AU2015221516A1

AU2015221516A1 - Improved Harmonic Transposition

Info

Publication number: AU2015221516A1
Application number: AU2015221516A
Authority: AU
Inventors: Per Ekstrand; Lars Falck Villemoes
Original assignee: Dolby International AB
Current assignee: Dolby International AB
Priority date: 2009-01-28
Filing date: 2015-09-03
Publication date: 2015-09-24
Anticipated expiration: 2030-03-12
Also published as: AU2017258839B2; AU2021204779A1; AU2021204779B2; AU2020201239A1; AU2020201239B2; AU2015221516B2; AU2017258839A1

Abstract

The invention is directed to a system for transposing an input audio signal by a transposition factor T. The system comprises means for extracting a frame of L time-domain samples of the input signal using an analysis window having the function v(n) = sin (n+ 0.5) 0 < n < L; means for (L transforming the L time-domain samples into M complex frequency-domain coefficients; a nonlinear processing unit for altering a phase of the complex frequency-domain coefficients using the transposition factor T; means for transforming the altered frequency-domain coefficients into M altered time-domain samples; and a means for generating a frame of L time-domain output samples from the M altered time-domain samples using a synthesis window; wherein M=F*L, with F being greater or equal to (T+1)/2.

Description

- 1 Improved Harmonic Transposition TECHNICAL FIELD 5 The present invention relates to transposing signals in frequency and/or stretch ing/compressing a signal in time and in particular to coding of audio signals. In other words, the present invention relates to time-scale and/or frequency-scale modification. More particularly, the present invention relates to high frequency reconstruction (HFR) 10 methods including a frequency domain harmonic transposer. This application is a divisional of Australian application no. 2013211560 and the con tents of which are incorporated herein by reference. 15 BACKGROUND OF THE INVENTION HFR technologies, such as the Spectral Band Replication (SBR) technology, allow to significantly improve the coding efficiency of traditional perceptual audio codecs. In combination with MPEG-4 Advanced Audio Coding (AAC) it forms a very efficient 20 audio codec, which is already in use within the XM Satellite Radio system and Digital Radio Mondiale, and also standardized within 3GPP, DVD Forum and others. The combination of AAC and SBR is called aacPlus. It is part of the MPEG-4 standard where it is referred to as the High Efficiency AAC Profile (HE-AAC). In general, HFR technology can be combined with any perceptual audio codec in a back and forward 25 compatible way, thus offering the possibility to upgrade already established broadcast ing systems like the MPEG Layer-2 used in the Eureka DAB system. HFR transposition methods can also be combined with speech codecs to allow wide band speech at ultra low bit rates. 30 The basic idea behind HRF is the observation that usually a strong correlation between the characteristics of the high frequency range of a signal and the characteristics of the low frequency range of the same signal is present. Thus, a good approximation for the -2 representation of the original input high frequency range of a signal can be achieved by a signal transposition from the low frequency range to the high frequency range. This concept of transposition was established in WO 98/57436 which is incorporated by 5 reference, as a method to recreate a high frequency band from a lower frequency band of an audio signal. A substantial saving in bit-rate can be obtained by using this concept in audio coding and/or speech coding. In the following, reference will be made to audio coding, but it should be noted that the described methods and systems are equally appli cable to speech coding and in unified speech and audio coding (USAC). 10 In a HFR based audio coding system, a low bandwidth signal is presented to a core waveform coder for encoding, and higher frequencies are regenerated at the decoder side using transposition of the low bandwidth signal and additional side information, which is typically encoded at very low bit-rates and which describes the target spectral 15 shape. For low bit-rates, where the bandwidth of the core coded signal is narrow, it be comes increasingly important to reproduce or synthesize a high band, i.e. the high fre quency range of the audio signal, with perceptually pleasant characteristics. In prior art there are several methods for high frequency reconstruction using, e.g. har 20 monic transposition, or time-stretching. One method is based on phase vocoders operat ing under the principle of performing a frequency analysis with a sufficiently high fre quency resolution. A signal modification is performed in the frequency domain prior to re-synthesising the signal. The signal modification may be a time-stretch or transposi tion operation. 25 One of the underlying problems that exist with these methods are the opposing con straints of an intended high frequency resolution in order to get a high quality transposition for stationary sounds, and the time response of the system for transient or percussive sounds. In other words, while the use of a high frequency resolution is bene 30 ficial for the transposition of stationary signals, such high frequency resolution typically requires large window sizes which are detrimental when dealing with transient portions of a signal. One approach to deal with this problem may be to adaptively change the -3 windows of the transposer, e.g. by using window-switching, as a function of input sig nal characteristics. Typically long windows will be used for stationary portions of a sig nal, in order to achieve high frequency resolution, while short windows will be used for transient portions of the signal, in order to implement a good transient response, i.e. a 5 good temporal resolution, of the transposer. However, this approach has the drawback that signal analysis measures such as transient detection or the like have to be incorpo rated into the transposition system. Such signal analysis measures often involve a deci sion step, e.g. a decision on the presence of a transient, which triggers a switching of signal processing. Furthermore, such measures typically affect the reliability of the sys 10 tem and they may introduce signal artifacts when switching the signal processing, e.g. when switching between window sizes. Embodiments of the present invention solves the aforementioned problems regarding the transient performance of harmonic transposition without the need for window 15 switching. Furthermore, improved harmonic transposition is achieved at a low addition al complexity. SUMMARY OF THE INVENTION 20 Embodiments of the present invention relates to the problem of improved transient per formance for harmonic transposition, as well as assorted improvements to known meth ods for harmonic transposition. Furthermore, the present invention outlines how addi tional complexity may be kept at a minimum while retaining the proposed improve 25 ments. Among others, embodiments of the present invention may comprise at least one of the following aspects: - Oversampling in frequency by a factor being a function of the transposition factor of 30 the operation point of the transposer; - Appropriate choice of the combination of analysis and synthesis windows; and -4 - Ensuring time-alignment of different transposed signals for the cases where such signals are combined. According to one aspect of the invention, there is provided a system for transposing an 5 input audio signal by a transposition factor T, the system comprising: means for extracting a frame of L time-domain samples of the input signal using an analysis window having the function v(n)= sin i (n + 0.5$ ,0 n < L; (L means for transforming the L time-domain samples into M complex frequency domain coefficients; 10 a nonlinear processing unit for altering a phase of the complex frequency-domain coefficients using the transposition factor T; means for transforming the altered frequency-domain coefficients into M altered time-domain samples; and a means for generating a frame of L time-domain output samples from the M al 15 tered time-domain samples using a synthesis window; wherein M=F*L, with F being greater or equal to (T+1)/2. The altering of the phase may comprise multiplying the phase by the transposition fac tor T. The analysis window may have a length L with zero padding by additional (F 20 1)*L zeros. The means for transforming the altered frequency-domain coefficients may comprise an analysis transformation unit of size M for transforming the L time-domain samples into M complex frequency-domain coefficients. 25 The system may further comprise: an analysis stride unit, shifting the analysis window by an analysis stride along the input signal, thereby generating successive frames of the input signal; a synthesis stride unit, shifting successive frames of L time-domain output sam 30 ples by a synthesis stride; and -5 an overlap-add unit, overlapping and adding the successive shifted frames of L time-domain output samples, thereby generating an output signal. The system may further comprise a contraction unit, increasing the sampling rate of the 5 output signal by the transposition factor T; thereby yielding a transposed output signal. The synthesis stride may be T times the analysis stride. The system may further comprise: a second nonlinear processing unit for altering a phase of the complex frequency 10 domain coefficients using a second transposition factor T2, thereby yielding a frame of L second time-domain output samples; and a second synthesis stride unit, shifting successive frames of L second time-domain output samples by a second synthesis stride, thereby generating a second output signal in the overlap-add unit. 15 The system may further comprise a second contraction unit, using the second transposition factor T2, thereby yielding a second transposed output signal; and a combining unit, merging the transposed output signal and the second transposed 20 output signal. A system for generating a transposed output signal from an input signal using a transpo sition factor T is described. The transposed output signal may be a time-stretched and/or frequency-shifted version of the input signal. Relative to the input signal, the transposed 25 output signal may be stretched in time by the transposition factor T. Alternatively, the frequency components of the transposed output signal may be shifted upwards by the transposition factor T. The system may comprise an analysis window of length L which extracts L samples of 30 the input signal. Typically, the L samples of the input signals are samples of the input signal, e.g. an audio signal, in the time domain. The extracted L samples are referred to as a frame of the input signal. The system comprises further an analysis transformation -6 unit of order M = F*L transforming the L time-domain samples into M complex coeffi cients with F being a frequency oversampling factor. The M complex coefficients are typically coefficients in the frequency domain. The analysis transformation may be a Fourier transform, a Fast Fourier Transform, a Discrete Fourier Transform, a Wavelet 5 Transform or an analysis stage of a (possibly modulated) filter bank. The oversampling factor F is based on or is a function of the transposition factor T. The oversampling operation may also be referred to as zero padding of the analysis window by additional (F-1)*L zeros. It may also be viewed as choosing a size of an 10 analysis transformation M which is larger than the size of the analysis window by a fac tor F. The system may also comprise a nonlinear processing unit altering the phase of the complex coefficients by using the transposition factor T. The altering of the phase may 15 comprise multiplying the phase of the complex coefficients by the transposition factor T. In addition, the system may comprise a synthesis transformation unit of order M transforming the altered coefficients into M altered samples and a synthesis window of length L for generating the output signal. The synthesis transform may be an inverse Fourier Transform, an inverse Fast Fourier Transform, an inverse Discrete Fourier 20 Transform, an inverse Wavelet Transform, or a synthesis stage of a (possibly) modulat ed filter bank. Typically, the analysis transform and the synthesis transform are related to each other, e.g. in order to achieve perfect reconstruction of an input signal when the transposition factor T = 1. 25 The oversampling factor F may be proportional to the transposition factor T. In particu lar, the oversampling factor F may be greater or equal to (T+1)/2. This selection of the oversampling factor F ensures that undesired signal artifacts, e.g. pre- and post-echoes, which may be incurred by the transposition are rejected by the synthesis window. 30 It should be noted that in more general terms, the length of the analysis window may be La and the length of the synthesis window may be Ls. Also in such cases, it may be ben eficial to select the order of the transformation unit M based on the transposition order -7 T, i.e. as a function of the transposition order T. Furthermore, it may be beneficial to select M to be greater than the average length of the analysis window and the synthesis window, i.e. greater than (La+Ls)/ 2 . In an embodiment, the difference between the order of the transformation unit M and the average window length is proportional to (T-1). In 5 a further embodiment, M is selected to be greater or equal to (TLa+Ls)/2. It should be noted that the case where the length of the analysis window and the synthesis window is equal, i.e. La=Ls=L, is a special case of the above generic case. For the generic case, the oversampling factor F may be 10 F 1+(T-1) a L. + L The system may further comprise an analysis stride unit shifting the analysis window by an analysis stride of Sa samples along the input signal. As a result of the analysis stride unit, a succession of frames of the input signal is generated. In addition, the system may 15 comprise a synthesis stride unit shifting the synthesis window and/or successive frames of the output signal by a synthesis stride of S, samples. As a result, a succession of shifted frames of the output signal is generated which may be overlapped and added in an overlap-add unit. 20 In other words, the analysis window may extract or isolate L or more generally La sam ples of the input signal, e.g. by multiplying a set of L samples of the input signal with non-zero window coefficients. Such a set of L samples may be referred to as an input signal frame or as a frame of the input signal. The analysis stride unit shifts the analysis window along the input signal and thereby selects a different frame of the input signal, 25 i.e. it generates a sequence of frames of the input signal. The sample distance between successive frames is given by the analysis stride. In a similar manner, the synthesis stride unit shifts the synthesis window and/or the frames of the output signal, i.e. it gen erates a sequence of shifted frames of the output signal. The sample distance between successive frames of the output signal is given by the synthesis stride. The output signal 30 may be determined by overlapping the sequence of frames of the output signal and by -8 adding sample values which coincide in time. The synthesis stride may be T times the analysis stride. In such cases, the output signal corresponds to the input signal, time-stretched by the transposition factor T. In other 5 words, by selecting the synthesis stride to be T times greater than the analysis stride, a time shift or time stretch of the output signal with regards to the input signal may be obtained. This time shift is of order T. In other words, the above mentioned system may be described as follows: Using an 10 analysis window unit, an analysis transformation unit and an analysis stride unit with an analysis stride Sa, a suite or sequence of sets of M complex coefficients may be deter mined from an input signal. The analysis stride defines the number of samples that the analysis window is moved forward along the input signal. As the elapsed time between two successive samples is given by the sampling rate, the analysis stride also defines the 15 elapsed time between two frames of the input signal. By consequences, also the elapsed time between two successive sets of M complex coefficients is given by the analysis stride Sa. After passing the nonlinear processing unit where the phase of the complex coefficients 20 may be altered, e.g. by multiplying it with the transposition factor T, the suite or se quence of sets of M complex coefficients may be re-converted into the time-domain. Each set of M altered complex coefficients may be transformed into M altered samples using the synthesis transformation unit. In a following overlap-add operation involving the synthesis window unit and the synthesis stride unit with a synthesis stride S, the 25 suite of sets of M altered samples may be overlapped and added to form the output sig nal. In this overlap-add operation, successive sets of M altered samples may be shifted by S, samples with respect to one another, before they may be multiplied with the syn thesis window and subsequently added to yield the output signal. Consequently, if the synthesis stride S, is T times the analysis stride Sa, the signal may be time stretched by a 30 factor T.

-9 The synthesis window may be derived from the analysis window and the synthesis stride. In particular, the synthesis window may be given by the formula: v, (n) = v. (n) (v,(n - k -At)) 5 with v, (n) being the synthesis window, v, (n) being the analysis window, and At being the synthesis stride S. The analysis and/or synthesis window may be one of a Gaussian window, a cosine window, a Hamming window, a Hann window, a rectangular window, a Bartlett windows, a Blackman windows, a window having the function 10 v(n)= sin j (n + 0.5) ,0 n < L, wherein in the case of different lengths of the analy SL sis window and the synthesis window, L may be La or Ls, respectively. The system may comprise a contraction unit performing e.g. a rate conversion of the output signal by the transposition order T, thereby yielding a transposed output signal. 15 By selecting the synthesis stride to be T times the analysis stride, a time-stretched out put signal may be obtained as outlined above. If the sampling rate of the time-stretched signal is increased by a factor T or if the time-stretched signal is down-sampled by a factor T, a transposed output signal may be generated that corresponds to the input sig nal, frequency-shifted by the transposition factor T. The downsampling operation may 20 comprise the step of selecting only a subset of samples of the output signal. Typically, only every T sample of the output signal is retained. Alternatively, the sampling rate may be increased by a factor T, i.e. the sampling rate is interpreted as being T times higher. In other words, re-sampling or sampling rate conversion means that the sam pling rate is changed, either to a higher or a lower value. Downsampling means rate 25 conversion to a lower value. The system may generate a second output signal from the input signal. The system may comprise a second nonlinear processing unit altering the phase of the complex coeffi cients by using a second transposition factor T 2 and a second synthesis stride unit shift- - 10 ing the synthesis window and/or the frames of the second output signal by a second syn thesis stride. Altering of the phase may comprise multiplying the phase by a factor T 2 . By altering the phase of the complex coefficients using the second transposition factor and by transforming the second altered coefficients into M second altered samples and 5 by applying the synthesis window, frames of the second output signal may be generated from a frame of the input signal. By applying the second synthesis stride to the se quence of frames of the second output signal, the second output signal may be generated in the overlap-add unit. 10 The second output signal may be contracted in a second contracting unit performing e.g. a rate conversion of the second output signal by the second transposition order T 2 . This yields a second transposed output signal. In summary, a first transposed output signal can be generated using the first transposition factor T and a second transposed output signal can be generated using the second transposition factor T 2 . These two transposed 15 output signals may then be merged in a combining unit to yield the overall transposed output signal. The merging operation may comprise adding of the two transposed output signals. Such generation and combining of a plurality of transposed output signals may be beneficial to obtain good approximations of the high frequency signal component which is to be synthesized. It should be noted that any number of transposed output sig 20 nals may be generated using a plurality of transposition orders. This plurality of trans posed outputs signals may then be merged, e.g. added, in a combining unit to yield an overall transposed output signal. It may be beneficial that the combining unit weights the first and second transposed 25 output signals prior to merging. The weighting may be performed such that the energy or the energy per bandwidth of the first and second transposed output signals corre sponds to the energy or energy per bandwidth of the input signal, respectively. The system may comprise an alignment unit which applies a time offset to the first and 30 second transposed output signals prior to entering the combining unit. Such time offset may comprise the shifting of the two transposed output signals with respect to one an- - 11 other in the time domain. The time offset may be a function of the transposition order and/or the length of the windows. In particular, the time offset may be determined as (T -2)L 4 5 The above described transposition system may be embedded into a system for decoding a received multimedia signal comprising an audio signal. The decoding system may comprise a transposition unit which corresponds to the system outlined above, wherein the input signal typically is a low frequency component of the audio signal and the out 10 put signal is a high frequency component of the audio signal. In other words, the input signal typically is a low pass signal with a certain bandwidth and the output signal is a bandpass signal of typically a higher bandwidth. Furthermore, it may comprise a core decoder for decoding the low frequency component of the audio signal from the re ceived bitstream. Such core decoder may be based on a coding scheme such as Dolby E, 15 Dolby Digital or AAC. In particular, such decoding system may be a set-top box for decoding a received multimedia signal comprising an audio signal and other signals such as video. According to another aspect of the invention, there is provided a method for transposing 20 an input audio signal by a transposition factor T, the method comprising: extracting a frame of L time-domain samples of the input signal using an analysis window having the function v(n)= sin ' (n + 0.5) ,0 n < L; SL transforming the L time-domain samples into M complex frequency-domain coef ficients; 25 altering a phase of the complex frequency-domain coefficients using the transpo sition factor T; transforming the altered frequency-domain coefficients into M altered time domain samples; and - 12 generating a frame of L time-domain output samples from the M altered time domain samples using a synthesis window; wherein M=F*L, with F being greater or equal to (T+1)/2. 5 Transforming the L time-domain samples into M complex frequency-domain coeffi cients may be performing one of a Fourier Transform, a Fast Fourier Transform, a Dis crete Fourier Transform, a Wavelet Transform. The method may further comprise the steps of: 10 shifting the analysis window by an analysis stride along the input signal, thereby generating successive frames of the input signal; shifting successive frames of L time-domain output samples by a synthesis stride; and overlapping and adding the successive shifted frames of L time-domain output 15 samples, thereby generating an output signal. The method may further comprise the step of performing downsampling of the output signal by the transposition factor T while keeping the sampling rate unchanged, thereby yielding a transposed output signal. A z transform of the analysis window may have 20 dual zeros on the unit circle. There is also described herein, a method for transposing an input signal by a transposi tion factor T. The method corresponds to the system outlined above and may comprise any combination of the above mentioned aspects. It may comprise the steps of extract 25 ing samples of the input signal using an analysis window of length L, and of selecting an oversampling factor F as a function of the transposition factor T. It may further com prise the steps of transforming the L samples from the time domain into the frequency domain yielding F * L complex coefficients, and of altering the phase of the complex coefficients with the transposition factor T. In additional steps, the method may trans 30 form the F * L altered complex coefficients into the time domain yielding F * L altered samples, and it may generate the output signal using a synthesis window of length L. It - 13 should be noted that the method may also be adapted to general lengths of the analysis and synthesis window, i.e. to general La and Ls, at outlined above. The method may comprise the steps of shifting the analysis window by an analysis 5 stride of Sa samples along the input signal, and/or by shifting the synthesis window and/or the frames of the output signal by a synthesis stride of S, samples. By selecting the synthesis stride to be T times the analysis stride, the output signal may be time stretched with respect to the input signal by a factor T. When executing an additional step of performing a rate conversion of the output signal by the transposition order T, a 10 transposed output signal may be obtained. Such transposed output signal may comprise frequency components that are upshifted by a factor T with respect to the corresponding frequency components of the input signal. The method may further comprise steps for generating a second output signal. This may 15 be implemented by altering the phase of the complex coefficients by using a second transposition factor T 2 , by shifting the synthesis window and/or the frames of the sec ond output signal by a second synthesis stride a second output signal may be generated using the second transposition factor T 2 and the second synthesis stride. By performing a rate conversion of the second output signal by the second transposition order T 2 , a 20 second transposed output signal may be generated. Eventually, by merging the first and second transposed output signals a merged or overall transposed output signal including high frequency signal components generated by two or more transpositions with differ ent transposition factors may be obtained. 25 There is also described herein, a software program adapted for execution on a processor and for performing the method steps as previously described when carried out on a computing device. There is also described a storage medium comprising a software pro gram adapted for execution on a processor and for performing the method steps previ ously described when carried out on a computing device. Furthermore, there is de 30 scribed a computer program product comprising executable instructions for performing the method when executed on a computer.

- 14 Another method and system for transposing an input signal by a transposition factor T is described. This method and system may be used standalone or in combination with the methods and systems outlined above. Any of the features outlined in the present docu ment may be applied to this method / system and vice versa. 5 The method may comprise the step of extracting a frame of samples of the input signal using an analysis window of length L. Then, the frame of the input signal may be trans formed from the time domain into the frequency domain yielding M complex coeffi cients. The phase of the complex coefficients may be altered with the transposition fac 10 tor T and the M altered complex coefficients may be transformed into the time domain yielding M altered samples. Eventually, a frame of an output signal may be generated using a synthesis window of length L. The method and system may use an analysis window and a synthesis window which are different from each other. The analysis and the synthesis window may be different with regards to their shape, their length, the 15 number of coefficients defining the windows and/or the values of the coefficients defin ing the windows. By doing this, additional degrees of freedom in the selection of the analysis and synthesis windows may be obtained such that aliasing of the transposed output signal may be reduced or removed. 20 The analysis window and the synthesis window may be bi-orthogonal with respect to one another. The synthesis window vs(n) may be given by: v,(n) s(n(mod At)) with c being a constant, va(n) being the analysis window (311), At, being a timestride of the synthesis window and s(n) being given by: L/(At -1) 25 s~m= V(m+ Atsi) OmAt 25 i=4 , ( +m < At, The time stride of the synthesis window At, typically corresponds to the synthesis stride Ss.

- 15 The analysis window may be selected such that its z transform has dual zeros on the unit circle. Preferably, the z transform of the analysis window only has dual zeros on the unit circle. By way of example, the analysis window may be a squared sine window. In another example, the analysis window of length L may be determined by convolving 5 two sine windows of length L, yielding a squared sine window of length 2L- 1. In a fur ther step a zero is appended to the squared sine window, yielding a base window of length 2L. Eventually, the base window may be resampled using linear interpolation, thereby yielding an even symmetric window of length L as the analysis window. 10 The methods and systems described in the present document may be implemented as software, firmware and/or hardware. Certain components may e.g. be implemented as software running on a digital signal processor or microprocessor. Other component may e.g. be implemented as hardware and or as application specific integrated circuits. The signals encountered in the described methods and systems may be stored on media such 15 as random access memory or optical storage media. They may be transferred via net works, such as radio networks, satellite networks, wireless networks or wireline net works, e.g. the internet. Typical devices making use of the method and system described in the present document are set-top boxes or other customer premises equipment which decode audio signals. On the encoding side, the method and system may be used in 20 broadcasting stations, e.g. in video or TV head end systems. It should be noted that the embodiments and aspects of the invention described in this document may be arbitrarily combined. In particular, it should be noted that the aspects outlined for a system are also applicable to the corresponding method embraced by the 25 present invention. Furthermore, it should be noted that the disclosure of the invention also covers other claim combinations than the claim combinations which are explicitly given by the back references in the dependent claims, i.e., the claims and their technical features can be combined in any order and any formation. 30 - 16 BRIEF DESCRIPTION OF THE DRAWINGS The present invention will now be described by way of illustrative examples, not limit ing the scope or spirit of the invention, with reference to the accompanying drawings, in 5 which: Fig. 1 illustrates a Dirac at a particular position as it appears in the analysis and synthe sis windows of a harmonic transposer; Fig. 2 illustrates a Dirac at a different position as it appears in the analysis and synthesis 10 windows of a harmonic transposer; Fig. 3 illustrates a Dirac for the position of Fig. 2 as it will appear according to the pre sent invention; Fig. 4 illustrates the operation of an HFR enhanced audio decoder; Fig. 5 illustrates the operation of a harmonic transposer using several orders; 15 Fig. 6 illustrates the operation of a frequency domain (FD) harmonic transposer Fig. 7 shows a succession of analysis synthesis windows; Fig. 8 illustrates analysis and synthesis windows at different strides; Fig. 9 illustrates the effect of the re-sampling on the synthesis stride of windows; Figs. 10 and 11 illustrate embodiments of an encoder and a decoder, respectively, using 20 the enhanced harmonic transposition schemes outlined in the present document; and Fig. 12 illustrates an embodiment of a transposition unit shown in Figs. 10 and 11. DETAILED DESCRIPTION 25 The below-described embodiments are merely illustrative for the principles of the pre sent invention for Improved Harmonic Transposition. 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, therefore, to be limited only by the scope of the impending patent claims and not by the specific details presented by way of description 30 and explanation of the embodiments herein.

- 17 In the following, the principle of harmonic transposition in the frequency domain and the proposed improvements as taught by the present invention are outlined. A key com ponent of the harmonic transposition is time stretching by an integer transposition factor T which preserves the frequency of sinusoids. In other words, the harmonic transposi 5 tion is based on time stretching of the underlying signal by a factor T . The time stretch ing is performed such that frequencies of sinusoids which compose the input signal are maintained. Such time stretching may be performed using a phase vocoder. The phase vocoder is based on a frequency domain representation furnished by a windowed DFT filter bank with analysis window v, (n) and synthesis window v, (n) . Such analy 10 sis/synthesis transform is also referred to as short-time Fourier Transform (STFT). A short-time Fourier transform is performed on a time-domain input signal to obtain a succession of overlapped spectral frames. In order to minimize possible side-band effects, appropriate analysis/synthesis windows, e.g. Gaussian windows, co 15 sine windows, Hamming windows, Hann windows, rectangular windows, Bartlett win dows, Blackman windows, and others, should be selected. The time delay at which eve ry spectral frame is picked up from the input signal is referred to as the hop size or stride. The STFT of the input signal is referred to as the analysis stage and leads to a frequency domain representation of the input signal. The frequency domain representa 20 tion comprises a plurality of subband signals, wherein each subband signal represents a certain frequency component of the input signal. The frequency domain representation of the input signal may then be processed in a desired way. For the purpose of time-stretching of the input signal, each subband signal 25 may be time-stretched, e.g. by delaying the subband signal samples. This may be achieved by using a synthesis hop-size which is greater than the analysis hop-size. The time domain signal may be rebuilt by performing an inverse (Fast) Fourier transform on all frames followed by a successive accumulation of the frames. This operation of the synthesis stage is referred to as overlap-add operation. The resulting output signal is a 30 time-stretched version of the input signal comprising the same frequency components as the input signal. In other words, the resulting output signal has the same spectral com- - 18 position as the input signal, but it is slower than the input signal i.e. its progression is stretched in time. The transposition to higher frequencies may then be obtained subsequently, or in an 5 integrated manner, through downsampling of the stretched signals. As a result the trans posed signal has the length in time of the initial signal, but comprises frequency compo nents which are shifted upwards by a pre-defined transposition factor. In mathematical terms, the phase vocoder may be described as follows. An input signal 10 x(t) is sampled at a sampling rate R to yield the discrete input signal x(n) . During the analysis stage, a STFT is determined for the input signal x(n) at particular analysis time instants tk for successive values k. The analysis time instants are preferably selected uniformly through tk =k -At, , where Ata is the analysis hop factor or analysis stride. At each of these analysis time instants t, a Fourier transform is calculated over a win 15 dowed portion of the original signal x(n), wherein the analysis window V, (t) is cen tered around tk, i.e. V,(t -t). This windowed portion of the input signal x(n) is re ferred to as a frame. The result is the STFT representation of the input signal x(n), which may be denoted as: 20 X(tam) va (n -t)x(n)exp(-jQmn), where Qm = 2c -m is the center frequency of the m" subband signal of the STFT analy M sis and M is the size of the discrete Fourier transform (DFT). In practice, the window function va (n) has a limited time span, i.e. it covers only a limited number of samples 25 L, which is typically equal to the size M of the DFT. By consequence, the above sum has a finite number of terms. The subband signals X(t, Om) are both a function of time, via index k, and frequency, via the subband center frequency Q.

- 19 The synthesis stage may be performed at synthesis time instants t< which are typically uniformly distributed according to tk =k -At 5 , where At, is the synthesis hop factor or synthesis stride. At each of these synthesis time instants, a short-time signal yk(n) is obtained by inverse-Fourier-transforming the STFT subband signal Y(t, Qm), which 5 may be identical to X(t, Qm), at the synthesis time instants tk . However, typically the STFT subband signals are modified, e.g. time-stretched and/or phase modulated and/or amplitude modulated, such that the analysis subband signal X(t, Qm) differs from the synthesis subband signal Y(t,Qm). In a preferred embodiment, the STFT subband sig nals are phase modulated, i.e. the phase of the STFT subband signals is modified. The 10 short-term synthesis signal yk(n) can be denoted as 1 M-1 M m-o The short-term signal yk (n) may be viewed as a component of the overall output signal 15 y(n) comprising the synthesis subband signals Y(t, Qm) for m= 0,..., M -1, at the synthesis time instant t . J.e. the short-term signal yk(n) is the inverse DFT for a specif ic signal frame. The overall output signal y(n) can be obtained by overlapping and add ing windowed short-time signals yk(n) at all synthesis time instants t< . .e. the output signal y(n) may be denoted as 20 y(n)= vS (n -t)yk (n- tb, where v, (n -t)is the synthesis window centered around the synthesis time instant t. It should be noted that the synthesis window typically has a limited number of samples 25 L, such that the above mentioned sum only comprises a limited number of terms.

- 20 In the following, the implementation of time-stretching in the frequency domain is out lined. A suitable starting point in order to describe aspects of the time stretcher is to consider the case T =1, i.e. the case where the transposition factor T equals 1 and where no stretching occurs. Assuming the analysis time stride Ata and the synthesis 5 time stride At, of the DFT filter bank to be equal, i.e. Ata = At, = At, the combined effect of analysis followed by synthesis is that of an amplitude modula tion with the At -periodic function 10 K(n) q(n -kAt), (1) where q(n) =v,(n)v,(n)is the point-wise product of the two windows, i.e. the point wise product of the analysis window and the synthesis window. It is advantageous to choose the windows such that K(n) =1 or another constant value, since then the win 15 dowed DFT filter bank achieves perfect reconstruction. If the analysis window v, (n) is given, and if the analysis window is of sufficiently long duration compared to the stride At, one can obtain perfect reconstruction by choosing the synthesis window according to 20 v, (n) = v,, (n) av, (n - k -At)) . (2) For T > 1, i.e. for a transposition factor greater than 1, a time stretch may be obtained At by performing the analysis at stride At, = whereas the synthesis stride is maintained T at At, = At. In other words, a time stretch by a factor T may be obtained by applying a 25 hop factor or stride at the analysis stage which is T times smaller than the hop factor or stride at the synthesis stage. As can be seen from the formulas provided above, the use of a synthesis stride which is T times greater than the analysis stride will shift the short- - 21 term synthesis signals yk(n) by T times greater intervals in the overlap-add operation. This will eventually result in a time-stretch of the output signal y(n). It should be noted that the time stretch by the factor T may further involve a phase mul 5 tiplication by a factor T between the analysis and the synthesis. In other words, time stretching by a factor T involves phase multiplication by a factor T of the subband sig nals. In the following it is outlined how the above described time-stretching operation may be 10 translated into a harmonic transposition operation. The pitch-scale modification or har monic transposition may be obtained by performing a sample-rate conversion of the time stretched output signal y(n). For performing a harmonic transposition by a factor T , an output signal y(n) which is a time-stretched version by the factor T of the input signal x(n) may be obtained using the above described phase vocoding method. The 15 harmonic transposition may then be obtained by downsampling the output signal y(n) by a factor T or by converting the sampling rate from R to TR. In other words, instead of interpreting the output signal y(n) as having the same sampling rate as the input signal x(n) but of T times duration, the output signal y(n) may be interpreted as being of the same duration but of T times the sampling rate. The subsequent downsam 20 pling of T may then be interpreted as making the output sampling rate equal to the input sampling rate so that the signals eventually may be added. During these operations, care should be taken when downsampling the transposed signal so that no aliasing occurs. When assuming the input signal x(n) to be a sinusoid and when assuming a symmetric 25 analysis windows va (n), the method of time stretching based on the above described phase vocoder will work perfectly for odd values of T , and it will result in a time stretched version of the input signal x(n)having the same frequency. In combination with a subsequent downsampling, a sinusoid y(n) with a frequency which is T times the frequency of the input signal x(n) will be obtained. 30 - 22 For even values of T, the time stretching/harmonic transposition method outlined above will be more approximate, since negative valued side lobes of the frequency response of the analysis window v, (n) will be reproduced with different fidelity by the phase multiplication. The negative side lobes typically come from the 5 fact that most practical windows (or prototype filters) have numerous discrete zeros located on the unit circle, resulting in 180 degree phase shifts. When multiplying the phase angles using even transposition factors the phase shifts are typically translated to 0 (or rather multiples of 360) degrees depending on the transposition factor used. In other words, when using even transposition factors, the phase shifts vanish. This will 10 typically give rise to aliasing in the transposed output signal y(n). A particularly disad vantageous scenario may arise when a sinusoidal is located in a frequency correspond ing to the top of the first side lobe of the analysis filter. Depending on the rejection of this lobe in the magnitude response, the aliasing will be more or less audible in the out put signal. It should be noted that, for even factors T , decreasing the overall stride 15 At typically improves the performance of the time stretcher at the expense of a higher computational complexity. In EP0940015B 1 / W098/57436 entitled "Source coding enhancement using spectral band replication" which is incorporated by reference, a method has been described on 20 how to avoid aliasing emerging from a harmonic transposer when using even transposi tion factors. This method, called relative phase locking, assesses the relative phase dif ference between adjacent channels, and determines whether a sinusoidal is phase invert ed in either channel. The detection is performed by using equation (32) of EP0940015B 1. The channels detected as phase inverted are corrected after the phase 25 angles are multiplied with the actual transposition factor. In the following a novel method for avoiding aliasing when using even and/or odd transposition factors T is described. In contrary to the relative phase locking method of EP0940015B 1, this method does not require the detection and correction of phase an 30 gles. The novel solution to the above problem makes use of analysis and synthesis trans form windows that are not identical. In the perfect reconstruct - 23 tion (PR) case, this corresponds to a bi-orthogonal transform/filter bank rather than an orthogonal transform/filter bank. To obtain a bi-orthogonal transform given a certain analysis window va(n), the synthesis 5 window vs(n) is chosen to follow L/(At,-1) Yv,(m+Atsi)vs(m+Atsi)=c ,0! m<At, i=O where c is a constant, At, is the synthesis time stride and L is the window length. If the 10 sequence s(n) is defined as L/(AtI -1) s 2 m+ Atsi), 0 m<Ats, i=0 i.e. va(n) = vs(n) is used for both analysis and synthesis windowing, then the condition 15 for an orthogonal transform is s(m)=c, Os!m<At,. However, in the following another sequence w(n) is introduced, wherein w(n) is a 20 measure on how much the synthesis window vs(n) deviates from the analysis window va(n), i.e. how much the bi-orthogonal transform differs from the orthogonal case. The sequence w(n) is given by v (n) w(n)= , O, n<L. v,, (n) 25 The condition for perfect reconstruction is then given by - 24 L/(At, -1) v(m+ Atsi)w(m+ Atsi) =c, O mAs i=O For a possible solution, w(n) could be restricted to be periodic with the synthesis time stride At, i.e. w(n)= w(n + Atsi), Vi, n. Then, one obtains 5 L/(At, -1 L /(Ats -1) v(m+ Atsi)w(m+ Atsi)= w(m) v(m+ Atsi) =w(m)s(m)= c , i=O i=O 0 m < At. The condition on the synthesis window vs(n) is hence 10 v (n)~ v (n) = w(n(mod Ats ))va (n)= c a''(n ) , 0 < n < L. s(n(mod At )) By deriving the synthesis windows vs(n) as outlined above, a much larger freedom when designing the analysis window va(n) is provided. This additional freedom may be used 15 to design a pair of analysis/synthesis windows which does not exhibit aliasing of the transposed signal. To obtain an analysis/synthesis window pair that suppresses aliasing for even transposi tion factors, several embodiments will be outlined in the following. According to a first 20 embodiment the windows or prototype filters are made long enough to attenuate the level of the first side lobe in the frequency response below a certain "aliasing" level. The analysis time stride Ata will in this case only be a (small) fraction of the window length L. This typically results in smearing of transients, e.g. in percussive signals. 25 According to a second embodiment, the analysis window va(n) is chosen to have dual zeros on the unit circle. The phase response resulting from a dual zero is a 360 degree phase shift. These phase shifts are retained when the phase angles are multi plied with the transposition factors, regardless if the transposition factors are odd or - 25 even. When a proper and smooth analysis filter va(n), having dual zeros on the unit cir cle, is obtained, the synthesis window is obtained from the equations outlined above. In an example of the second embodiment, the analysis filter / window va(n) is the 5 "squared sine window", i.e. the sine window v(n) sin j (n + 0.5) ,0! n < L (L convolved with itself as v, (n)= v(n) 0 v(n). However, it should be noted that the re 10 sulting filter / window va(n) will be odd symmetric with length La=2L-1, i.e. an odd number of filter / window coefficients. When a filter / window with an even length is more appropriate, in particular an even symmetric filter, the filter may be obtained by first convolving two sine windows of length L. Then, a zero is appended to the end of the resulting filter. Subsequently, the 2L long filter is resampled using linear interpola 15 tion to a length L even symmetric filter, which still has dual zeros only on the unit cir cle. Overall, it has been outlined, how a pair of analysis and synthesis windows may be se lected such that aliasing in the transposed output signal may be avoided or significantly 20 reduced. The method is particularly relevant when using even transposition factors. Another aspect to consider in the context of vocoder based harmonic transposers is phase unwrapping. It should be noted that whereas great care has to be taken related to phase unwrapping issues in general purpose phase vocoders, the harmonic transposer 25 has unambiguously defined phase operations when integer transposition factors T are used. Thus, in preferred embodiments the transposition order T is an integer value. Otherwise, phase unwrapping techniques could be applied, wherein phase unwrapping is a process whereby the phase increment between two con secutive frames is used to estimate the instantaneous frequency of a nearby sinusoid in 30 each channel.

- 26 Yet another aspect to consider, when dealing with the transposition of audio and/or voice signals, is the processing of stationary and/or transient signal sections. Typically, in order to be able to transpose stationary audio signals without intermodulation arti facts, the frequency resolution of the DFT filter bank has to be rather high, and therefore 5 the windows are long compared to transients in the input signals x(n), notably audio and/or voice signals. As a result, the transposer has a poor transient response. However, as will be described in the following, this problem can be solved by a modification of the window design, the transform size and the time stride parameters. Hence, unlike many state of the art methods for phase vocoder transient response enhancement, the 10 proposed solution does not rely on any signal adaptive operation such as transient detec tion. In the following, the harmonic transposition of transient signals using vocoders is out lined. As a starting point, a prototype transient signal, a discrete time Dirac pulse at time 15 instant t =to (5(t -to)= , t 0, t # t 0 is considered. The Fourier transform of such a Dirac pulse has unit magnitude and a 20 linear phase with a slope proportional to to: X(m)= (S(n -t o )exp(-jQmn) = exp(-jQmt 0 ). Such Fourier transform can be considered as the analysis stage of the phase vocoder 25 described above, wherein a flat analysis window v, (n) of infinite duration is used. In order to generate an output signal y(n) which is time-stretched by a factor T , i.e. a Di rac pulse 3(t -Tto) at the time instant t = Tto, the phase of the analysis subband signals should be multiplied by the factor T in order to obtain the synthesis subband signal - 27 Y(Qm) = exp(-jQmTto) which yields the desired Dirac pulse J(t -Tto) as an output of an inverse Fourier Transform. This shows that the operation of phase multiplication of the analysis subband signals by 5 a factor T leads to the desired time-shift of a Dirac pulse, i.e. of a transient input signal. It should be noted that for more realistic transient signals comprising more than one non-zero sample, the further operations of time-stretching of the analysis subband sig nals by a factor T should be performed. In other words, different hop sizes should be used at the analysis and the synthesis side. 10 However, it should be noted that the above considerations refer to an analysis/synthesis stage using analysis and synthesis windows of infinite lengths. Indeed, a theoretical transposer with a window of infinite duration would give the correct stretch of a Dirac pulse J(t -to). For a finite duration windowed analysis, the situation is scrambled by 15 the fact that each analysis block is to be interpreted as one period interval of a periodic signal with period equal to the size of the DFT. This is illustrated in Fig. 1 which shows the analysis and synthesis 100 of a Dirac pulse J(t -to). The upper part of Fig. 1 shows the input to the analysis stage 110 and the low 20 er part of Fig. 1 shows the output of the synthesis stage 120. The upper and lower graphs represent the time domain. The stylized analysis window 111 and synthesis win dow 121 are depicted as triangular (Bartlett) windows. The input pulse J(t -to) 112 at time instant t =to is depicted on the top graph 110 as a vertical arrow. It is assumed that the DFT transform block is of size M = L, i.e. the size 25 of the DFT transform is chosen to be equal to the size of the windows. The phase multi plication of the subband signals by the factor T will produce the DFT analysis of a Di rac pulse J(t -Tto) at t = Tto, however, periodized to a Dirac pulse train with period L. This is due to the finite length of the applied window and Fourier Transform. The periodized pulse train with period Lis depicted by the dashed arrows 123, 124 on the 30 lower graph.

- 28 In a real-world system, where both the analysis and synthesis windows are of finite length, the pulse train actually contains a few pulses only (depending on the transposi tion factor), one main pulse, i.e. the wanted term, a few pre-pulses and a few post pulses, i.e. the unwanted terms. The pre- and post-pulses emerge because the DFT is 5 periodic (with L). When a pulse is located within an analysis window, so that the com plex phase gets wrapped when multiplied by T (i.e. the pulse is shifted outside the end of the window and wraps back to the beginning), an unwanted pulse emerges. The un wanted pulses may have, or may not have, the same polarity as the input pulse, depend ing on the location in the analysis window and the transposition factor. 10 This can be seen mathematically when transforming the Dirac pulse J(t -to) situated in the interval -L/2 to < L/ 2 using a DFT with length L centered around t =0, L/2-1 X(Qm) 13(n -to)exp(-jQmn)= exp(-jQmto). n=-L/2 15 The analysis subband signals are phase multiplied with a factor T to obtain the synthesis subband signals Y(Qm)= exp(-jQmTto). Then the inverse DFT is applied to obtain the periodic synthesis signal: 1 L/2-1 20 y(n) = - exp(- j Q m To) exp( j Qn)= S(n - Tto + kL). m=-L/2 k-o i.e. a Dirac pulse train with period L. In the example of Fig. 1, the synthesis windowing uses a finite window v, (n) 121. The 25 finite synthesis window 121 picks the desired pulse J(t -Tto) at t = Tto which is de picted as a solid arrow 122 and cancels the other contributions which are shown as dashed arrows 123, 124.

- 29 As the analysis and synthesis stage move along the time axis according to the hop factor or time stride At, the pulse J(t -to) 112 will have another position relative to the center of the respective analysis window 111. As outlined above, the operation to achieve time-stretching consists in moving the pulse 112 to T times its position relative to the 5 center of the window. As long as this position is within the window 121, this time stretch operation guarantees that all contributions add up to a single time stretched syn thesized pulse J(t - Tto) at t = Tto . However, a problem occurs for the situation of Fig. 2, where the pulse J(t -to)212 10 moves further out towards the edge of the DFT block. Fig. 2 illustrates a similar analy sis/synthesis configuration 200 as Fig. 1. The upper graph 210 shows the input to the analysis stage and the analysis window 211, and the lower graph 220 illustrates the out put of the synthesis stage and the synthesis window 221. When time-stretching the input Dirac pulse 212 by a factor T , the time stretched Dirac pulse 222, i.e. J(t -Tto), is out 15 side the synthesis window 221. At the same time, another Dirac pulse 224 of the pulse train, i.e. 3(t -TtO + L) at time instant t = Tto - L, is picked up by the synthesis win dow. In other words, the input Dirac pulse 212 is not delayed to a T times later time instant, but it is moved forward to a time instant that lies before the input Dirac pulse 212. The final effect on the audio signal is the occurrence of a pre-echo at a time dis 20 tance of the scale of the rather long transposer windows, i.e. at a time instant t = Tto - L which is L - (T -1)tO earlier than the input Dirac pulse 212. The principle of the solution proposed by the present invention is described in reference to Fig. 3. Fig. 3 illustrates an analysis/synthesis scenario 300 similar to Fig. 2. The up 25 per graph 310 shows the input to the analysis stage with the analysis window 311, and the lower graph 320 shows the output of the synthesis stage with the synthesis window 321. The basic idea of the invention is to adapt the DFT size so as to avoid pre-echoes. This may be achieved by setting the size M of the DFT such that no unwanted Dirac pulse images from the resulting pulse train are picked up by the synthesis window. The 30 size of the DFT transform 301 is increased to M = FL, where Lis the length of the - 30 window function 302 and the factor F is a frequency domain oversampling factor. In other words, the size of the DFT transform 301 is selected to be larger than the window size 302. In particular, the size of the DFT transform 301 may be selected to be larger than the window size 302 of the synthesis window. Due to the increased length 301 of 5 the DFT transform, the period of the pulse train comprising the Dirac pulses 322, 324 is FL. By selecting a sufficiently large value of F , i.e. by selecting a sufficiently large frequency domain oversampling factor, undesired contributions to the pulse stretch can be cancelled. This is shown in Fig. 3, where the Dirac pulse 324 at time instant t = Tto - FL lies outside the synthesis window 321. Therefore, the Dirac pulse 324 is not 10 picked up by the synthesis window 321 and by consequence, pre-echoes can be avoided. It should be noted that in a preferred embodiment the synthesis window and the analysis window have equal ,,nominal" lengths. However, when using implicit resampling of the output signal by discarding or inserting samples in the frequency bands of the transform 15 or filter bank, the synthesis window size will typically be different from the analysis size, depending on the resampling or transposition factor. The minimum value of F , i.e. the minimum frequency domain oversampling factor, can be deduced from Fig. 3. The condition for not picking up undesired Dirac pulse images L. 20 may be formulated as follows: For any input pulse J(t -to) at position t = to <- , i.e. 2 for any input pulse comprised within the analysis window 311, the undesired image 3(t -TtO + FL) at time instant t Tto - FL must be located to the left of the left edge of L L L the synthesis window at t - . Equivalently, the condition T - _ FL < -- must be 2 2 2 met, which leads to the rule T+1 25 F> . (3) 2 As can be seen from formula (3), the minimum frequency domain oversampling factor F is a function of the transposition / time-stretching factor T . More specifically, the -31 minimum frequency domain oversampling factor F is proportional to the transposition / time-stretching factor T . By repeating the line of thinking above for the case where the analysis and synthesis 5 windows have different lengths one obtains a more general formula. Let L, and Ls be the lengths of the analysis and synthesis windows, respectively, and let M be the DFT size employed. The rule extending formula (3) is then M > TA+Ls (4) 2 10 That this rule indeed is an extension of (3) can be verified by inserting M = FL, and LA = Is = L in (4) and dividing by L on both side of the resulting equation. The above analysis is performed for a rather special model of a transient, i.e. a Dirac 15 pulse. However, the reasoning can be extended to show that when using the above de scribed time-stretching scheme, input signals which have a near flat spectral envelope and which vanish outside a time interval [a,b] will be stretched to output signals which are small outside the interval [Ta,Th]. It can also be checked by studying spectrograms of real audio and/or speech signals that pre-echoes disappear in the stretched signals 20 when the above described rule for selecting an appropriate frequency domain over sampling factor is respected. A more quantitative analysis also reveals that pre-echoes are still reduced when using frequency domain oversampling factors which are slightly inferior to the value imposed by the condition of formula (3). This is due to the fact that typical window functions v, (n) are small near their edges, thereby attenuating undesired 25 pre-echoes which are positioned near the edges of the window functions. In summary, the present invention teaches a new way to improve the transient response of frequency domain harmonic transposers, or time-stretchers, by introducing an over sampled transform, where the amount of oversampling is a function of the transposition 30 factor chosen.

- 32 In the following, the application of harmonic transposition according to the invention in audio decoders is described in further detail. A common use case for a harmonic trans poser is in an audio/speech codec system employing so-called bandwidth extension or high frequency regeneration (HFR). It should be noted that even though reference may 5 be made to audio coding, the described methods and systems are equally applicable to speech coding and in unified speech and audio coding (USAC). In such HFR systems the transposer may be used to generate a high frequency signal component from a low frequency signal component provided by the so-called core de 10 coder. The envelope of the high frequency component may be shaped in time and fre quency based on side information conveyed in the bit-stream. Fig. 4 illustrates the operation of an HFR enhanced audio decoder. The core audio de coder 401 outputs a low bandwidth audio signal which is fed to an up-sampler 404 15 which may be required in order to produce a final audio output contribution at the de sired full sampling rate. Such up-sampling is required for dual rate systems, where the band limited core audio codec is operating at half the external audio sampling rate, while the HFR part is processed at the full sampling frequency. Consequently, for a sin gle rate system, this up-sampler 404 is omitted. The low bandwidth output of 401 is also 20 sent to the transposer or the transposition unit 402 which outputs a transposed signal, i.e. a signal comprising the desired high frequency range. This transposed signal may be shaped in time and frequency by the envelope adjuster 403. The final audio output is the sum of low bandwidth core signal and the envelope adjusted transposed signal. 25 As outlined in the context of Fig. 4, the core decoder output signal may be up-sampled as a pre-processing step by a factor 2 in the transposition unit 402. A transposition by a factor T results in a signal having T times the length of the un-transposed signal, in case of time-stretching. In order to achieve the desired pitch-shifting or frequency transposi tion to T times higher frequencies, down-sampling or rate-conversion of the time 30 stretched signal is subsequently performed. As mentioned above, this operation may be achieved through the use of different analysis and synthesis strides in the phase vocod er.

- 33 The overall transposition order may be obtained in different ways. A first possibility is to up-sample the decoder output signal by the factor 2 at the entrance to the transposer as pointed out above. In such cases, the time-stretched signal would need to be down 5 sampled by a factor T, in order to obtain the desired output signal which is frequency transposed by a factor T. A second possibility would be to omit the pre-processing step and to directly perform the time-stretching operations on the core decoder output signal. In such cases, the transposed signals must be down-sampled by a factor T/2 to retain the global up-sampling factor of 2 and in order to achieve frequency transposition by a fac 10 tor T. In other words, the up-sampling of the core decoder signal may be omitted when performing a down-sampling of the output signal of the transposer 402 of T/2 instead of T. It should be noted, however, that the core signal still needs to be up-sampled in the up-sampler 404 prior to combining the signal with the transposed signal. 15 It should also be noted that the transposer 402 may use several different integer transpo sition factors in order to generate the high frequency component. This is shown in Fig. 5 which illustrates the operation of a harmonic transposer 501, which corresponds to the transposer 402 of Fig. 4, comprising several transposers of different transposition order or transposition factor T. The signal to be transposed is passed to the bank of individual 20 transposers 501-2, 501-3, ... , 501-Tmax having orders of transposition T = 2,3,.... , respectively. Typically a transposition order T. = 4 suffices for most audio coding applications. The contributions of the different transposers 501-2, 501-3, ... , 501-Tmax are summed in 502 to yield the combined transposer output. In a first embodiment, this summing operation may comprise the adding up of the individual contributions. In an 25 other embodiment, the contributions are weighted with different weights, such that the effect of adding multiple contributions to certain frequencies is mitigated. For instance, the third order contribution may be added with a lower gain than the second order con tribution. Finally, the summing unit 502 may add the contributions selectively depend ing on the output frequency. For instance, the second order transposition may be used 30 for a first lower target frequency range, and the third order transposition may be used for a second higher target frequency range.

- 34 Fig. 6 illustrates the operation of a harmonic transposer, such as one of the individual blocks of 501, i.e. one of the transposers 501-T of transposition order T. An analysis stride unit 601 selects successive frames of the input signal which is to be transposed. 5 These frames are super-imposed, e.g. multiplied, in an analysis window unit 602 with an analysis window. It should be noted that the operations of selecting frames of an in put signal and multiplying the samples of the input signal with an analysis window function may be performed in a unique step, e.g. by using a window function which is shifted along the input signal by the analysis stride. In the analysis transformation unit 10 603, the windowed frames of the input signal are transformed into the frequency do main. The analysis transformation unit 603 may e.g. perform a DFT. The size of the DFT is selected to be F times greater than the size L of the analysis window, thereby generating M=F*L complex frequency domain coefficients. These complex coefficients are altered in the non-linear processing unit 604, e.g. by multiplying their phase with the 15 transposition factor T. The sequence of complex frequency domain coefficients, i.e. the complex coefficients of the sequence of frames of the input signal, may be viewed as subband signals. The combination of analysis stride unit 601, analysis window unit 602 and analysis transformation unit 603 may be viewed as a combined analysis stage or analysis filter bank. 20 The altered coefficients or altered subband signals are retransformed into the time do main using the synthesis transformation unit 605. For each set of altered complex coef ficients, this yields a frame of altered samples, i.e. a set of M altered samples. Using the synthesis window unit 606, L samples may be extracted from each set of altered sam 25 ples, thereby yielding a frame of the output signal. Overall, a sequence of frames of the output signal may be generated for the sequence of frames of the input signal. This se quence of frames is shifted with respect to one another by the synthesis stride in the synthesis stride unit 607. The synthesis stride may be T times greater than the analysis stride. The output signal is generated in the overlap-add unit 608, where the shifted 30 frames of the output signal are overlapped and samples at the same time instant are add ed. By traversing the above system, the input signal may be time-stretched by a factor T, i.e. the output signal may be a time-stretched version of the input signal.

- 35 Finally, the output signal may be contracted in time using the contracting unit 609. The contracting unit 609 may perform a sampling rate conversion of order T, i.e. it may in crease the sampling rate of the output signal by a factor T, while keeping the number of samples unchanged. This yields a transposed output signal, having the same length in 5 time as the input signal but comprising frequency components which are up-shifted by a factor T with respect to the input signal. The combining unit 609 may also perform a down-sampling operation by a factor T, i.e. it may retain only every Tth sample while discarding the other samples. This down-sampling operation may also be accompanied by a low pass filter operation. If the overall sampling rate remains unchanged, then the 10 transposed output signal comprises frequency components which are up-shifted by a factor T with respect to the frequency components of the input signal. It should be noted that the contracting unit 609 may perform a combination of rate conversion and down-sampling. By way of example, the sampling rate may be in 15 creased by a factor 2. At the same time the signal may be down-sampled by a factor T/2. Overall, such combination of rate-conversion and down-sampling also leads to an out put signal which is a harmonic transposition of the input signal by a factor T. In general, it may be stated that the contracting unit 609 performs a combination of rate conversion and/or down-sampling in order to yield a harmonic transposition by the transposition 20 order T. This is particularly useful when performing harmonic transposition of the low bandwidth output of the core audio decoder 401. As outlined above, such low band width output may have been down-sampled by a factor 2 at the encoder and may there fore require up-sampling in the up-sampling unit 404 prior to merging it with the recon structed high frequency component. Nevertheless, it may be beneficial for reducing 25 computation complexity to perform harmonic transposition in the transposition unit 402 using the "non-up-sampled" low bandwidth output. In such cases, the contracting unit 609 of the transposition unit 402 may perform a rate-conversion of order 2 and thereby implicitly perform the required up-sampling operation of the high fre - 36 quency component. By consequence, transposed output signals of order T are down sampled in the contracting unit 609 by the factor T/2. In the case of multiple parallel transposers of different transposition orders such as 5 shown in Fig. 5, some transformation or filter bank operations may be shared between different transposers 501-2, 501-3, ... , 501-Tmax. The sharing of filter bank operations may be done preferably for the analysis in order to obtain more effective implementa tions of transposition units 402. It should be noted that a preferred way to resample the outputs from different tranposers is to discard DFT-bins or subband channels before the 10 synthesis stage. This way, resampling filters may be omitted and complexity may be reduced when performing an inverse DFT/synthesis filter bank of smaller size. As just mentioned, the analysis window may be common to the signals of different transposition factors. When using a common analysis window, an example of the stride 15 of windows 700 applied to the low band signal is depicted in Fig. 7. Fig. 7 shows a stride of analysis windows 701, 702, 703 and 704, which are displaced with respect to one another by the analysis hop factor or analysis time stride Ata An example of the stride of windows applied to the low band signal, e.g. the output sig 20 nal of the core decoder, is depicted in Figure 8(a). The stride with which the analysis window of length L is moved for each analysis transform is denoted Ata . Each such analysis transform and the windowed portion of the input signal is also referred to as a frame. The analysis transform converts/transforms the frame of input samples into a set of complex FFT coefficient. After the analysis transform, the complex FFT coefficients 25 may be transformed from Cartesian to polar coordinates. The suite of FFT coefficients for subsequent frames makes up the analysis subband signals. For each of the transposi tion factors T = 2,3,...,T_ used, the phase angles of the FFT coefficients are multiplied by the respective transposition factor T and transformed back to Cartesian coordinates.

- 37 Hence, there will be a different set of complex FFT coefficients representing a particular frame for every transposition factor T. In other words, for each of the transposition fac tors T = 2,3,...,T_ and for each frame, a separate set of FFT coefficients is determined. By consequence, for every transposition order T a different set of synthesis subband 5 signals Y(tk, m) is generated. In the synthesis stages, the synthesis strides At, of the synthesis windows are deter mined as a function of the transposition order T used in the respective transposer. As outlined above, the time-stretch operation also involves time stretching of the subband 10 signals, i.e. time stretching of the suite of frames. This operation may be performed by choosing a synthesis hop factor or synthesis stride At, which is increased over the anal ysis stride Ata by a factor T. Consequently, the synthesis stride Ats, for the transposer of order T is given by Ats, = TAt, . Figs. 8 (b) and 8 (c) show the synthesis stride At, of synthesis windows for the transposition factors T=2 and T=3, respectively, where 15 At 2 = 2At, and Ats 3 = 3At, . Fig. 8 also indicates the reference time tr which has been "stretched" by a factor T=2 and T=3 in Figs. 8 (b) and 8 (c) compared to Fig. 8(a), respectively. However, at the outputs this reference time tr needs to be aligned for the two transposition factors. To 20 align the output, the third order transposed signal, i.e. Fig. 8(c), needs to be down sampled or rate-converted with the factor 3/2. This down-sampling leads to a harmonic transposition in respect to the second order transposed signal. Fig.9 illustrates the effect of the re-sampling on the synthesis stride of windows for T = 3. If it is assumed that the analysed signal is the output signal of a core decoder which has not been up-sampled, 25 then the signal of Fig. 8 (b) has been effectively frequency transposed by a factor 2 and the signal of Fig. 8 (c) has been effectively frequency transposed by a factor 3.

- 38 In the following, the aspect of time alignment of transposed sequences of different transposition factors when using common analysis windows is addressed. In other words, the aspect of aligning the output signals of frequency transposers employing a different transposition order is addressed. When using the methods outlined above, Di 5 rac-functions J(t -to) are time-stretched, i.e. moved along the time axis, by the amount of time given by the applied transposition factor T . In order to convert the time stretching operation into a frequency shifting operation, a decimation or down-sampling using the same transposition factor T is performed. If such decimation by the transposi tion factor or transposition order T is performed on the time-stretched Dirac-function 10 J(t -Tto), the down-sampled Dirac pulse will be time aligned with respect to the zero reference time 710 in the middle of the first analysis window 701. This is illustrated in Fig. 7. However, when using different orders of transposition T, the decimations will result in 15 different offsets for the zero-reference, unless the zero-reference is aligned with "zero" time of the input signal. By consequence, a time offset adjustment of the decimated transposed signals need to be performed, before they can be summed up in the summing unit 502. As an example, a first transposer of order T = 3 and a second transposer of order T = 4 are assumed. Furthermore, it is assumed that the output signal of the core 20 decoder is not up-sampled. Then the transposer decimates the third order time-stretched signal by a factor 3/2, and the fourth order time-stretched signal by a factor 2. The sec ond order time-stretched signal, i.e. T = 2, will just be interpreted as having a higher sampling frequency compared to the input signal, i.e. a factor 2 higher sampling fre quency, effectively making the output signal pitch-shifted by a factor 2. 25 It can be shown that in order to align the transposed and down-sampled signals, time offsets by (T - 2)L need to be applied to the transposed signals before decimation, i.e. 4 L for the third and fourth order transpositions, offsets of - and 4 - 39 L - have to be applied respectively. To verify this in a concrete example, the zero 2 reference for a second order time-stretched signal will be assumed to correspond to time L instant or sample - , i.e. to the zero-reference 710 in Fig. 7. This is so, because no dec 2 imation is used. For a third order time-stretched signal, the reference will translate to 5 -(2- = -, due to down-sampling by a factor of - . If the time offset according to the 2 3 3 2 above mentioned rule is added before decimation, the reference will translate into - +- -2= - . This means that the reference of the down-sampled transposed sig 2 4 3 2 nal is aligned with the zero-reference 710. In a similar manner, for the fourth order transposition without offset the zero-reference corresponds to -(- = -, but when 2 2 4 10 using the proposed offset, the reference translates into -+- -= -L, which again is 2 2 2 2 aligned with the 2 "d order zero-reference 710, i.e. the zero-reference for the transposed signal using T = 2. Another aspect to be considered when simultaneously using multiple orders of transpo 15 sition relates to the gains applied to the transposed sequences of different transposition factors. In other words, the aspect of combining the output signals of transposers of dif ferent transposition order may be addressed. There are two principles when selecting the gain of the transposed signals, which may be considered under different theoretical ap proaches. Either, the transposed signals are supposed to be energy conserving, meaning 20 that the total energy in the low band signal which subsequently is transposed to consti tute a factor-T transposed high band signal is preserved. In this case the energy per bandwidth should be reduced by the transposition factor T since the signal is stretched by the same amount T in frequency. However, sinusoids, which have their energy with in an infinitesimally small bandwidth, will retain their energy after transposition. This is 25 due to the fact - 40 that in the same way as a Dirac pulse is moved in time by the transposer when time stretching, i.e. in the same way that the duration in time of the pulse is not changed by the time-stretching operation, a sinusoidal is moved in frequency when transposing, i.e. the duration in frequency (in other words the bandwidth) is not changed by the frequen 5 cy transposing operation. I.e. even though the energy per bandwidth is reduced by T, the sinusoidal has all its energy in one point in frequency so that the point-wise energy will be preserved. The other option when selecting the gain of the transposed signals is to keep the energy 10 per bandwidth after transposition. In this case, broadband white noise and transients will display a flat frequency response after transposition, while the energy of sinusoids will increase by a factor T. A further aspect of the invention is the choice of analysis and synthesis phase vocoder 15 windows when using common analysis windows. It is beneficial to carefully choose the analysis and synthesis phase vocoder windows, i.e. v, (n) and v, (n) . Not only should the synthesis window v, (n) adhere to Formula 2 above, in order to allow for perfect reconstruction. Furthermore, the analysis window va (n) should also have adequate re jection of the side lobe levels. Otherwise, unwanted "aliasing" terms will typically be 20 audible as interference with the main terms for frequency varying sinusoids. Such un wanted "aliasing" terms may also appear for stationary sinusoids in the case of even transposition factors as mentioned above. The present invention proposes the use of sine windows because of their good side lobe rejection ratio. Hence, the analysis window is proposed to be 25 va(n)= sin (n+0.5) ,0 n < L (4) (L The synthesis windows vs (n) will be either identical to the analysis window va(n)or given by formula (2) above if the synthesis hop-size At, is not a factor of 30 - 41 the analysis window length L, i.e. if the analysis window length L is not integer divida ble by the synthesis hop-size. By way of example, if L-1024, and At,= 384, then 1024/384 = 2.667 is not an integer. It should be noted that it is also possible to select a pair of bi-orthogonal analysis and synthesis windows as outlined above. This may be 5 beneficial for the reduction of aliasing in the output signal, notably when using even transposition orders T. In the following, reference is made to Fig. 10 and Fig. 11 which illustrate an exemplary encoder 1000 and an exemplary decoder 1100, respectively, for unified speech and au 10 dio coding (USAC). The general structure of the USAC encoder 1000 and decoder 1100 is described as follows: First there may be a common pre/postprocessing consisting of an MPEG Surround (MPEGS) functional unit to handle stereo or multi-channel pro cessing and an enhanced Spectral Band Replication (eSBR) unit 1001 and 1101, respec tively, which handles the parametric representation of the higher audio frequencies in 15 the input signal and which may make use of the harmonic transposition methods out lined in the present document. Then there are two branches, one consisting of a modi fied Advanced Audio Coding (AAC) tool path and the other consisting of a linear pre diction coding (LP or LPC domain) based path, which in turn features either a frequen cy domain representation or a time domain representation of the LPC residual. All 20 transmitted spectra for both, AAC and LPC, may be represented in MDCT domain fol lowed by quantization and arithmetic coding. The time domain representation may use an ACELP excitation coding scheme. The enhanced Spectral Band Replication (eSBR) unit 1001 of the encoder 1000 may 25 comprise high frequency reconstruction components outlined in the present document. In some embodiments, the eSBR unit 1001 may comprise a transposition unit outlined in the context of Fig. 4, 5 and 6. Encoded data related to harmonic transposition, e.g. the order of transposition used, the amount of frequency domain oversampling needed, or the gains employed, may be derived in the encoder 1000 and merged with the other en 30 coded information in a bitstream multiplexer and forwarded as an encoded audio stream to a corresponding decoder 1100.

- 42 The decoder 1100 shown in Fig. 11 also comprises an enhanced Spectral Bandwidth Replication (eSBR) unit 1101. This eSBR unit 1101 receives the encoded audio bit stream or the encoded signal from the encoder 1000 and uses the methods outlined in the present document to generate a high frequency component or high band of the sig 5 nal, which is merged with the decoded low frequency component or low band to yield a decoded signal. The eSBR unit 1101 may comprise the different components outlined in the present document. In particular, it may comprise the transposition unit outlined in the context of Figs. 4, 5 and 6. The eSBR unit 1101 may use information on the high frequency component provided by the encoder 1000 via the bitstream in order to per 10 form the high frequency reconstruction. Such information may be the spectral envelope of the original high frequency component to generate the synthesis subband signals and ultimately the high frequency component of the decoded signal, as well as the order of transposition used, the amount of frequency domain oversampling needed, or the gains employed. 15 Furthermore, Figs. 10 and 11 illustrate possible additional components of a USAC en coder/decoder, such as: * a bitstream payload demultiplexer tool, which separates the bitstream payload into the parts for each tool, and provides each of the tools with the bitstream 20 payload information related to that tool; e a scalefactor noiseless decoding tool, which takes information from the bitstream payload demultiplexer, parses that information, and decodes the Huffman and DPCM coded scalefactors; e a spectral noiseless decoding tool, which takes information from the bitstream 25 payload demultiplexer, parses that information, decodes the arithmetically coded data, and reconstructs the quantized spectra; e an inverse quantizer tool, which takes the quantized values for the spectra, and converts the integer values to the non-scaled, reconstructed spectra; this quantiz er is preferably a companding quantizer, whose companding factor depends on 30 the chosen core coding mode; - 43 * a noise filling tool, which is used to fill spectral gaps in the decoded spectra, which occur when spectral values are quantized to zero e.g. due to a strong re striction on bit demand in the encoder; e a resealing tool, which converts the integer representation of the scalefactors to 5 the actual values, and multiplies the un-scaled inversely quantized spectra by the relevant scalefactors; e a M/S tool, as described in ISO/IEC 14496-3; e a temporal noise shaping (TNS) tool, as described in ISO/IEC 14496-3; e a filter bank / block switching tool, which applies the inverse of the frequency 10 mapping that was carried out in the encoder; an inverse modified discrete cosine transform (IMDCT) is preferably used for the filter bank tool; e a time-warped filter bank / block switching tool, which replaces the normal filter bank / block switching tool when the time warping mode is enabled; the filter bank preferably is the same (IMDCT) as for the normal filter bank, additionally 15 the windowed time domain samples are mapped from the warped time domain to the linear time domain by time-varying resampling; e an MPEG Surround (MPEGS) tool, which produces multiple signals from one or more input signals by applying a sophisticated upmix procedure to the input sig nal(s) controlled by appropriate spatial parameters; in the USAC context, 20 MPEGS is preferably used for coding a multichannel signal, by transmitting parametric side information alongside a transmitted downmixed signal; e a signal classifier tool, which analyses the original input signal and generates from it control information which triggers the selection of the different coding modes; the analysis of the input signal is typically implementation dependent 25 and will try to choose the optimal core coding mode for a given input signal frame; the output of the signal classifier may optionally also be used to influence the behaviour of other tools, for example MPEG Surround, enhanced SBR, time warped filterbank and others; e an LPC filter tool, which produces a time domain signal from an excitation do 30 main signal by filtering the reconstructed excitation signal through a linear pre diction synthesis filter; and - 44 * an ACELP tool, which provides a way to efficiently represent a time domain ex citation signal by combining a long term predictor (adaptive codeword) with a pulse-like sequence (innovation codeword). 5 Fig. 12 illustrates an embodiment of the eSBR units shown in Figs. 10 and 11. The eSBR unit 1200 will be described in the following in the context of a decoder, where the input to the eSBR unit 1200 is the low frequency component, also known as the low band, of a signal. 10 In Fig. 12 the low frequency component 1213 is fed into a QMF filter bank, in order to generate QMF frequency bands. These QMF frequency bands are not to be mistaken with the analysis subbands outlined in this document. The QMF frequency bands are used for the purpose of manipulating and merging the low and high frequency compo nent of the signal in the frequency domain, rather than in the time domain. The low fre 15 quency component 1214 is fed into the transposition unit 1204 which corresponds to the systems for high frequency reconstruction outlined in the present document. The trans position unit 1204 generates a high frequency component 1212, also known as high band, of the signal, which is transformed into the frequency domain by a QMF filter bank 1203. Both, the QMF transformed low frequency component and the QMF trans 20 formed high frequency component are fed into a manipulation and merging unit 1205. This unit 1205 may perform an envelope adjustment of the high frequency component and combines the adjusted high frequency component and the low frequency compo nent.The combined output signal is re-transformed into the time domain by an inverse QMF filter bank 1201. 25 Typically the QMF filter bank 1202 comprise 32 QMF frequency bands. In such cases, the low frequency component 1213 has a bandwidth of f, /4, where f, /2 is the sam pling frequency of the signal 1213. The high frequency component 1212 typically has a bandwidth of f, /2 and is filtered through the QMF bank 1203 comprising 64 QMF 30 frequency bands.

- 45 In the present document, a method for harmonic transposition has been outlined. This method of harmonic transposition is particularly well suited for the transposition of transient signals. It comprises the combination of frequency domain oversampling with harmonic transposition using vocoders. The transposition operation depends on the 5 combination of analysis window, analysis window stride, transform size, synthesis win dow, synthesis window stride, as well as on phase adjustments of the analysed sig nal.Through the use of this method undesired effects, such as pre- and post-echoes, may be avoided. Furthermore, the method does not make use of signal analysis measures, such as transient detection, which typically introduce signal distortions due to disconti 10 nuities in the signal processing. In addition, the proposed method only has reduced computational complexity. The harmonic transposition method according to the inven tion may be further improved by an appropriate selection of analysis/synthesis win dows, gain values and/or time alignment. 15 The above references to and descriptions of prior proposals or products are not intended to be, and are not to be construed as, statements or admissions of common general knowledge in the art. In particular, the above prior art discussion does not relate to what is commonly or well known by the person skilled in the art, but assists in the understanding of the inventive step of the present invention of which the identification 20 of pertinent prior art proposals is but one part. Throughout the specification and claims the word "comprise" and its derivatives are intended to have an inclusive rather than exclusive meaning unless the contrary is expressly stated or the context requires otherwise. That is, the word "comprise" and its 25 derivatives will be taken to indicate the inclusion of not only the listed components, steps or features that it directly references, but also other components, steps or features not specifically listed, unless the contrary is expressly stated or the context requires otherwise. 30

Claims

1. A system for transposing an input audio signal by a transposition factor T, the system comprising: 5 -means for extracting a frame of L time-domain samples of the input signal using an analysis window having the function v(n)= sin i(n+0. 5 ) ,0 n < L, SL -means for transforming the L time-domain samples into M complex frequency-domain coefficients; 10 -a nonlinear processing unit for altering a phase of the complex frequency domain coefficients using the transposition factor T; -means for transforming the altered frequency-domain coefficients into M altered time-domain samples; and -a means for generating a frame of L time-domain output samples from the 15 M altered time-domain samples using a synthesis window; wherein M=F*L, with F being greater or equal to (T+1)/2.

2. The system of any one of the previous claims, wherein the altering of the phase comprises multiplying the phase by the transposition factor T. 20

3. The system of any one of the previous claims, wherein the analysis window has a length L with zero padding by additional (F-1)*L zeros.

4. The system of any one of the previous claims, wherein the means for 25 transforming the altered frequency-domain coefficients comprise an analysis transformation unit of size M for transforming the L time-domain samples into M complex frequency-domain coefficients.

5. The system of any one of the previous claims, further comprising: 30 -an analysis stride unit, shifting the analysis window by an analysis stride along the input signal, thereby generating successive frames of the input signal; - 47 -a synthesis stride unit, shifting successive frames of L time-domain output samples by a synthesis stride; and -an overlap-add unit, overlapping and adding the successive shifted frames of L time-domain output samples, thereby generating an output signal. 5

6. The system of claim 5, further comprising a contraction unit, increasing the sampling rate of the output signal by the transposition factor T; thereby yielding a transposed output signal. 10

7. The system of claim 6, wherein the synthesis stride is T times the analysis stride.

8. The system of claim 6, further comprising: - a second nonlinear processing unit for altering a phase of the complex 15 frequency-domain coefficients using a second transposition factor T2, thereby yielding a frame of L second time-domain output samples; and - a second synthesis stride unit, shifting successive frames of L second time domain output samples by a second synthesis stride, thereby generating a second output signal in the overlap-add unit. 20

9. The system of claim 8, further comprising - a second contraction unit, using the second transposition factor T2, thereby yielding a second transposed output signal; and - a combining unit, merging the transposed output signal and the second 25 transposed output signal.

10. A method for transposing an input audio signal by a transposition factor T, the method comprising: -extracting a frame of L time-domain samples of the input signal using an 30 analysis window having the function v(n)= sin !(n + 0.5) ,0 n < L, SL - 48 -transforming the L time-domain samples into M complex frequency domain coefficients, -altering a phase of the complex frequency-domain coefficients using the transposition factor T; 5 -transforming the altered frequency-domain coefficients into M altered time-domain samples; and -generating a frame of L time-domain output samples from the M altered time-domain samples using a synthesis window; wherein M=F*L, with F being greater or equal to (T+1)/2. 10

11. The method of claim 10, wherein transforming the L time-domain samples into M complex frequency-domain coefficients is performing one of a Fourier Transform, a Fast Fourier Transform, a Discrete Fourier Transform, a Wavelet Transform. 15

12. The method of claim 10, further comprising the steps of: -shifting the analysis window by an analysis stride along the input signal, thereby generating successive frames of the input signal; -shifting successive frames of L time-domain output samples by a synthesis 20 stride; and -overlapping and adding the successive shifted frames of L time-domain output samples, thereby generating an output signal.

13. The method of claim 12, further comprising the step of performing 25 downsampling of the output signal by the transposition factor T while keeping the sampling rate unchanged, thereby yielding a transposed output signal.

14. The method of claim 10, wherein a z transform of the analysis window has dual zeros on the unit circle. 30 - 49

15. A storage medium comprising a software program adapted for execution on a processor and for performing the method steps of any of claims 10 to 14 when carried out on a computing device. 5