EP1525576B1 - Arrangement and method for the generation of a complex spectral representation of a time-discrete signal - Google Patents

Abstract

A filter bank device for generating a complex spectral representation of a discrete-time signal includes a generator for generating a block-wise real spectral representation, which, for example, implements an MDCT, to obtain temporally successive blocks of real spectral coefficients. The output values of this spectral conversion device are fed to a post-processor for post-processing the block-wise real spectral representation to obtain an approximated complex spectral representation having successive blocks, each block having a set of complex approximated spectral coefficients, wherein a complex approximated spectral coefficient can be represented by a first partial spectral coefficient and by a second partial spectral coefficient, wherein at least one of the first and second partial spectral coefficients is determined by combining at least two real spectral coefficients. A good approximation for a complex spectral representation of the discrete-time signal is obtained by combining two real spectral coefficients, preferably by a weighted linear combination, wherein additionally more degrees of freedom for optimizing the entire system are available.

Description

The present invention relates to time-frequency conversion algorithms, and more particularly to such algorithms in conjunction with audio compression concepts.

For some coding applications for data compression purposes, and in particular for audio coding, it is necessary to present real-valued discrete-time signals in the form of complex-valued spectral components. A complex special coefficient can be represented by a first and a second partial spectral coefficient, the first part spectral coefficient being the real part and the second part spectral coefficient being the imaginary part, as desired. Alternatively, the complex spectral coefficient may also be represented by the magnitude as the first partial spectral coefficient and the phase as the second partial spectral coefficient.

Such complex spectral coefficients are also found in Vinton et al: "Scalable and Progressive Audio Codec", 2001 IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, pp. 3277-3280, vol. 5 , used.

In particular, in audio coding often real-valued transformation methods are used, such. For example, the well-known MDCT Analysis / Synthesis Filter Bank Design Based on Time Domain Aliasing Cancellation ", J. Princen, A. Bradley, IEEE Trans. Acoust., Speech, and Signal Processing 34, pp. 1153-1161, 1986 , is described. There is z. For example, within the psychoacoustic model there is a need for a complex spectrum. Reference is made to the psychoacoustic model in Annex D.2.4 of the ISO / IEC 11172-3 standard, which is also referred to as the MPEG1 standard. In certain applications, in addition to the MDCT (modified discrete cosine transformation) transformation, a complex discrete Fourier transform is included to calculate psychoacoustic parameters such as: For example, the psychoacoustic masking threshold.

In this discrete Fourier transformation (DFT), the input signal is first divided into blocks of a predetermined length by means of multiplication with temporally staggered window functions. Each of these blocks is then converted to a spectral representation by application of the DFT. Do the blocks used each contain L samples, i. H. If the window length is L, the output of the DFT can again be completely described in the form of a total of L values (real and imaginary parts or magnitude and phase values). For example, if the input signal is real, L / 2 results in complex values. When using suitable window functions, the input signal can be reconstructed from this representation with the aid of an inverse DFT.

However, this approach is subject to some limitations. For example, a critical scan is possible only if consecutive windows do not overlap. Otherwise, with a time offset of N <L values for each N, new input values of the DFT L values would have to be transmitted in the spectral representation, which is undesirable, in particular in the case of data compression methods.

However, the use of non-overlapping window functions means a strong limitation on the achievable quality of the spectral decomposition, in particular the separation of different frequency bands.

On the other hand, better band separation can be achieved with real-valued transformations with overlapping window functions. A special class of these transformations are the so-called modulated filter banks, which are characterized by the possibility of an efficient implementation. Among these modulated filter banks, the modified discrete cosine transformation (MDCT), in which the window length L may assume values between N and 2N - 1 due to different degrees of overlap.

Fig. 6 shows the decomposition of a time discrete input signal x (n) into the spectral components u _{k, m} , where m represents the temporal block index, ie the time index after the sampling rate reduction, while k is the frequency index or subband index. The sampling frequencies are the same in all subbands, ie the original sampling frequency is reduced by the factor N. In the Fig. 6 shown filter bank with filters 60 and downstream downsampling elements 62 provides a uniform band division.

In the case of a modulated filter bank, the individual subband filters are formed by multiplying a prototype impulse response h _P (n) by a subband-specific modulation function, the following rule being used for the MDCT and similar transformations: $${\mathrm{H}}_{\mathrm{k}}\left(\mathrm{n}\right)\mathrm{=}{\mathrm{H}}_{\mathrm{P}}\left(\mathrm{n}\right)\cos \left(\frac{\mathrm{\pi }}{\mathrm{N}}\left(\mathrm{n}\mathrm{-}\frac{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">N</figure-callout>}}{\mathrm{2}}\mathrm{+}\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{k}\mathrm{+}\frac{\mathrm{1}}{\mathrm{2}}\right)\right)$$

The above transformation rule may also differ from the above equation, e.g. For example, when the sine function is used instead of the cosine function, or when "+ N / 2" is used instead of "-N / 2". It is also conceivable to use the alternating MDCT / MDST mentioned later (when using k instead of k + 1/2).

In the above equation, _hP (n) represents the prototype impulse response. _Hk (n) is the filter impulse response for the filter associated with subband k. n is the counting index of the time-discrete input signal x (n), while N indicates the number of spectral coefficients.

The output values of a real-valued transformation, such. As the MDCT, which is known not energy conserving, but are only partially usable for applications that require complex-valued spectral components. If, for example, the amounts of the real output values are used as an approximation for the amounts of complex-valued spectral components in the corresponding frequency ranges, then even with sinusoidal input signals of constant amplitude there will be strong fluctuations. Such a procedure thus provides only poor approximations for short-term magnitude spectrums of the input signal.

In the technical publication " A Scalable and Progressive Audio Codec ", Vinton and Atlas, IEEE ICASSP 2001, 7-11 May 2001 , Salt Lake City, is an audio encoder with a transformation algorithm consisting of a base transformation and a second transformation. The input signal is windowed by an Kaiser-Bessel window function to produce temporally successive blocks of samples. The blocks of input values are then transformed either by a modified Discrete Cosine Transform (MDCT) or by a Modified Discrete Sine Transform (MDST) depending on a shift index. This basic transformation process essentially corresponds to the TDAC filter bank described in the cited reference by Princen and Bradley. Then, two temporally adjacent blocks of spectral coefficients are combined into a single complex transformation such that the MDCT block represents the real parts of complex spectral coefficients, while the temporally consecutive MDST block represents the associated imaginary parts of the complex spectral coefficients. From this, a time-frequency distribution of the magnitude of the complex spectrum is generated, windowing a two-dimensional magnitude distribution over time in each frequency band, again with 50% overlapping window functions. Then, using the second transformation, an amount matrix calculated. The phase information is not subjected to the second transformation.

The alternate use of the initial values of a MDCT as a real and imaginary part is also described in the technical publication " MDCT Filters Banks with Perfect Reconstruction, Karp and Fly, Proc. IEEE ISCAS 1995, Seattle, WA introduced as "MDFT".

It has also been found that this approximation of a complex spectrum from a real-valued spectral representation of the time-discrete input signal is also problematic in that it is not possible to obtain an appropriate magnitude representation for tones of certain frequencies. Thus, even with this transformation, the determination of short-term magnitude spectra is only possible to a limited extent.

The object of the present invention is to provide an improved concept for generating a complex spectral representation of a time-discrete signal.

This object is achieved by a device for generating a complex spectral representation according to claim 1, a method for generating a complex spectral representation according to claim 18, a device for encoding a discrete-time signal according to claim 19, a method for encoding a discrete-time signal according to claim 20, an apparatus for generating a real spectral representation according to claim 21, a method for generating a real spectral representation according to claim 22 or solved by a computer program according to claim 23.

The present invention is based on the finding that a good approximation for a spectral representation of a time-discrete signal from a block-wise real-valued spectral representation of the time-discrete signal can be determined by a first Teilspektralkoeffizient and / or a second partial spectral coefficient is calculated by combining at least two real spectral coefficients. This is z. B. the real part / or the imaginary part of an approximated complex spectral coefficient for a particular frequency index by combining two or more real spectral coefficients, preferably in temporal and / or frequency proximity to the complex spectral coefficients to be calculated. Preferably, the combination is a linear combination, wherein furthermore the real spectral coefficients to be combined before the linear combination, ie an addition or subtraction, can be weighted with constant weighting factors.

It should be noted at this point that a linear combination is an addition or subtraction of different linear combination partners, which may or may not be weighted with weighting factors before the linear combination. the weighting factors can be positive or negative real numbers including zero.

In a preferred embodiment of the present invention, the two or more real spectral coefficients that are combined to obtain a complex partial spectral coefficient for a frequency index and a (temporal) block index are arranged in frequency and / or temporal proximity. In frequency proximity, the real spectral coefficients are at a higher or lower by 1 frequency index from the current (temporal) block. In addition, the corresponding real spectral coefficients are located in temporal proximity from the immediately preceding time block or the immediately following time block with the same frequency index. Also in temporal and frequency proximity are the real spectral coefficients of the immediately preceding or immediately following temporal block having a frequency index higher or lower by a frequency index than that Frequency index of the partial spectral coefficient just calculated.

Preferably, the combination rule for calculating a partial spectral coefficient varies depending on whether the frequency index is even or odd.

According to the invention, it has been found that a combination of real spectral coefficients in temporal and / or frequency proximity to the complex spectral coefficient to be determined is a good approximation to a desired frequency response of the entire arrangement of the block-wise real-valued spectral representation and the device for Processing the block-wise real-valued spectral representation delivers, the frequency response - which usually has a bandpass character - should have a desired course for positive frequencies, and should be as small as possible or equal to 0 for negative frequencies. Such a frequency response results from the inventive concept and is considered advantageous for many applications.

The properties of this frequency response can be in preferred embodiments z. B. by appropriate adjustment of the weighting factors or by appropriate modification of the window functions of the first transformation to generate the real-valued spectral coefficients are manipulated. The system thus provides many degrees of freedom for adaptation to particular needs, in particular the possibility of not only combining two real spectral coefficients, but also combining more than two real spectral coefficients to provide an even better approximation to a desired frequency response of the overall arrangement to reach.

Fig. 1

ein Blockschaltbild der erfindungsgemäßen Vorrichtung zum Erzeugen einer komplexen Spektraldarstellung;

Fig. 2a

bis 2c eine Darstellung der einer Teilspektralkomponente für einen komplexen Spektralkoeffizient mit Frequenzindex k und Blockindex m benachbarten reellen Spektralkoeffizienten;

Fig. 3

eine schematische Darstellung zur Berechnung komplexer Teilbandsignale mit einer reellwertigen Transformation T₁ und einer Nachverarbeitungstransformation T₂;

Fig. 4

ein Blockschaltbild der erfindungsgemäßen Vorrichtung gemäß einem bevorzugten Ausführungsbeispiel der vorliegenden Erfindung mit kritischer Abtastung;

Fig. 5

ein Blockschaltbild der erfindungsgemäßen Vorrichtung gemäß einem weiteren Ausführungsbeispiel der vorliegenden Erfindung ohne kritische Abtastung; und

Fig. 6

eine bekannte reellwertige Filterbank mit gleichförmiger Bandaufteilung.

Preferred embodiments of the present invention will be explained below in detail with reference to the accompanying drawings. Show it:

Fig. 1

a block diagram of the inventive device for generating a complex spectral representation;

Fig. 2a

2c shows a representation of the real spectral coefficients which are adjacent to a partial spectral component for a complex spectral coefficient with frequency index k and block index m;

Fig. 3

a schematic representation for the calculation of complex subband signals with a real-valued transformation T ₁ and a Nachverarbeitungstransformation T ₂ ;

Fig. 4

a block diagram of the inventive device according to a preferred embodiment of the present invention with critical scanning;

Fig. 5

a block diagram of the device according to the invention according to another embodiment of the present invention without critical scanning; and

Fig. 6

a known real-valued filter bank with uniform band division.

Fig. 1 shows an apparatus for generating a complex spectral representation of a time-discrete signal x (n). The discrete-time signal x (n) is fed to a means 10 for generating a block-wise real-valued spectral representation of the discrete-time signal, the spectral representation having temporally consecutive blocks, each block having a set of spectral coefficients as shown in FIG Fig. 2a to 2b will be explained in more detail. At the output of the device 10 is thus a sequence of consecutive blocks of spectral coefficients that are real-valued spectral coefficients due to the property of the device 10. This sequence of temporally successive blocks of spectral coefficients is fed to a post-processing means 12 to obtain a block-wise complex approximated spectral representation comprising successive blocks, each block having a set of complex approximated spectral coefficients, a complex approximated spectral coefficient being determined by a first Part spectral coefficient and a second spectral coefficient can be displayed, wherein at least the first or the second spectral coefficient is determined by a combination of at least two real spectral coefficients.

The Fig. 2a to 2c Together, they show a sequence of blocks of real-valued spectral coefficients, as determined by means 10 of FIG Fig. 1 be generated. m represents a block index while k represents a frequency index. Fig. 2 shows a block of real-valued spectral coefficients plotted along the frequency axis at the time point or block index (m-1). The block of spectral coefficients comprises spectral coefficients u _{i, m-1} , where i is a run index, while m-1 is the block index. In particular, in Fig. 2a a spectral line with the frequency index i = k and a spectral component with the frequency index i = (k-1) and i = (k + 1) shown.

Fig. 2b shows the same situation, but now for the temporally following block m. Finally shows Fig. 2c the same situation again, but now for the block index (m + 1). This results in the episode of Fig. 2a, 2b, 2c a time course, by an arrow 20 in the Fig. 2a to 2c is symbolized.

Fig. 3 shows an alternative representation of the device for generating a complex spectral representation, wherein the discrete-time input signal x (n) in the device 10 for Generating a block-wise real spectral representation is fed in Fig. 3 is denoted by T ₁ . It should be noted that this is a first conversion of the time signal, which has been windowed to be in block, into a spectral representation at the output of the device 10. Fig. 3 shows a snapshot at the time or block index m, so refers to Fig. 2b which has been described above. The output values of the device 10, ie the real-valued spectral coefficients, which may be MDCT coefficients, for example, are fed to the device 12 for post-processing to obtain a complex spectrum on the output side, which for each frequency index k a first Teilspektralkoeffizienten p _{k, m} and a second partial spectral coefficients q _{k, m} , where p _{k, m is} the real part and q _{k, m is} the imaginary part of the complex spectral coefficient for the frequency index k, where m denotes the block index.

According to the invention, therefore, real-valued transformations in the form of modulated filter banks are used for the actual spectral decomposition to generate complex-valued spectral components. Real spectral coefficients from temporally successive and / or spectrally adjacent output values of the real-valued transformation are now used Fig. 3 is designated T ₁ and 10, respectively. From these, for example, a real and an imaginary part p, q are formed for a specific frequency index and for a specific (temporal) block index. Alternatively, of course, amount and phase could be generated. Here, special phase relationships of the modulation functions can be exploited, which are the basis of a modulated filter bank.

In a preferred embodiment, the operation T ₂ or 12, respectively, which is connected after the first transformation, is again an invertible, critically sampled transformation. This results in a total system, which also has the property of critical sampling and at the same time allows a reconstruction of the spectral components obtained.

T ₂ is now a two-dimensional transformation, since in the preferred embodiment of the present invention both temporally adjacent and frequency adjacent real valued spectral coefficients are combined, ie as their input values extend along the time and frequency axes, as shown in FIG Fig. 2a to 2c has been shown. Since a real and an imaginary part are formed from each transformation operation using the device 12, a value pair is to be calculated for a critical scan only for every second scanning position of the time / frequency plane. This is achieved in a preferred embodiment of the present invention by sampling rate reduction along the time axis, ie computation only for every other block of the first transform T ₁ . Alternatively, this is achieved by sampling rate reduction along the frequency axis, ie computation only for every second subband i of the first transformation. Again, alternatively, this is offset, ie achieved in the form of a checkerboard pattern, in which alternately every second block and every second band are used.

The transformation coefficients of the second transformation, with which the output values of T ₁ are each weighted before their summation, ie the weighting factors, preferably fulfill the conditions for the exact reconstruction according to the respective sampling scheme. The system according to the invention contains a number of degrees of freedom, which can be used for optimizing the properties of the overall system, ie for optimizing the frequency response of the entire system as a complex filter bank.

It should also be noted that for some applications, critical sampling is not mandatory is. This can be z. B. be the case with a post-processing of the decoded but not yet transformed back into the time domain signals in an audio decoder. In this case, one has a higher degree of freedom in the choice of the transformation coefficients in T ₂ . This higher degree of freedom is preferably used for a better optimization of the overall behavior.

The following is based on Fig. 4 A first embodiment of the present invention for the detailed specification of the device 12 for post-processing shown. It is preferable to distinguish between a straight frequency index k and an odd frequency index k + 1. In the case of a even frequency index, that is, when p _{k, m} and q _{k, m are} to be calculated (m is the block index and k is the frequency index), according to the first embodiment of the present invention, the real part p _{k, m} is summed by two temporally successive real-valued spectral coefficients. p _{k, m} thus results either from the summation of the spectral coefficient with the index k from the Fig. 2b and 2a or from the Fig. 2c and 2b ,

The associated imaginary part q _{k, m} is inventively either by summing two successive values with the frequency index k-1 again the Fig. 2a, 2b (Block m-1 and block m) or the Fig. 2b and 2c (Block m and block m + 1).

For an odd frequency index k + 1, the real part p _{k + 1, m is} calculated as the difference between two consecutive values, ie as the difference between the spectral coefficients k + 1 of the Fig. 2a, 2b or 2b, 2c , The associated imaginary part q _{k + 1, m} results as the difference between two successive values with the frequency index k, ie as the difference between the real-valued spectral coefficients with the index k der Fig. 2a, 2b or 2b, 2c ,

This results in the in Fig. 4 shown transformation function, which is generally designated by the reference numeral 12 a, wherein the transformation function has two transformation sub-regulations h _L (m) and h _H (m), which, as shown in Fig. 4 shown in pairs alternately applied to the output values of the device 10. In particular, the first subfunction h _L (m) has the form {1, 1}, while the second subfunction has the form {1, -1}. The notation of the subfunctions h _L (m) and h _H (m) is intended to mean that a sum or difference of the corresponding spectral coefficients is to be formed from two (temporally) adjacent blocks.

The critical sampling is achieved by a factor of 2 temporal sampling rate reduction, as indicated by the device labeled 12b in FIG Fig. 4 is shown symbolically. If an orthogonality of the second transformation (12a, 12b) is desired, then all the output values p, q can be normalized by multiplication by the factor 1 / √2.

The second transformation (12a, 12b) connected downstream of the first transformation, which is, for example, an MDCT, respectively engages over the two adjacent bands from which the real part p _{k, m} and the imaginary part q _{k, m are formed} for a frequency index k. In addition, as represented by the functions h _L and h _H , temporally successive real-valued spectral coefficients are taken into account in the combination, ie the summation or subtraction.

Since at the in Fig. 4 In the exemplary embodiment shown, the downstream transformation 12a, 12b does not include any degrees of freedom for optimizing the overall system in terms of adjustable weighting factors contained in the functions h _L and h _H , it is preferable to optimize the overall system by the window function of the first transformation, for example the MDCT manipulate, ie in To change comparison to a given known window function. In this case one obtains a degree of freedom N / 2 at a frequency resolution of N subbands and a window length of L = 2 N values.

• für k gerade: $${\mathrm{p}}_{\mathrm{k}\mathrm{,}\mathrm{m}}\mathrm{=}{\mathrm{u}}_{\mathrm{k}\mathrm{,}\mathrm{m}}+{\mathrm{u}}_{\mathrm{k}\mathrm{,}\mathrm{m}\mathrm{-}\mathrm{1}}$$
  
  $${\mathrm{q}}_{\mathrm{k}\mathrm{,}\mathrm{m}}\mathrm{=}{\mathrm{u}}_{\mathrm{k}-1\mathrm{,}\mathrm{m}}+{\mathrm{u}}_{\mathrm{k}-1\mathrm{,}\mathrm{m}\mathrm{-}\mathrm{1}}$$
  
• für k+1: $${\mathrm{p}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{,}\mathrm{m}}\mathrm{=}{\mathrm{u}}_{\mathrm{k}+1\mathrm{,}\mathrm{m}}\mathrm{-}{\mathrm{u}}_{\mathrm{k}+1\mathrm{,}\mathrm{m}\mathrm{-}\mathrm{1}}$$
  
  $${\mathrm{q}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{,}\mathrm{m}}\mathrm{=}{\mathrm{u}}_{\mathrm{k}\mathrm{,}\mathrm{m}}\mathrm{-}{\mathrm{u}}_{\mathrm{k}\mathrm{,}\mathrm{m}\mathrm{-}\mathrm{1}}$$
  

In summary, the in Fig. 4 illustrated transformation rule T _{2 as} follows:

• for k straight: $${\mathrm{p}}_{\mathrm{k}\mathrm{.}\mathrm{m}}\mathrm{=}{\mathrm{u}}_{\mathrm{k}\mathrm{.}\mathrm{m}}+{\mathrm{u}}_{\mathrm{k}\mathrm{.}\mathrm{m}\mathrm{-}\mathrm{1}}$$
  
  $${\mathrm{q}}_{\mathrm{k}\mathrm{.}\mathrm{m}}\mathrm{=}{\mathrm{u}}_{\mathrm{k}-1\mathrm{.}\mathrm{m}}+{\mathrm{u}}_{\mathrm{k}-1\mathrm{.}\mathrm{m}\mathrm{-}\mathrm{1}}$$
  
• for k + 1: $${\mathrm{p}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{m}}\mathrm{=}{\mathrm{u}}_{\mathrm{k}+1\mathrm{.}\mathrm{m}}\mathrm{-}{\mathrm{u}}_{\mathrm{k}+1\mathrm{.}\mathrm{m}\mathrm{-}\mathrm{1}}$$
  
  $${\mathrm{q}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{m}}\mathrm{=}{\mathrm{u}}_{\mathrm{k}\mathrm{.}\mathrm{m}}\mathrm{-}{\mathrm{u}}_{\mathrm{k}\mathrm{.}\mathrm{m}\mathrm{-}\mathrm{1}}$$
  

To undo the transformation T ₂ , as for Fig. 4 by way of example in the equations (1) to (4) is an inverse to the transform rule T ₂ T ₂ transformation rule used ^-1. If equations (1) to (4) are considered, it turns out that the real spectral components u _{k, m-1} and u _{k, m} from the real part p _{k, m} and the imaginary part q _{k + 1, m} from the Equations (1) and (4) can be calculated by solving two equations (1) and (4) for two unknowns according to the sought real spectral _coefficients u _{k, m-1} and u _{k, m} . By using this inverse combination rule T ₂ ^-1 , knowing the sequence of blocks of complex approximated spectral coefficients, it is possible to calculate back to the sequence of real spectral coefficients by performing the inverse combination rule.

• für den Realteil p: $${\mathrm{h}}_{\mathrm{R}}\left(\mathrm{m}\right)\mathrm{=}\left\{0,1,0\right\}\mathrm{,}$$
  
• für den Imaginärteil q: $${\mathrm{h}}_{\mathrm{A}}\left(\mathrm{m}\right)\mathrm{=}\left\{\mathrm{a}\mathrm{,}\mathrm{-}\mathrm{b}\mathrm{,}\mathrm{a}\right\}\mathrm{,}{\mathrm{h}}_{\mathrm{B}}\left(\mathrm{m}\right)\mathrm{=}\left\{\mathrm{c}\mathrm{,}\mathrm{0}\mathrm{,}\mathrm{-}\mathrm{c}\right\}\mathrm{,}{\mathrm{h}}_{\mathrm{C}}\left(\mathrm{m}\right)\mathrm{=}\left\{\mathrm{a},\mathrm{b},\mathrm{a}\right\}$$
  

The following is based on Fig. 5 an alternative embodiment is described in which no critical sampling is provided. Here, the output value u _{k, m of} the m-th MDCT operation with the frequency index k is used directly to form the real part. The associated imaginary part is calculated as the weighted sum of the MDCT output values _{uk-1, m-1} , _{uk-1, m} , _{uk-1, m + 1} , _{uk, m-1} in the time-frequency plane , u _{k, m + 1} , u _{k + 1, m-1} , u _{k + 1, m} and u _{k + 1, m + 1} calculated. A possible combination of the corresponding filters according to Fig. 5 (in the example for k odd) is as follows:

• for the real part p: $${\mathrm{H}}_{\mathrm{R}}\left(\mathrm{m}\right)\mathrm{=}\left\{0,1,0\right\}\mathrm{.}$$
  
• for the imaginary part q: $${\mathrm{H}}_{\mathrm{A}}\left(\mathrm{m}\right)\mathrm{=}\left\{\mathrm{a}\mathrm{.}\mathrm{-}\mathrm{b}\mathrm{.}\mathrm{a}\right\}\mathrm{.}{\mathrm{H}}_{\mathrm{B}}\left(\mathrm{m}\right)\mathrm{=}\left\{\mathrm{c}\mathrm{.}\mathrm{0}\mathrm{.}\mathrm{-}\mathrm{c}\right\}\mathrm{.}{\mathrm{H}}_{\mathrm{C}}\left(\mathrm{m}\right)\mathrm{=}\left\{\mathrm{a},\mathrm{b},\mathrm{a}\right\}$$
  

In the above expression, the values of the coefficients a, b, and c can be used to optimize the overall system, again to achieve a desired frequency response of the overall arrangement, which, as has been stated, is desirable, for example positive frequencies a bandpass characteristic is available as a frequency response, while for negative frequencies the greatest possible attenuation is desired.

• für k ungerade: $${\mathrm{p}}_{\mathrm{k}\mathrm{,}\mathrm{m}}\mathrm{=}{\mathrm{u}}_{\mathrm{k}\mathrm{,}\mathrm{m}\mathrm{;}}$$
  
  $${\mathrm{q}}_{\mathrm{k}\mathrm{,}\mathrm{m}}\mathrm{=}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{-}\mathrm{1}\mathrm{,}\mathrm{m}\mathrm{+}\mathrm{1}}\mathrm{+}\left(\mathrm{-}\mathrm{b}\right)\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{-}\mathrm{1}\mathrm{,}\mathrm{m}}\mathrm{+}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{-}\mathrm{1}\mathrm{,}\mathrm{m}\mathrm{-}\mathrm{1}}\mathrm{+}\left(\mathrm{-}\mathrm{c}\right)\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{,}\mathrm{m}\mathrm{+}\mathrm{1}}\mathrm{+}\mathrm{c}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{,}\mathrm{m}\mathrm{-}\mathrm{1}}\mathrm{+}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{,}\mathrm{m}\mathrm{+}\mathrm{1}}\mathrm{+}\mathrm{b}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{,}\mathrm{m}}\mathrm{+}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{,}\mathrm{m}\mathrm{-}\mathrm{1}}\mathrm{;}$$
  

Expressed in terms of equations, the in Fig. 5 illustrated transformation rule T ₂ , which consists of the individual filters 50a, 50b, 50c, 50d and a summer 50e, as follows:

• odd for k: $${\mathrm{p}}_{\mathrm{k}\mathrm{.}\mathrm{m}}\mathrm{=}{\mathrm{u}}_{\mathrm{k}\mathrm{.}\mathrm{m}\mathrm{;}}$$
  
  $${\mathrm{q}}_{\mathrm{k}\mathrm{.}\mathrm{m}}\mathrm{=}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{-}\mathrm{1}\mathrm{.}\mathrm{m}\mathrm{+}\mathrm{1}}\mathrm{+}\left(\mathrm{-}\mathrm{b}\right)\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{-}\mathrm{1}\mathrm{.}\mathrm{m}}\mathrm{+}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{-}\mathrm{1}\mathrm{.}\mathrm{m}\mathrm{-}\mathrm{1}}\mathrm{+}\left(\mathrm{-}\mathrm{c}\right)\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{.}\mathrm{m}\mathrm{+}\mathrm{1}}\mathrm{+}\mathrm{c}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{.}\mathrm{m}\mathrm{-}\mathrm{1}}\mathrm{+}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{m}\mathrm{+}\mathrm{1}}\mathrm{+}\mathrm{b}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{m}}\mathrm{+}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{m}\mathrm{-}\mathrm{1}}\mathrm{;}$$
  

For the calculation of qk _{, m} , weighting factors a, b, c are used to weight all the real spectral _coefficients adjacent to the real spectral _coefficient u _{k, m} in the time-frequency plane more or less, as shown in equation (6) ,

It should be noted that for even k, the same equations (4) to (6) can be used. The weighting factors in this case preferably have the same amounts but partly different signs.

To reverse the in Fig. 5 For the determination of u _{k, m,} only one trivial operation is to be performed since this value results directly from equation (5). After the in Fig. 5 shown system is a non-critically sampled system, the real and imaginary parts are presented redundant information. This manifests itself in the inverted transformation instruction T ₂ ^-1 in that the real spectral coefficients can be calculated from the real parts alone. Therefore equation (6) does not have to be used for the evaluation. The transformation rule inverse transformation rule is thus in the in Fig. 5 identical embodiment and given by equation (5).
It should be noted that in the case described above, where the complex approximated spectral representation is needed, for example, in a psychoacoustic model, the quantizer step size in an encoder set back, a recalculation of the complex approximated spectral representation to the real spectral representation is no longer needed. Alternatively, however, there may be cases in which a corresponding inversion is required, in which case the underlying real spectral representation must be calculated from the complex approximated spectral representation again.

Depending on the circumstances, the methods according to the invention can be implemented in hardware or in software. The implementation may be on a digital storage medium, in particular a floppy disk or CD with electronically readable control signals, which interact with a programmable computer system such that the corresponding method is executed. In general, the invention thus also consists in a computer program product with program code stored on a machine-readable carrier for carrying out one or more of the inventive methods when the computer program product runs on a computer. In other words, the invention is also a computer program having a program code for performing one or more of the methods when the computer program runs on a computer.

Claims (23)

1. Device for generating a complex spectral representation of a discrete-time signal, comprising:

   means (10) for generating a block-wise real-valued spectral representation of the discrete-time signal, the spectral representation comprising temporally successive blocks, each block comprising a set of real spectral coefficients; and

   means (12) for post-processing the block-wise real-valued spectral representation to obtain a block-wise complex approximated spectral representation comprising successive blocks, each block comprising a set of complex approximated spectral coefficients, wherein a complex approximated spectral coefficient can be represented by a first partial spectral coefficient and a second partial spectral coefficient, wherein at least one of the first and the second partial spectral coefficients is to be determined by combining at least two temporally and/or frequency-adjacent real spectral coefficients.
2. Device according to claim 1,
   wherein the first partial spectral coefficient is a real part of the complex approximated spectral coefficient and the second partial spectral coefficient is an imaginary part of the complex approximated spectral coefficient.
3. Device according to claim 1 or 2,
   wherein the combination is a linear combination.
4. Device according to one of the preceding claims,
   wherein the means (12) for post-processing is formed to combine a real spectral coefficient of the frequency and a real spectral coefficient of an adjacent higher or lower frequency for determining a complex spectral coefficient.
5. Device according to one of the preceding claims,
   wherein the means (12) for post-processing is formed to combine a real spectral coefficient in a current block and a real spectral coefficient in a temporally preceding block or a temporally subsequent block for determining a complex spectral coefficient of a certain frequency.
6. Device according to one of the preceding claims, formed to operate, in a critical sampling, such that a real spectral value is generated for each discrete-time sample value by the means (10) for generating a block-wise real spectral representation and that a complex spectral coefficient is generated for two real spectral coefficients.
7. Device according to claim 6,
   wherein the means (12) for post-processing is formed to only be active for every second block of real-valued spectral coefficients to reduce a sampling rate or to be active for every second real spectral coefficient to reduce the sampling rate or to only be active for every second block or for every second real spectral coefficient alternatingly to reduce the sampling rate.
8. Device according to one of the preceding claims,
   wherein the means (12) for post-processing is formed to sum two real spectral coefficients having the same frequency index from a current block and from a temporally preceding block for the first partial spectral coefficient having an even frequency index, and to sum two real spectral coefficients having a frequency index lower by 1 from the current block and the temporally preceding block for the second partial spectral coefficient having the even frequency index.
9. Device according to one of the preceding claims,
   wherein the means (12) for post-processing is formed to form a difference of two real spectral coefficients having an odd frequency index from a current block and from a temporally preceding block for the first partial spectral coefficient having the odd frequency index, and to form a difference of two real spectral coefficients having a frequency index lower by 1 from the current block and the temporally preceding block for the second partial spectral coefficient.
10. Device according to one of the preceding claims,
    wherein the means (12) for post-processing is formed to normalize the first and second partial spectral coefficients each by a factor of 1/√2.
11. Device according to one of claims 1 to 7,
    wherein the means (12) for post-processing is formed to use a real spectral coefficient having a frequency index as the first partial spectral coefficient for the frequency index, and to use a weighted sum of the real spectral coefficients having adjacent frequency indices of a current block, from one or several preceding blocks or from one or several subsequent blocks for calculating the second partial spectral coefficient, at least two weighting factors being unequal to 0.
12. Device according to claim 11,
    wherein the means (12) for post-processing is formed not to use the real spectral coefficient forming the first partial spectral coefficient for calculating the second partial spectral coefficient.
13. Device according to claim 11 or 12,
    wherein the means for post-processing is formed to apply the following rule for calculating the second spectral coefficient: $${\mathrm{q}}_{\mathrm{k}\mathrm{,}\mathrm{m}}\mathrm{=}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{-}\mathrm{1}\mathrm{,}\mathrm{m}\mathrm{+}\mathrm{1}}\mathrm{+}\left(\mathrm{-}\mathrm{b}\right)\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{-}\mathrm{1}\mathrm{,}\mathrm{m}}\mathrm{+}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{-}\mathrm{1}\mathrm{,}\mathrm{m}\mathrm{-}\mathrm{1}}\mathrm{+}\left(\mathrm{-}\mathrm{c}\right)\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{,}\mathrm{m}\mathrm{+}\mathrm{1}}\mathrm{+}\mathrm{c}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{,}\mathrm{m}\mathrm{-}\mathrm{1}}\mathrm{+}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{,}\mathrm{m}\mathrm{+}\mathrm{1}}\mathrm{+}\mathrm{b}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{,}\mathrm{m}}\mathrm{+}\mathrm{a}\cdot {\mathrm{u}}_{\mathrm{k}\mathrm{+}\mathrm{1}\mathrm{,}\mathrm{m}\mathrm{-}\mathrm{1}}\mathrm{;}$$

    

    
    a, b, c being positive or negative weighting factors, k-1 being a current frequency index k minus 1, m-1 being a current block index m minus 1, k+1 being a current frequency index k plus 1, m+1 being a current block index m plus 1, and u_k-1,m-1 being a real spectral coefficient of a temporally preceding block having a frequency index k-1, u_k-1,m being a real spectral coefficient of a current block having a frequency index k-1, u_k-1,m+1 being a real spectral coefficient of a temporally subsequent block having a frequency index k-1, u_k,m-1 being a real spectral coefficient having the frequency index of k from the temporally preceding block, u_k,m+1 being a real spectral coefficient having the frequency index for the temporally subsequent block, u_k+1,m-1 being a real spectral coefficient having the frequency index k+1 from the temporally preceding block, u_k+1,m being a real spectral coefficient for the frequency index k+1 from the current block, and u_k+1,m+1 being a real spectral coefficient having the frequency index k+1 from the temporally subsequent block.
14. Device according to claim 13,
    wherein the signs from one or several weighting factors are different for even and odd frequency indices k.
15. Device according to claim 13 or 14,
    wherein the weighting factors are adjusted to provide a desired frequency response for the device for generating a complex spectral representation.
16. Device according to one of the preceding claims,
    wherein the means (10) for generating is formed to execute a modified discrete cosine transform.
17. Device according to claim 16,
    wherein the means (10) for generating is formed to execute a modified discrete cosine transform with a window overlapping of 50%.
18. Method for generating a complex spectral representation of a discrete-time signal, comprising the steps of:

    generating (10) a block-wise real-valued spectral representation of the discrete-time signal, the spectral representation comprising temporally successive blocks, each block comprising a set of real spectral coefficients; and

    post-processing (12) the block-wise real-valued spectral representation to obtain a block-wise complex approximated spectral representation comprising successive blocks, each block comprising a set of complex approximated spectral coefficients, wherein a complex approximated spectral coefficient can be represented by a first partial spectral coefficient and a second partial spectral coefficient, wherein at least one of the first and second partial spectral coefficients is to be determined by combining at least two temporally and/or frequency-adjacent real spectral coefficients.
19. Device for coding a discrete-time signal, comprising:

    means for generating a block-wise real-valued spectral representation of the discrete-time signal, the spectral representation comprising temporally successive blocks, each block comprising a set of real spectral coefficients;

    a psycho-acoustic module for calculating a psycho-acoustic masking threshold depending on the discrete-time signal;

    means for quantizing a block of real-valued spectral coefficients using the psycho-acoustic masking threshold,

    wherein the psycho-acoustic module comprises means (12) for post-processing the block-wise real spectral representation to obtain a block-wise complex approximated spectral representation comprising successive blocks, each block comprising a set of complex approximated spectral coefficients, wherein a complex approximated spectral coefficient can be represented by a first partial spectral coefficient and a second partial spectral coefficient, wherein at least one of the first and second partial spectral coefficients is to be determined by combining at least two temporally and/or frequency-adjacent real spectral coefficients.
20. Method for coding a discrete-time signal, comprising the steps of:

    generating a block-wise real-valued spectral representation of the discrete-time signal, the spectral representation comprising temporally successive blocks, each block comprising a set of real spectral coefficients;

    calculating a psycho-acoustic masking threshold depending on the discrete-time signal;

    quantizing a block of real-valued spectral coefficients using the psycho-acoustic masking threshold,

    wherein a step of post-processing (12) the block-wise real spectral representation is performed in the step of calculating to obtain a block-wise complex approximated spectral representation comprising successive blocks, each comprising a set of complex approximated spectral coefficients, wherein a complex approximated spectral coefficient can be represented by a first partial spectral coefficient and a second partial spectral coefficient, wherein at least one of the first and second partial spectral coefficients is to be determined by combining at least two temporally and/or frequency-adjacent real spectral coefficients.
21. Device for generating a real spectral representation from a complex approximated spectral representation, the real spectral representation to be determined comprising temporally successive blocks, each block comprising a set of real spectral coefficients, the complex approximated spectral representation comprising temporally successive blocks, each block comprising a set of complex approximated spectral coefficients, wherein a complex approximated spectral coefficient can be represented by a first partial spectral coefficient and a second partial spectral coefficient, the complex approximated spectral coefficients having been calculated by a transform rule from the real spectral coefficients, the transform rule including a combination of at least two temporally and/or frequency-adjacent real spectral coefficients to calculate at least one of the first and second partial spectral coefficients of a complex approximated spectral coefficient, comprising:

    means for performing a combining rule inverse to the transform rule (T₂) to calculate the real spectral coefficients from the complex approximated spectral coefficients.
22. Method for generating a real spectral representation of a complex approximated spectral representation, the real spectral representation to be determined comprising temporally successive blocks, each block comprising a set of real spectral coefficients, the complex approximated spectral representation comprising temporally successive blocks, each block comprising a set of complex approximated spectral coefficients, wherein a complex approximated spectral coefficient can be represented by a first partial spectral coefficient and a second partial spectral coefficient, the complex approximated spectral coefficients having been calculated by a transform rule from the real spectral coefficients, the transform rule including a combination of at least two temporally and/or frequency-adjacent real spectral coefficients to calculate at least one of the first and second partial spectral coefficients of a complex approximated spectral coefficient, comprising the step of:

    performing a combination rule inverse to the transform rule (T₂) to calculate the real spectral coefficients from the complex approximated spectral coefficients.
23. Computer program product having a program code for performing the method according to claim 18, claim 20 or claim 22, when the program runs on a computer.

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