[51] < 0, 17068 0.18058 < q[52] < 0, 18060 0.19067 < q[53] < 0.19069
10 0.20095 < q[54] < 0.20097 0.21143 < q[55] < 0, 21145 0.22211 < q[56] < 0.22213 0.23300 < q[57] < 0.23302 0.24412 < q[58] < 0.24414
15 0.25549 < q[59] < 0.25551 0.26711 < q[60] < 0.26713 0.27899 < q[61] < 0.27901 0.29117 < q[62] < 0.29119 0.30364 < q[63] < 0.30366
20 0.90252 < q[64] < 0.90254 0.91035 < q[65] < 0.91037 0.91769 < q[66] < 0.91771 0.92457 < q[67] < 0.92459 0.93101 < q[68] < 0.93103
25 0.93705 < q[69] < 0.93707 0.94270 < q[70] < 0.94272 0.94800 < q[71] < 0.94802 0.95295 < q[72] < 0.95297 0.95758 < q[73] < 0.95760
30 0.96190 < q[74] < 0.96192 0.96593 < q[75] < 0.96595 0.96968 < q[76] < 0.96970 0.97317 < q[77] < 0.97319 0.97641 < q[78] < 0.97643
35 0.97940 < q[79] < 0.97942 0.98217 < q[80] < 0.98219 0.98472 < q[81] < 0.98474 0.98706 ≤ q[82] < 0.98708
89
0.98919 < q [83] < 0.98921
0 .99113 < q [84] < 0.99115
0 .99288 < q [85] < 0.99290
0 .99444 < q [86] < 0.99446
0 .99583 < q [87] < 0.99585
0 .99704 < q [88] < 0.99706
0 .99809 < q [89] < 0.99811
0 .99896 < q [90] < 0.99898
0 .99967 < q [91] < 0.99969
10 1 .00023 < q [92] < 1.00025
1 .00062 < q [93] < 1.00064
1 .00086 < q [94] < 1.00088
1 .00093 < q [95] < 1.00095
1 .00086 < q [96] < 1.00088
15 1 .00062 < q [97] < 1.00064
1 .00023 < q [98] < 1.00025
0 .99967 < q [99] < 0.99969
0. 99896 < q[100] < 0.99898
0. 99809 < q[ 101] < 0.99811
20 0. 99704 < q[ 102] < 0.99706
0. 99583 < qC 103] < 0.99585
0. 99444 < q[ 104] < 0.99446
0. 99288 < q[ 105] < 0.99290
0. 99113 < q[106] < 0.99115
25 0. 98919 < q[ 107] < 0.98921
0. 98706 < q[ 108] < 0.98708
0. 98472 < q[109] < 0.98474
0. 98217 < qt 110] < 0.98219
0. 97940 < q[ 111] < 0.97942
30 0. 97641 < q[ 112] < 0.97643
0. 97317 < q[H3] < 0.97319
0. 96968 < qt 114] < 0.96970
0. 96593 < q[115] < 0.96595
0. 96190 < q[H6] < 0.96192
35 0. 95758 < q[117] < 0.95760
0. 95295 < q[H8] < 0.95297
0. 94800 < q[ 119] < 0.94802
0. 94270 < q[120] < 0.94272
90
0.93705 < q[121] < 0, 93707 0.93101 < q[122] < 0, 93103 0.92457 < q[123] < 0, 92459 0.91769 < q[124] < 0, 91771 0.91035 < q[125] < 0.91037 0.90252 < q[126] < 0.90254 0.89416 < q[127] < 0.89418 0.29117 < q[128] < 0, 29119 0.27899 < q[129] < 0, 27901
10 0.26711 < q[130] < 0, 26713 0.25549 < q[131] < 0.25551 0.24412 < q[132] < 0.24414 0.23300 < q[133] < 0.23302 0.22211 < q[134] < 0.22213
15 0.21143 < q[135] < 0.21145 0.20095 < q[136] < 0.20097 0.19067 < q[137] < 0.19069 0.18058 < q[138] < 0.18060 0.17066 < q[139] < 0.17068
20 0.16091 < q[140] < 0.16093 0.15132 < q[141] < 0.15134 0.14189 < q[142] < 0.14191 0.13259 < q[143] < 0.13261 0.12344 < q[144] < 0.12346
25 0.11442 < q[145] < 0.11444 0.10552 < q[146] < 0.10554 0.09675 < q[147] < 0.09677 0.08809 < q[148] < 0.08811 0.07954 < q[149] < 0.07956
30 0.07110 < q[150] < 0.07112 0.06275 < q[151] < 0.06277 0.05451 < q[152] < 0.05453 0.04635 < q[153] < 0.04637 0.03828 < q[154] < 0.03830
35 0.03030 < q[155] < 0.03032 0.02240 < q[156] < 0.02242 0.01458 ≤ q[157] < 0.01460 0.00683 < q[158] < 0.00685
91 -0.00084 < q[159] < -0.00082
-0.00845 < q[160] < -0.00843
-0.01598 < q[161] < -0.01596
-0.02345 < q[162] < -0.02343
-0.03085 < q[163] < -0.03083
-0.03819 < q[164] < -0.03817
-0.04547 < q[165] < -0.04545
-0.05269 < q[166] < -0.05267
-0.05984 < q[167] < -0.05982
-0.06694 < q[168] < -0..06692
-0.07397 < q[169] < -0..07395
-0.08095 < q[170] < -0..08093
-0.08786 < q[171] < -0..08784
-0.09471 < q[172] < -0..09469
-0.10149 < q[173] < -0..10147
-0.10821 < q[174] < -0..10819
-0.11486 < q[175] < -0..11484
-0.12144 < q[176] < -0..12142
-0.12794 < q[177] < -0..12792
-0.13437 < q[178] < -0..13435
-0.14071 < q[179] < -0..14069
-0.14697 < q[180] < -0..14695
-0.15313 < q[181] < -0..15311
-0.15919 < q[182] < -0..15917
-0.16514 < q[183] < -0..16512
-0.17097 < q[184] < -0..17095
-0.17668 < q[185] < -0..17666
-0.18226 < q[186] < -0..18224
-0.18768 < q[187] < -0.18766
-0.19295 < q[188] < -0.19293
-0.19804 < q[189] < -0.19802
-0.20294 < q[190] < -0.20292
-0.20764 < q[191] < -0.20762
36. Filter generator (104) according to any of the claims 32 to 35, wherein the complex modulated filter bank (301) is adapted so that the real valued prototype
92 filter coefficients q{v) for integer υ in the range from 0 to 191 are given by
q[0] = -0.2029343380 q[l] = -0.1980331588 q[2] = -0.1929411519 q[3] = -0.1876744222 q[4] = -0.1822474011 q[5] = -0.1766730202 q[6] = -0.1709628636 q[7] = -0.1651273005 q[8] = -0.1591756024 q[9] = -0.1531160455 q[10] = -0.1469560005 q[ll] = -0.1407020132 q[12] = -0.1343598738 q[13] = -0.1279346790 q[14] = -0.1214308876 q[15] = -0.1148523686 q[16] = -0.1082024454 q[17] = -0.1014839341 q[18] = -0.0946991783 q[19] = -0.0878500799 q[20] = -0.0809381268 q[21] = -0.0739644174 q[22] = -0.0669296831 q[23] = -0.0598343081 q[24] = -0.0526783466 q[25] = -0.0454615388 q[26] = -0.0381833249 q[27] = -0.0308428572 q[28] = -0.0234390115 q[29] = -0.0159703957 q[30] = -0.0084353584 q[31] = -0.0008319956 q[32] = 0.0068418435 q[33] = 0.0145885527 q[34] = 0.0224107648
93 q[35] = 0.0303113495 q[36] = 0.0382934126 q[37] = 0.0463602959 q[38] = 0.0545155789
5 q[39] = 0.0627630810 q[40] = 0.0711068657 q[41] = 0.0795512453 q[42] = 0.0881007879 q[43] = 0.0967603259
10 q[44] = 0.1055349658 q[45] = 0.1144301000 q[46] - 0.1234514222 q[47] = 0.1326049434 q[48] = 0.1418970123
15 q[49] = 0.1513343370 q[50] = 0.1609240126 q[51] = 0.1706735517 q[52] = 0.1805909194 q[53] = 0.1906845753
20 q[54] = 0.2009635191 q[55] = 0.2114373458 q[56] = 0.2221163080 q[57] = 0.2330113868 q[58] = 0.2441343742
25 q [ 59 ] = 0 . 2554979664 q[60] = 0.2671158700 q[61] = 0.2790029236 q[62] = 0.2911752349 q[63] = 0.3036503350
30 q[64] = 0.9025275713 q[65] = 0.9103585196 q[66] = 0.9176977825 q[67] = 0.9245760683 q[68] = 0.9310214581
35 q[69] = 0.9370596739 q[70] = 0.9427143143 q[71] = 0.9480070606 q[72] = 0.9529578566
94 q[73] = 0.9575850672 q[74] = 0.9619056158 q[75] = 0.9659351065 q[76] = 0.9696879297 q[77] = 0.9731773547 q[78] = 0.9764156119 q[79] = 0.9794139640 q[80] = 0.9821827692 q[81] = 0.9847315377
10 q[82] = 0.9870689790 q[83] = 0.9892030462 q[84] = 0.9911409728 q[85] = 0.9928893067 q[86] = 0.9944539395
15 q[87] = 0.9958401318 q[88] = 0.9970525352 q[89] = 0.9980952118 q[90] = 0.9989716504 q[91] = 0.9996847806
20 q[92] = 1.0002369837 q[93] = 1.0006301028 q[94] = 1.0008654482 q[95] = 1.0009438063 q[96] = 1.0008654482
25 qt97] = 1.0006301028 q[98] = 1.0002369837 q[99] = 0.9996847806 q[100] = 0.9989716504 q[101] = 0.9980952118
30 q[102] = 0.9970525352 q[103] = 0.9958401318 q[104] = 0.9944539395 q[105] = 0.9928893067 q[106] = 0.9911409728
35 q[107] = 0.9892030462 q[108] = 0.9870689790 q[109] = 0.9847315377 qfllO] = 0.9821827692
95 q [ l ll ] = 0 . 9794139640 q [ 112 ] = 0 . 97 64156119 q[113] = 0.9731773547 q[114] = 0.9696879297
5 q[115] = 0.9659351065 q[116] = 0.9619056158 q[117] = 0.9575850672 q[118] = 0.9529578566 q[119] = 0.9480070606
10 q[120] = 0.9427143143 q[121] = 0.9370596739 q[122] = 0.9310214581 q[123] = 0.9245760683 q[124] = 0.9176977825
15 q[125] = 0.9103585196 q[126] = 0.9025275713 q[127] = 0.8941712974 q[128] = 0.2911752349 q[129] = 0.2790029236
20 q[130] = 0.2671158700 q[131] = 0.2554979664 q[132] = 0.2441343742 q[133] = 0.2330113868 q[134] = 0.2221163080
25 q[135] = 0.2114373458 q[136] = 0.2009635191 q[137] = 0.1906845753 q[138] = 0.1805909194 q[139] = 0.1706735517
30 q[140] = 0.1609240126 q[141] = 0.1513343370 q[142] = 0.1418970123 q[143] = 0.1326049434 q[144] = 0.1234514222
35 q[145] = 0.1144301000 q[146] = 0.1055349658 q[147] = 0.0967603259 q[148] = 0.0881007879
96 q[149] = 0.0795512453 q[150] = 0.0711068657 q[151] = 0.0627630810 q[152] = 0.0545155789
5 q[153] = 0.0463602959 q[154] = 0.0382934126 q[155] = 0.0303113495 q[156] = 0.0224107648 q[157] = 0.0145885527
10 q[158] = 0.0068418435 q[159] = -0.0008319956 q[160] = -0.0084353584 q[161] = -0.0159703957 q[162] = -0.0234390115
15 q[163] = -0.0308428572 q[164] = -0.0381833249 q[165] = -0.0454615388 q[166] = -0.0526783466 q[167] = -0.0598343081
20 q[168] = -0.0669296831 q[169] = -0.0739644174 q[170] = -0.0809381268 q[171] = -0.0878500799 q[172] = -0.0946991783
25 q[173] = -0.1014839341 q[174] = -0.1082024454 q[175] = -0.1148523686 q[176] = -0.1214308876 q[177] = -0.1279346790
30 q[178] = -0.1343598738 q[179] = -0.1407020132 q[180] = -0.1469560005 q[181] = -0.1531160455 q[182] = -0.1591756024
35 q[183j = -0.1651273005 q[184] = -0.1709628636 q[185] = -0.1766730202 q[186] = -0.1822474011
97 q[187] = -0.1876744222 q[188] = -0.1929411519 q[189] = -0.1980331588 q[190] = -0.2029343380 q[191] = -0.2076267137
37. Filter generator (104) according to any of the claims 25 to 36, wherein the complex modulated filter bank (301) further comprises a gain adjuster for adjusting at least one complex valued subband signal with respect to its value before outputting the gain adjusted complex valued subband signal as the intermediate filter definition signal.
38. Filter generator (104) according to any of the claims 25 to 37, wherein the complex modulated filter bank (301) further comprises an impulse response generator (610) for generating the impulse response signal based on a filter definition signal provided to the filter generator (104) , wherein the impulse response signal output by the impulse response generator (610) is provided to the complex modulated filter bank (301) .
39. Filter generator (104) according to claim 38, wherein the impulse response generator (610) is adapted for generating the impulse response signal based on at least one of an amplitude/frequency filter characteristic, a phase/frequency filter characteristic and a signal comprising a set of filter taps indicative of the amplitude/frequency filter characteristic in the time domain as a filter definition signal.
40. Filter system for filtering the time domain input signal to obtain time domain output signal,
comprising:
98 a filter apparatus according to any of the claims 1 to 24, to which the time domain input signal is provided to as the time domain input signal, and from which the time domain output signal is obtained as the time domain output signal of the filter system; and
a filter generator (104) according to any of the claims 25 to 39, wherein the filter generator (104) is coupled to the filter apparatus to provide the plurality of the intermediate filters (190) with an intermediate filter definition,
wherein the plurality of intermediate filters (190) of the filter apparatus are adapted to have impulse responses based on the intermediate filter definition signal .
41. Method for filtering the time domain input signal to obtain a time domain output signal, which is a representation of the time domain input signal filtered using a filter characteristic having a nonuniform amplitude/frequency characteristic,
comprising the steps:
generating a plurality of complex subband signals based on a complex filtering of the time domain input signal;
filtering each of the complex subband signals, wherein at least one of the complex subband signals is filtered using an non-uniform amplitude/frequency characteristic, wherein each of the subband signals is filtered based on an impulse response being shorter than the impulse response of a filter having the filter characteristic, and wherein the non-uniform amplitude/frequency characteristic of the impulse responses used for filtering the plurality of subband
99 signals together represent the non-uniform filter characteristic; and
synthesizing from the output of the filtering of the complex subband signals the time domain output signal.
42. Method for providing an intermediate filter definition signal,
comprising the steps:
filtering an impulse response signal indicative of an amplitude/frequency filter characteristic in a time domain to obtain a plurality of complex valued subband signals as the intermediate filter definition signal,
wherein each complex valued subband signal corresponds to an impulse response for an intermediate filter for subband signal;
wherein at least one of the complex valued subband signals comprises at least two different non-vanishing values; and
wherein each complex valued subband signal is shorter than the impulse response signal.
43. Computer program for performing, when running on a computer, a method in accordance with one of the methods of claims 41 or 42.
100
PCT/EP2006/008565 2006-01-27 2006-09-01 Efficient filtering with a complex modulated filterbank WO2007085275A1 (en)

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BR122018017208-8A BR122018017208B1 (en) 2006-01-27 2006-09-01 EFFICIENT FILTERING WITH A COMPLEX MODULATED FILTER BANK
EP22214715.9A EP4178110B1 (en) 2006-01-27 2006-09-01 Efficient filtering with a complex modulated filterbank
JP2008551652A JP5452936B2 (en) 2006-01-27 2006-09-01 Efficient filtering using complex modulation filter banks
EP21204932.4A EP3979497B1 (en) 2006-01-27 2006-09-01 Efficient filtering with a complex modulated filterbank
BRPI0621207-7A BRPI0621207B1 (en) 2006-01-27 2006-09-01 EFFICIENT FILTERING WITH A COMPLEX MODULATED FILTER BANK
AT06777144T ATE503300T1 (en) 2006-01-27 2006-09-01 EFFICIENT FILTERING WITH A COMPLEX MODULATED FILTER BANK
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DE602006020930T DE602006020930D1 (en) 2006-01-27 2006-09-01 EFFICIENT FILTRATION WITH A COMPLEX MODULATED FILTER BANK
EP24168191.5A EP4372743A3 (en) 2006-01-27 2006-09-01 Efficient filtering with a complex modulated filterbank
CA2640431A CA2640431C (en) 2006-01-27 2006-09-01 Efficient filtering with a complex modulated filterbank
EP06777144A EP1977510B1 (en) 2006-01-27 2006-09-01 Efficient filtering with a complex modulated filterbank
EP18171733.1A EP3454471B1 (en) 2006-01-27 2006-09-01 Efficient filtering with a complex modulated filterbank
EP18153681.4A EP3334043B1 (en) 2006-01-27 2006-09-01 Efficient filtering with a complex modulated filterbank
NO20083675A NO339847B1 (en) 2006-01-27 2008-08-26 Effective filtration with a complex, modulated filter bank
HK09100077.7A HK1120938A1 (en) 2006-01-27 2009-01-06 Efficient filtering with a complex modulated filterbank
AU2010257205A AU2010257205B2 (en) 2006-01-27 2010-12-15 Efficient filtering with a complex modulated filterbank
NO20161716A NO342163B1 (en) 2006-01-27 2016-10-31 Effective filtration with a complex, modulated filter bank
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