Patent Description:
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-<NUM> Advanced Audio Coding (AAC) it forms a very efficient audio codec, which is already in use within the XM Satellite Radio system and Digital Radio Mondiale. The combination of AAC and SBR is called aacPlus. It is part of the MPEG-<NUM> standard where it is referred to as the High Efficiency AAC Profile. In general, HFR technology can be combined with any perceptual audio codec in a back and forward compatible way, thus offering the possibility to upgrade already established broadcasting systems like the MPEG Layer-<NUM> 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.

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 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 <CIT>, 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 applicable to speech coding and in unified speech and audio coding (USAC).

In a HFR based audio coding system, a low bandwidth signal is presented to a core waveform coder and the 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 shape. For low bit-rates, where the bandwidth of the core coded signal is narrow, it becomes increasingly important to recreate a high band, i.e. the high frequency range of the audio signal, with perceptually pleasant characteristics. Two variants of harmonic frequency reconstruction methods are mentioned in the following, one is referred to as harmonic transposition and the other one is referred to as single sideband modulation.

The principle of harmonic transposition defined in <CIT> is that a sinusoid with frequency ω is mapped to a sinusoid with frequency T ω where T > <NUM> is an integer defining the order of the transposition. An attractive feature of the harmonic transposition is that it stretches a source frequency range into a target frequency range by a factor equal to the order of transposition, i.e. by a factor equal to T. The harmonic transposition performs well for complex musical material. Furthermore, harmonic transposition exhibits low cross over frequencies, i.e. a large high frequency range above the cross over frequency can be generated from a relatively small low frequency range below the cross over frequency.

In contrast to harmonic transposition, a single sideband modulation (SSB) based HFR maps a sinusoid with frequency ω to a sinusoid with frequency ω+ Δω where Δω is a fixed frequency shift. It has been observed that, given a core signal with low bandwidth, a dissonant ringing artifact may result from the SSB transposition. It should also be noted that for a low cross-over frequency, i.e. a small source frequency range, harmonic transposition will require a smaller number of patches in order to fill a desired target frequency range than SSB based transposition. By way of example, if the high frequency range of (ω, <NUM>ω] should be filled, then using an order of transposition T = <NUM> harmonic transposition can fill this frequency range from a low frequency range of <MAT>. On the other hand, a SSB based transposition using the same low frequency range must use a frequency shift of <MAT> and it is necessary to repeat the process four times in order to fill the high frequency range (ω, <NUM>ω].

On the other hand, as already pointed out in <CIT>, harmonic transposition has drawbacks for signals with a prominent periodic structure. Such signals are superimpositions of harmonically related sinusoids with frequencies Ω, 2Ω, 3Ω,. , where Ω is the fundamental frequency.

Upon harmonic transposition of order T , the output sinusoids have frequencies TΩ, <NUM>TΩ, <NUM>TΩ,. , which, in case of T > <NUM>, is only a strict subset of the desired full harmonic series. In terms of resulting audio quality a "ghost" pitch corresponding to the transposed fundamental frequency TΩ will typically be perceived. Often the harmonic transposition results in a "metallic" sound character of the encoded and decoded audio signal. The situation may be alleviated to a certain degree by adding several orders of transposition T = <NUM>,<NUM>,. , Tmax to the HFR, but this method is computationally complex if most spectral gaps are to be avoided.

An alternative solution for avoiding the appearance of "ghost" pitches when using harmonic transposition has been presented in <CIT>. The solution consists in using two types of transposition, i.e. a typical harmonic transposition and a special "pulse transposition". The described method teaches to switch to the dedicated "pulse transposition" for parts of the audio signal that are detected to be periodic with pulse-train like character. The problem with this approach is that the application of "pulse transposition" on complex music material often degrades the quality compared to harmonic transposition based on a high resolution filter bank. Hence, the detection mechanisms have to be tuned rather conservatively such that pulse transposition is not used for complex material. Inevitably, single pitch instruments and voices will sometimes be classified as complex signals, hereby invoking harmonic transposition and therefore missing harmonics. Moreover, if switching occurs in the middle of a single pitched signal, or a signal with a dominating pitch in a weaker complex background, the switching itself between the two transposition methods having very different spectrum filling properties will generate audible artifacts. Another variant for performing harmonic frequency reconstruction is proposed in <CIT>.

Embodiments of the present invention are defined by the independent claims. Additional features of embodiments of the invention are presented in the dependent claims. In the following, parts of the description and drawings referring to former embodiments which do not necessarily comprise all features to implement embodiments of the claimed invention are not represented as embodiments of the invention but as examples useful for understanding the embodiments of the invention.

The present invention will now be described by way of illustrative examples, not limiting the scope of the invention. It will be described with reference to the accompanying drawings, in which:.

The below-described embodiments are merely illustrative for the principles of the present invention for the so-called CROSS PRODUCT ENHANCED 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 and explanation of the embodiments herein.

<FIG> illustrates the operation of an HFR enhanced audio decoder. The core audio decoder <NUM> outputs a low bandwidth audio signal which is fed to an upsampler <NUM> which may be required in order to produce a final audio output contribution at the desired full sampling rate. Such upsampling 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 single rate system, this upsampler <NUM> is omitted. The low bandwidth output of <NUM> is also sent to the transposer or the transposition unit <NUM> 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 <NUM>. The final audio output is the sum of low bandwidth core signal and the envelope adjusted transposed signal.

<FIG> illustrates the operation of a harmonic transposer <NUM>, which corresponds to the transposer <NUM> of <FIG>, comprising several transposers of different transposition order T. The signal to be transposed is passed to the bank of individual transposers <NUM>-<NUM>, <NUM>-<NUM>,. , <NUM>-Tmax having orders of transposition T = <NUM>,<NUM>,. ,Tmax, respectively. Typically a transposition order Tmax = <NUM> suffices for most audio coding applications. The contributions of the different transposers <NUM>-<NUM>, <NUM>-<NUM>,. , <NUM>-Tmax are summed in <NUM> to yield the combined transposer output. In a first embodiment, this summing operation may comprise the adding up of the individual contributions. In another 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 contributions may be added with a lower gain than the second order contributions. Finally, the summing unit <NUM> may add the contributions selectively depending on the output frequency. For instance, the second order transposition may be used for a first lower target frequency range, and the third order transposition may be used for a second higher target frequency range.

<FIG> illustrates the operation of a frequency domain (FD) harmonic transposer, such as one of the individual blocks of <NUM>, i.e. one of the transposers <NUM>-T of transposition order T. An analysis filter bank <NUM> outputs complex subbands that are submitted to nonlinear processing <NUM>, which modifies the phase and/or amplitude of the subband signal according to the chosen transposition order T. The modified subbands are fed to a synthesis filterbank <NUM> which outputs the transposed time domain signal. In the case of multiple parallel transposers of different transposition orders such as shown in <FIG>, some filter bank operations may be shared between different transposers <NUM>-<NUM>, <NUM>-<NUM>,. , <NUM>-Tmax. The sharing of filter bank operations may be done for analysis or synthesis. In the case of shared synthesis <NUM>, the summing <NUM> can be performed in the subband domain, i.e. before the synthesis <NUM>.

<FIG> illustrates the operation of cross term processing <NUM> in addition to the direct processing <NUM>. The cross term processing <NUM> and the direct processing <NUM> are performed in parallel within the nonlinear processing block <NUM> of the frequency domain harmonic transposer of <FIG>. The transposed output signals are combined, e.g. added, in order to provide a joint transposed signal. This combination of transposed output signals may consist in the superposition of the transposed output signals. Optionally, the selective addition of cross terms may be implemented in the gain computation.

<FIG> illustrates in more detail the operation of the direct processing block <NUM> of <FIG> within the frequency domain harmonic transposer of <FIG>. Single-input-single-output (SISO) units <NUM>-<NUM>,. , <NUM>-n,. , <NUM>-N map each analysis subband from a source range into one synthesis subband in a target range. According to the <FIG>, an analysis subband of index n is mapped by the SISO unit <NUM>-n to a synthesis subband of the same index n. It should be noted that the frequency range of the subband with index n in the synthesis filter bank may vary depending on the exact version or type of harmonic transposition. In the version or type illustrated in <FIG>, the frequency spacing of the analysis bank <NUM> is a factor T smaller than that of the synthesis bank <NUM>. Hence, the index n in the synthesis bank <NUM> corresponds to a frequency, which is T times higher than the frequency of the subband with the same index n in the analysis bank <NUM>. By way of example, an analysis subband [(n - <NUM>)ω, nω] is transposed into a synthesis subband [(n - <NUM>)Tω, nTω].

<FIG> illustrates the direct nonlinear processing of a single subband contained in each of the SISO units of <NUM>-n. The nonlinearity of block <NUM> performs a multiplication of the phase of the complex subband signal by a factor equal to the transposition order T. The optional gain unit <NUM> modifies the magnitude of the phase modified subband signal. In mathematical terms, the outputy of the SISO unit <NUM>-n can be written as a function of the input x to the SISO system <NUM>-n and the gain parameter g as follows: <MAT>.

In words, the phase of the complex subband signal x is multiplied by the transposition order T and the amplitude of the complex subband signal x is modified by the gain parameter g.

<FIG> illustrates the components of the cross term processing <NUM> for an harmonic transposition of order T. There are T -<NUM> cross term processing blocks in parallel, <NUM>-<NUM>,. , <NUM>-r,. <NUM>-(T-<NUM>), whose outputs are summed in the summing unit <NUM> to produce a combined output. As already pointed out in the introductory section, it is a target to map a pair of sinusoids with frequencies (ω, ω+ Ω) to a sinusoid with frequency (T - r)ω + r(ω + Ω) = Tω + rΩ, wherein the variable r varies from <NUM> to T -<NUM>. In other words, two subbands from the analysis filter bank <NUM> are to be mapped to one subband of the high frequency range. For a particular value of r and a given transposition order T , this mapping step is performed in the cross term processing block <NUM>-r. <FIG> illustrates the operation of a cross term processing block <NUM>-r for a fixed value r = <NUM>,<NUM>,. Each output subband <NUM> is obtained in a multiple-input-single-output (MISO) unit <NUM>-n from two input subbands <NUM> and <NUM>. For an output subband <NUM> of index n, the two inputs of the MISO unit <NUM>-n are subbands n - p<NUM>, <NUM>, and n + p<NUM>, <NUM>, where p<NUM> and p<NUM> are positive integer index shifts, which depend on the transposition order T, the variable r, and the cross product enhancement pitch parameter Ω. The analysis and synthesis subband numbering convention is kept in line with that of <FIG>, that is, the spacing in frequency of the analysis bank <NUM> is a factor T smaller than that of the synthesis bank <NUM> and consequently the above comments given on variations of the factor T remain relevant.

In relation to the usage of cross term processing, the following remarks should be considered. The pitch parameter Ω does not have to be known with high precision, and certainly not with better frequency resolution than the frequency resolution obtained by the analysis filter bank <NUM>. In fact, in some embodiments of the present invention, the underlying cross product enhancement pitch parameter Ω is not entered in the decoder at all. Instead, the chosen pair of integer index shifts (p<NUM>, p<NUM>) is selected from a list of possible candidates by following an optimization criterion such as the maximization of the cross product output magnitude, i.e. the maximization of the energy of the cross product output. By way of example, for given values of T and r, a list of candidates given by the formula (p<NUM>, p<NUM>) = (rl, (T - r)l), l ∈ L , where L is a list of positive integers, could be used. This is shown in further detail below in the context of formula (<NUM>). All positive integers are in principle OK as candidates. In some cases pitch information may help to identify which l to choose as appropriate index shifts.

Furthermore, even though the example cross product processing illustrated in <FIG> suggests that the applied index shifts (p<NUM>, p<NUM>) are the same for a certain range of output subbands, e.g. synthesis subbands (n-<NUM>), n and (n+<NUM>) are composed from analysis subbands having a fixed distance p<NUM> + p<NUM>, this need not be the case. As a matter of fact, the index shifts (p<NUM>, p<NUM>) may differ for each and every output subband. This means that for each subband n a different value Ω of the cross product enhancement pitch parameter may be selected.

<FIG> illustrates the nonlinear processing contained in each of the MISO units <NUM>-n. The product operation <NUM> creates a subband signal with a phase equal to a weighted sum of the phases of the two complex input subband signals and a magnitude equal to a generalized mean value of the magnitudes of the two input subband samples. The optional gain unit <NUM> modifies the magnitude of the phase modified subband samples. In mathematical terms, the output y can be written as a function of the inputs u<NUM> <NUM> and u<NUM> <NUM> to the MISO unit <NUM>-n and the gain parameter g as follows, <MAT>.

This may also be written as: <MAT> where µ(|u<NUM>|,|u<NUM>|) is a magnitude generation function. In words, the phase of the complex subband signal u<NUM> is multiplied by the transposition order T- r and the phase of the complex subband signal u<NUM> is multiplied by the transposition order r. The sum of those two phases is used as the phase of the output y whose magnitude is obtained by the magnitude generation function. Comparing with the formula (<NUM>) the magnitude generation function is expressed as the geometric mean of magnitudes modified by the gain parameter g, that is µ(|u<NUM>|,|u<NUM>|) = g·|u<NUM>|<NUM>-r/T |u<NUM>|r/T. By allowing the gain parameter to depend on the inputs this of course covers all possibilities.

It should be noted that the formula (<NUM>) results from the underlying target that a pair of sinusoids with frequencies (ω, ω+Ω) are to be mapped to a sinusoid with frequency Tω + rΩ, which can also be written as (T - r)ω + r(ω+Ω).

In the following text, a mathematical description of the present invention will be outlined. For simplicity, continuous time signals are considered. The synthesis filter bank <NUM> is assumed to achieve perfect reconstruction from a corresponding complex modulated analysis filter bank <NUM> with a real valued symmetric window function or prototype filter w(t). The synthesis filter bank will often, but not always, use the same window in the synthesis process. The modulation is assumed to be of an evenly stacked type, the stride is normalized to one and the angular frequency spacing of the synthesis subbands is normalized to π. Hence, a target signal s(t) will be achieved at the output of the synthesis filter bank if the input subband signals to the synthesis filter bank are given by synthesis subband signals yn(k), <MAT>.

Note that formula (<NUM>) is a normalized continuous time mathematical model of the usual operations in a complex modulated subband analysis filter bank, such as a windowed Discrete Fourier Transform (DFT), also denoted as a Short Time Fourier Transform (STFT). With a slight modification in the argument of the complex exponential of formula (<NUM>), one obtains continuous time models for complex modulated (pseudo) Quadrature Mirror Filterbank (QMF) and complexified Modified Discrete Cosine Transform (CMDCT), also denoted as a windowed oddly stacked windowed DFT. The subband index n runs through all nonnegative integers for the continuous time case. For the discrete time counterparts, the time variable t is sampled at step <NUM> / N , and the subband index n is limited by N , where N is the number of subbands in the filter bank, which is equal to the discrete time stride of the filter bank. In the discrete time case, a normalization factor related to N is also required in the transform operation if it is not incorporated in the scaling of the window.

For a real valued signal, there are as many complex subband samples out as there are real valued samples in for the chosen filter bank model. Therefore, there is a total oversampling (or redundancy) by a factor two. Filter banks with a higher degree of oversampling can also be employed, but the oversampling is kept small in the present description of embodiments for the clarity of exposition.

The main steps involved in the modulated filter bank analysis corresponding to formula (<NUM>) are that the signal is multiplied by a window centered around time t = k , and the resulting windowed signal is correlated with each of the complex sinusoids exp[-inπ(t - k)]. In discrete time implementations this correlation is efficiently implemented via a Fast Fourier Transform. The corresponding algorithmic steps for the synthesis filter bank are well known for those skilled in the art, and consist of synthesis modulation, synthesis windowing, and overlap add operations.

<FIG> illustrates the position in time and frequency corresponding to the information carried by the subband sample yn(k) for a selection of values of the time index k and the subband index n. As an example, the subband sample y<NUM>(<NUM>) is represented by the dark rectangle <NUM>.

For a sinusoid, s(t)=Acos(ωt+θ)=Re{Cexp(iωt)}, the subband signals of (<NUM>) are for sufficiently large n with good approximation given by <MAT> where the hat denotes the Fourier transform, i.e. ŵ is the Fourier transform of the window function w. Strictly speaking, formula (<NUM>) is only true if one adds a term with -ω instead of ω. This term is neglected based on the assumption that the frequency response of the window decays sufficiently fast, and that the sum of ω and n is not close to zero.

<FIG> depicts the typical appearance of a window w, <NUM>, and its Fourier transform ŵ ,<NUM>.

<FIG> illustrates the analysis of a single sinusoid corresponding to formula (<NUM>). The subbands that are mainly affected by the sinusoid at frequency ω are those with index n such that nπ - ω is small. For the example of <FIG>, the frequency is ω=<NUM>π as indicated by the horizontal dashed line <NUM>. In that case, the three subbands for n = <NUM>, <NUM>, <NUM>, represented by reference signs <NUM>, <NUM>, <NUM>, respectively, contain significant nonzero subband signals. The shading of those three subbands reflects the relative amplitude of the complex sinusoids inside each subband obtained from formula (<NUM>). A darker shade means higher amplitude. In the concrete example, this means that the amplitude of subband <NUM>, i.e. <NUM>, is lower compared to the amplitude of subband <NUM>, i.e. <NUM>, which again is lower than the amplitude of subband <NUM>, i.e. <NUM>. It is important to note that several nonzero subbands may in general be necessary to be able to synthesize a high quality sinusoid at the output of the synthesis filter bank, especially in cases where the window has an appearance like the window <NUM> of <FIG>, with relatively short time duration and significant side lobes in frequency.

The synthesis subband signals yn(k) can also be determined as a result of the analysis filter bank <NUM> and the non-linear processing, i.e. harmonic transposer <NUM> illustrated in <FIG>. On the analysis filter bank side, the analysis subband signals xn(k) may be represented as a function of the source signal z(t). For a transposition of order T, a complex modulated analysis filter bank with window wT(t) = w(t/T)/T, a stride one, and a modulation frequency step, which is T times finer than the frequency step of the synthesis bank, is applied on the source signal z(t). <FIG> illustrates the appearance of the scaled window wT <NUM> and its Fourier transform ŵT <NUM>. Compared to <FIG>, the time window <NUM> is stretched out and the frequency window <NUM> is compressed.

The analysis by the modified filter bank gives rise to the analysis subband signals xn(k): <MAT>.

For a sinusoid, z(t) = Bcos(ξt+ϕ) = Re{Dexp(iξt)}, one finds that the subband signals of (<NUM>) for sufficiently large n with good approximation are given by <MAT>.

Hence, submitting these subband signals to the harmonic transposer <NUM> and applying the direct transposition rule (<NUM>) to (<NUM>) yields <MAT>.

The synthesis subband signals yn(k) given by formula (<NUM>) and the nonlinear subband signals obtained through harmonic transposition ỹn(k) given by formal (<NUM>) ideally should match.

For odd transposition orders T , the factor containing the influence of the window in (<NUM>) is equal to one, since the Fourier transform of the window is real valued by assumption, and T -<NUM> is an even number. Therefore, formula (<NUM>) can be matched exactly to formula (<NUM>) with ω=Tξ, for all subbands, such that the output of the synthesis filter bank with input subband signals according to formula (<NUM>) is a sinusoid with a frequency ω = Tξ, amplitude A = gB, and phase θ = Tϕ, wherein B and ϕ are determined from the formula: D = B exp(iϕ), which upon insertion yields <MAT>. Hence, a harmonic transposition of order T of the sinusoidal source signal z(t) is obtained.

For even T , the match is more approximate, but it still holds on the positive valued part of the window frequency response ŵ, which for a symmetric real valued window includes the most important main lobe. This means that also for even values of T a harmonic transposition of the sinusoidal source signal z(t) is obtained. In the particular case of a Gaussian window, ŵ is always positive and consequently, there is no difference in performance for even and odd orders of transposition.

Similarly to formula (<NUM>), the analysis of a sinusoid with frequency ξ+Ω, i.e. the sinusoidal source signal z(t) = B'cos((ξ + Ω)t + ϕ') = Re{E exp(i(ξ +Ω)t)}, is<MAT>.

Therefore, feeding the two subband signals u<NUM> = xn-p<NUM> (k), which corresponds to the signal <NUM> in <FIG>, and u<NUM> = x'n+p<NUM> (k), which corresponds to the signal <NUM> in <FIG>, into the cross product processing <NUM>-n illustrated in <FIG> and applying the cross product formula (<NUM>) yields the output subband signal <NUM> <MAT> where <MAT>.

From formula (<NUM>) it can be seen that the phase evolution of the output subband signal <NUM> of the MISO system <NUM>-n follows the phase evolution of an analysis of a sinusoid of frequency Tξ + rΩ. This holds independently of the choice of the index shifts p<NUM> and p<NUM>. In fact, if the subband signal (<NUM>) is fed into a subband channel n corresponding to the frequency Tξ + rΩ , that is if nπ ≈ Tξ + rΩ , then the output will be a contribution to the generation of a sinusoid at frequency Tξ + rΩ. However, it is advantageous to make sure that each contribution is significant, and that the contributions add up in a beneficial fashion. These aspects will be discussed below.

Given a cross product enhancement pitch parameter Ω , suitable choices for index shifts p<NUM> and p<NUM> can be derived in order for the complex magnitude M (n, ξ) of (<NUM>) to approximate ŵ(nπ - (Tξ + rΩ)) for a range of subbands n, in which case the final output will approximate a sinusoid at the frequency Tξ + rΩ. A first consideration on main lobes imposes all three values of (n - p<NUM>)π - Tξ, (n + p<NUM>)π - T(ξ + Ω), nπ - (Tξ + rΩ) to be small simultaneously, which leads to the approximate equalities <MAT>.

This means that when knowing the cross product enhancement pitch parameter Ω , the index shifts may be approximated by fomula (<NUM>), thereby allowing a simple selection of the analysis subbands. A more thorough analysis of the effects of the choice of the index shifts p<NUM> and p<NUM> according to formula (<NUM>) on the magnitude of the parameter M(n, ξ) according to formula (<NUM>) can be performed for important special cases of window functions w(t) such as the Gaussian window and a sine window. One finds that the desired approximation to ŵ(nπ - (Tξ + rΩ)) is very good for several subbands with nπ ≈ Tξ + rΩ.

It should be noted that the relation (<NUM>) is calibrated to the exemplary situation where the analysis filter bank <NUM> has an angular frequency subband spacing of π/T. In the general case, the resulting interpretation of (<NUM>) is that the cross term source span p<NUM> + p<NUM> is an integer approximating the underlying fundamental frequency Ω, measured in units of the analysis filter bank subband spacing, and that the pair (p<NUM>, p<NUM>) is chosen as a multiple of (r,T - r).

For the determination of the index shift pair (p<NUM>, p<NUM>) in the decoder the following modes may be used:.

It should be noted that phase modification of the subband signals u<NUM> and u<NUM> is performed with a weighting (T - r) and r, respectively, but the subband index distance p<NUM> and p<NUM> are chosen proportional to r and (T - r), respectively. Thus the closest subband to the synthesis subband n receives the strongest phase modification.

An advantageous method for the optimization procedure for the modes <NUM> and <NUM> outlined above may be to consider the Max-Min optimization: <MAT> and to use the winning pair together with its corresponding value of r to construct the cross product contribution for a given target subband index n. In the decoder search oriented modes <NUM> and partially also <NUM>, the addition of cross terms for different values r is preferably done independently, since there may be a risk of adding content to the same subband several times. If, on the other hand, the fundamental frequency Ω is used for selecting the subbands as in mode <NUM> or if only a narrow range of subband index distances are permitted as may be the case in mode <NUM>, this particular issue of adding content to the same subband several times may be avoided.

Furthermore, it should also be noted that for the embodiments of the cross term processing schemes outlined above an additional decoder modification of the cross product gain g may be beneficial. For instance, it is referred to the input subband signals u<NUM>, u<NUM> to the cross products MISO unit given by formula (<NUM>) and the input subband signal x to the transposition SISO unit given by formula (<NUM>). If all three signals are to be fed to the same output synthesis subband as shown in <FIG>, where the direct processing <NUM> and the cross product processing <NUM> provide components for the same output synthesis subband, it may be desirable to set the cross product gain g to zero, i.e. the gain unit <NUM> of <FIG>, if <MAT> for a pre-defined threshold q > <NUM>. In other words, the cross product addition is only performed if the direct term input subband magnitude |x| is small compared to both of the cross product input terms. In this context, x is the analysis subband sample for the direct term processing which leads to an output at the same synthesis subband as the cross product under consideration. This may be a precaution in order to not enhance further a harmonic component that has already been furnished by the direct transposition.

In the following, the harmonic transposition method outlined in the present document will be described for exemplary spectral configurations to illustrate the enhancements over the prior art. <FIG> illustrates the effect of direct harmonic transposition of order T = <NUM>. The top diagram <NUM> depicts the partial frequency components of the original signal by vertical arrows positioned at multiples of the fundamental frequency Ω. It illustrates the source signal, e.g. at the encoder side. The diagram <NUM> is segmented into a left sided source frequency range with the partial frequencies Ω,2Ω,3Ω,4Ω,5Ω and a right sided target frequency range with partial frequencies 6Ω,7Ω,8Ω. The source frequency range will typically be encoded and transmitted to the decoder. On the other hand, the right sided target frequency range, which comprises the partials 6Ω,7Ω,8Ω above the cross over frequency <NUM> of the HFR method, will typically not be transmitted to the decoder. It is an object of the harmonic transposition method to reconstruct the target frequency range above the cross-over frequency <NUM> of the source signal from the source frequency range. Consequently, the target frequency range, and notably the partials 6Ω,7Ω,8Ω in diagram <NUM> are not available as input to the transposer.

As outlined above, it is the aim of the harmonic transposition method to regenerate the signal components 6Ω,7Ω,8Ω of the source signal from frequency components available in the source frequency range. The bottom diagram <NUM> shows the output of the transposer in the right sided target frequency range. Such transposer may e.g. be placed at the decoder side. The partials at frequencies 6Ω and 8Ω are regenerated from the partials at frequencies 3Ω and 4Ω by harmonic transposition using an order of transposition T = <NUM>. As a result of a spectral stretching effect of the harmonic transposition, depicted here by the dotted arrows <NUM> and <NUM>, the target partial at 7Ω is missing. This target partial at 7Ω can not be generated using the underlying prior art harmonic transposition method.

<FIG> illustrates the effect of the invention for harmonic transposition of a periodic signal in the case where a second order harmonic transposer is enhanced by a single cross term, i.e. T = <NUM> and r = <NUM>. As outlined in the context of <FIG>, a transposer is used to generate the partials 6Ω,7Ω,8Ω in the target frequency range above the cross-over frequency <NUM> in the lower diagram <NUM> from the partials Ω,2Ω,3Ω,4Ω,5Ω in the source frequency range below the cross-over frequency <NUM> of diagram <NUM>. In addition to the prior art transposer output of <FIG>, the partial frequency component at 7Ω is regenerated from a combination of the source partials at 3Ω and 4Ω. The effect of the cross product addition is depicted by dashed arrows <NUM> and <NUM>. In terms of formulas, one has ω = 3Ω and therefore (T - r)ω + r(ω + Ω) = Tω + rΩ = 6Ω + Ω = 7Q. As can be seen from this example, all the target partials may be regenerated using the inventive HFR method outlined in the present document.

<FIG> illustrates a possible implementation of a prior art second order harmonic transposer in a modulated filter bank for the spectral configuration of <FIG>. The stylized frequency responses of the analysis filter bank subbands are shown by dotted lines, e.g. reference sign <NUM>, in the top diagram <NUM>. The subbands are enumerated by the subband index, of which the indexes <NUM>, <NUM> and <NUM> are shown in <FIG>. For the given example, the fundamental frequency Ω is equal to <NUM> times the analysis subband frequency spacing. This is illustrated by the fact that the partial Ω in diagram <NUM> is positioned between the two subbands with subband index <NUM> and <NUM>. The partial 2Ω is positioned in the center of the subband with subband index <NUM> and so forth.

The bottom diagram <NUM> shows the regenerated partials 6Ω and 8Ω superimposed with the stylized frequency responses, e.g. reference sign <NUM>, of selected synthesis filter bank subbands. As described earlier, these subbands have a T = <NUM> times coarser frequency spacing. Correspondingly, also the frequency responses are scaled by the factor T = <NUM>. As outlined above, the prior art direct term processing method modifies the phase of each analysis subband, i.e. of each subband below the cross-over frequency <NUM> in diagram <NUM>, by a factor T = <NUM> and maps the result into the synthesis subband with the same index, i.e. a subband above the cross-over frequency <NUM> in diagram <NUM>. This is symbolized in <FIG> by diagonal dotted arrows, e.g. arrow <NUM> for the analysis subband <NUM> and the synthesis subband <NUM>. The result of this direct term processing for subbands with subband indexes <NUM> to <NUM> from the analysis subband <NUM> is the regeneration of the two target partials at frequencies 6Ω and 8Ω in the synthesis subband <NUM> from the source partials at frequencies 3Ω and 4Ω. As can be seen from <FIG>, the main contribution to the target partial 6Ω comes from the subbands with the subband indexes <NUM> and <NUM>, i.e. reference signs <NUM> and <NUM>, and the main contribution to the target partial 8Ω comes from the subband with subband index <NUM>, i.e. reference sign <NUM>.

<FIG> illustrates a possible implementation of an additional cross term processing step in the modulated filter bank of <FIG>. The cross-term processing step corresponds to the one described for periodic signals with the fundamental frequency Ω in relation to <FIG>. The upper diagram <NUM> illustrates the analysis subbands, of which the source frequency range is to be transposed into the target frequency range of the synthesis subbands in the lower diagram <NUM>. The particular case of the generation of the synthesis subbands <NUM> and <NUM>, which are surrounding the partial 7Ω, from the analysis subbands is considered. For an order of transposition T = <NUM>, a possible value r = <NUM> may be selected. Choosing the list of candidate values (p<NUM>, p<NUM>) as a multiple of (r, T - r) = (<NUM>,<NUM>) such that p<NUM> + p<NUM> approximates <MAT>, i.e. the fundamental frequency Ω in units of the analysis subband frequency spacing, leads to the choice p<NUM> = p<NUM> = <NUM>. As outlined in the context of <FIG>, a synthesis subband with the subband index n may be generated from the cross-term product of the analysis subbands with the subband index (n - p<NUM>) and (n + p<NUM>). Consequently, for the synthesis subband with subband index <NUM>, i.e. reference sign <NUM>, a cross product is formed from the analysis subbands with subband index (n - p<NUM>) = <NUM> - <NUM> = <NUM>, i.e. reference sign <NUM>, and
(n + p<NUM>) = <NUM> + <NUM> = <NUM>, i.e. reference sign <NUM>. For the synthesis subband with subband index <NUM>, a cross product is formed from analysis subbands with and index (n - p<NUM>) = <NUM> - <NUM> = <NUM>, i.e. reference sign <NUM>, and (n + p<NUM>) = <NUM> + <NUM> = <NUM>, i.e. reference sign <NUM>. This process of cross-product generation is symbolized by the diagonal dashed/dotted arrow pairs, i.e. reference sign pairs <NUM>, <NUM> and <NUM>, <NUM>, respectively.

As can be seen from <FIG>, the partial 7Ω is placed primarily within the subband <NUM> with index <NUM> and only secondarily in the subband <NUM> with index <NUM>. Consequently, for more realistic filter responses, there will be more direct and/or cross terms around synthesis subband <NUM> with index <NUM> which add beneficially to the synthesis of a high quality sinusoid at frequency (T - r)ω + r(ω + Ω) = Tω + rΩ = 6Ω + Ω = 7Ω than terms around synthesis subband <NUM> with index <NUM>. Furthermore, as highlighted in the context of formula (<NUM>), a blind addition of all cross terms with p<NUM> = p<NUM> = <NUM> could lead to unwanted signal components for less periodic and academic input signals. Consequently, this phenomenon of unwanted signal components may require the application of an adaptive cross product cancellation rule such as the rule given by formula (<NUM>).

<FIG> illustrates the effect of prior art harmonic transposition of order T = <NUM>. The top diagram <NUM> depicts the partial frequency components of the original signal by vertical arrows positioned at multiples of the fundamental frequency Ω. The partials 6Ω,7Ω,8Ω,9Ω are in the target range above the cross over frequency <NUM> of the HFR method and therefore not available as input to the transposer. The aim of the harmonic transposition is to regenerate those signal components from the signal in the source range. The bottom diagram <NUM> shows the output of the transposer in the target frequency range. The partials at frequencies 6Ω , i.e. reference sign <NUM>, and 9Ω , i.e. reference sign <NUM>, have been regenerated from the partials at frequencies 2Ω, i.e. reference sign <NUM>, and 3Ω, i.e. reference sign <NUM>. As a result of a spectral stretching effect of the harmonic transposition, depicted here by the dotted arrows <NUM> and <NUM>, respectively, the target partials at 7Ω and 8Ω are missing.

<FIG> illustrates the effect of the invention for the harmonic transposition of a periodic signal in the case where a third order harmonic transposer is enhanced by the addition of two different cross terms, i.e. T = <NUM> and r = <NUM>,<NUM>. In addition to the prior art transposer output of <FIG>, the partial frequency component <NUM> at 7Ω is regenerated by the cross term for r = <NUM> from a combination of the source partials <NUM> at 2Ω and <NUM> at 3Ω. The effect of the cross product addition is depicted by the dashed arrows <NUM> and <NUM>. In terms of formulas, one has with ω = 2Ω, (T - r)ω + r(ω + Ω) = Tω + rΩ = 6Ω + Ω = 7Q. Likewise, the partial frequency component <NUM> at 8Ω is regenerated by the cross term for r = <NUM>. This partial frequency component <NUM> in the target range of the lower diagram <NUM> is generated from the partial frequency components <NUM> at 2Ω and <NUM> at 3Ω in the source frequency range of the upper diagram <NUM>. The generation of the cross term product is depicted by the arrows <NUM> and <NUM>. In terms of formulas, one has (T - r)ω + r(ω + Ω) = Tω + rΩ = 6Ω + 2Ω = 8Ω. As can be seen, all the target partials may be regenerated using the inventive HFR method described in the present document.

<FIG> illustrates a possible implementation of a prior art third order harmonic transposer in a modulated filter bank for the spectral situation of <FIG>. The stylized frequency responses of the analysis filter bank subbands are shown by dotted lines in the top diagram <NUM>. The subbands are enumerated by the subband indexes <NUM> through <NUM> of which the subbands <NUM>, with index <NUM>, <NUM>, with index <NUM> and <NUM>, with index <NUM>, are referenced in an exemplary manner. For the given example, the fundamental frequency Ω is equal to <NUM> times the analysis subband frequency spacing Δω. The bottom diagram <NUM> shows the regenerated partial frequency superimposed with the stylized frequency responses of selected synthesis filter bank subbands. By way of example, the subbands <NUM>, with subband index <NUM>, <NUM>, with subband index <NUM> and <NUM>, with subband index <NUM> are referenced. As described above, these subbands have a T = <NUM> times coarser frequency spacing Δω. Correspondingly, also the frequency responses are scaled accordingly.

The prior art direct term processing modifies the phase of the subband signals by a factor T = <NUM> for each analysis subband and maps the result into the synthesis subband with the same index, as symbolized by the diagonal dotted arrows. The result of this direct term processing for subbands <NUM> to <NUM> is the regeneration of the two target partial frequencies 6Ω and 9Ω from the source partials at frequencies 2Ω and 3Ω. As can be seen from <FIG>, the main contribution to the target partial 6Ω comes from subband with index <NUM>, i.e. reference sign <NUM>, and the main contributions to the target partial 9Ω comes from subbands with index <NUM> and <NUM>, i.e. reference signs <NUM> and <NUM>, respectively.

<FIG> illustrates a possible implementation of an additional cross term processing step for r = <NUM> in the modulated filter bank of <FIG> which leads to the regeneration of the partial at 7Ω. As was outlined in the context of <FIG> the index shifts (p<NUM>, p<NUM>) may be selected as a multiple of (r,T - r) = (<NUM>,<NUM>), such that p<NUM> + p<NUM> approximates <NUM>, i.e. the fundamental frequency Ω in units of the analysis subband frequency spacing Δω. In other words, the relative distance, i.e. the distance on the frequency axis divided by the analysis subband frequency spacing Δω, between the two analysis subbands contributing to the synthesis subband which is to be generated, should best approximate the relative fundamental frequency, i.e. the fundamental frequency Ω divided by the analysis subband frequency spacing Δω. This is also expressed by formulas (<NUM>) and leads to the choice p<NUM> = <NUM>, p<NUM> = <NUM>.

As shown in <FIG>, the synthesis subband with index <NUM>, i.e. reference sign <NUM>, is obtained from a cross product formed from the analysis subbands with index (n - p<NUM>) = <NUM> -<NUM> = <NUM>, i.e. reference sign <NUM>, and (n + p<NUM>) = <NUM> + <NUM> = <NUM>, i.e. reference sign <NUM>. For the synthesis subband with index <NUM>, a cross product is formed from analysis subbands with index (n - p<NUM>) = <NUM> -<NUM> = <NUM>, i.e. reference sign <NUM>, and (n + p<NUM>) = <NUM> + <NUM> = <NUM>, i.e. reference sign <NUM>. This process of forming cross products is symbolized by the diagonal dashed/dotted arrow pairs, i.e. arrow pair <NUM>, <NUM> and <NUM>, <NUM>, respectively. It can be seen from <FIG> that the partial frequency 7Ω is positioned more prominently in subband <NUM> than in subband <NUM>. Consequently, it is to be expected that for realistic filter responses, there will be more cross terms around synthesis subband with index <NUM>, i.e. subband <NUM>, which add beneficially to the synthesis of a high quality sinusoid at frequency (T - r)ω + r(ω + Ω) = Tω + rΩ = 6Ω + Ω = 7Q.

<FIG> illustrates a possible implementation of an additional cross term processing step for r = <NUM> in the modulated filterbank of <FIG> which leads to the regeneration of the partial frequency at 8Ω. The index shifts (p<NUM>, p<NUM>) may be selected as a multiple of (r,T - r) = (<NUM>,<NUM>), such that p<NUM> + p<NUM> approximates <NUM>, i.e. the fundamental frequency Ω in units of the analysis subband frequency spacing Δω. This leads to the choice p<NUM> = <NUM>, p<NUM> = <NUM>. As shown in <FIG>, the synthesis subband with index <NUM>, i.e. reference sign <NUM>, is obtained from a cross product formed from the analysis subbands with index (n - p<NUM>) = <NUM> - <NUM> = <NUM>, i.e. reference sign <NUM>, and (n + p<NUM>) = <NUM> +<NUM> = <NUM>, i.e. reference sign <NUM>. For the synthesis subband with index <NUM>, a cross product is formed from analysis subbands with index (n - p<NUM>) = <NUM> - <NUM> = <NUM>, i.e. reference sign <NUM>, and (n + p<NUM>) = <NUM> +<NUM> = <NUM>, i.e. reference sign <NUM>. This process of forming cross products is symbolized by the diagonal dashed/dotted arrow pairs, i.e. arrow pair <NUM>, <NUM> and <NUM>, <NUM>, respectively. It can be seen from <FIG> that the partial frequency 8Ω is positioned slightly more prominently in subband <NUM> than in subband <NUM>. Consequently, it is to be expected that for realistic filter responses, there will be more direct and/or cross terms around synthesis subband with index <NUM>, i.e. subband <NUM>, which add beneficially to the synthesis of a high quality sinusoid at frequency (T - r)ω + r(ω + Ω) = Tω + rΩ = 2Ω + 6Ω = 8Ω.

In the following, reference is made to <FIG> and <FIG> which illustrate the Max-Min optimization based selection procedure (<NUM>) for the index shift pair (p<NUM>, p<NUM>) and r according to this rule for T = <NUM>. The chosen target subband index is n = <NUM> and the top diagram furnishes an example of the magnitude of a subband signal for a given time index. The list of positive integers is given here by the seven values L = {<NUM>,<NUM>,.

<FIG> illustrates the search for candidates with r = <NUM>. The target or synthesis subband is shown with the index n = <NUM>. The dotted line <NUM> highlights the subband with the index n = <NUM> in the upper analysis subband range and the lower synthesis subband range. The possible index shift pairs are (p<NUM>, p<NUM>) = {(<NUM>,<NUM>),(<NUM>,<NUM>),. ,(<NUM>,<NUM>)} , for l = <NUM>,<NUM>,. ,<NUM>, respectively, and the corresponding analysis subband magnitude sample index pairs, i.e. the list of subband index pairs that are considered for determining the optimal cross term, are {(<NUM>, <NUM>), (<NUM>,<NUM>),. , (<NUM>,<NUM>)}. The set of arrows illustrate the pairs under consideration. As an example, the pair (<NUM>,<NUM>) denoted by the reference signs <NUM> and <NUM> is shown. Evaluating the minimum of these magnitude pairs gives the list (<NUM>, <NUM>,<NUM>, <NUM>, <NUM>, <NUM>, <NUM>) of respective minimum magnitudes for the possible list of cross terms. Since the second entry for l = <NUM> is maximal, the pair (<NUM>,<NUM>) wins among the candidates with r = <NUM>, and this selection is depicted by the thick arrows.

<FIG> similarly illustrates the search for candidates with r = <NUM>. The target or synthesis subband is shown with the index n = <NUM>. The dotted line <NUM> highlights the subband with the index n = <NUM> in the upper analysis subband range and the lower synthesis subband range. In this case, the possible index shift pairs are (p<NUM>, p<NUM>) = {(<NUM>, <NUM>), (<NUM>,<NUM>),. , (<NUM>, <NUM>)} and the corresponding analysis subband magnitude sample index pairs are {(<NUM>,<NUM>), (<NUM>,<NUM>),. , (<NUM>,<NUM>)} , of which the pair (<NUM>,<NUM>) is represented by the reference signs <NUM> and <NUM>. Evaluating the minimum of these magnitude pairs gives the list (<NUM>, <NUM>, <NUM>, <NUM>, <NUM>,<NUM>, <NUM>). Since the fifth entry is maximal, i.e. / = <NUM>, the pair (<NUM>,<NUM>) wins among the candidates with r = <NUM>, as depicted by the thick arrows. Overall, since the minimum of the corresponding magnitude pair is smaller than that of the selected subband pair for r = <NUM>, the final selection for target subband index n = <NUM> falls on the pair (<NUM>,<NUM>) and r = <NUM>.

It should further more be noted that when the input signal z(t) is a harmonic series with a fundamental frequency Ω, i.e. with a fundamental frequency which corresponds to the cross product enhancement pitch parameter, and Ω is sufficiently large compared to the frequency resolution of the analysis filter bank, the analysis subband signals xn(k) given by formula (<NUM>) and <MAT> given by formula (<NUM>) are good approximations of the analysis of the input signal z(t) where the approximation is valid in different subband regions. It follows from a comparison of the formulas (<NUM>) and (<NUM>-<NUM>) that a harmonic phase evolution along the frequency axis of the input signal z(t) will be extrapolated correctly by the present invention. This holds in particular for a pure pulse train. For the output audio quality, this is an attractive feature for signals of pulse train like character, such as those produced by human voices and some musical instruments.

<FIG>, <FIG> illustrate the performance of an exemplary implementation of the inventive transposition for a harmonic signal in the case T = <NUM>. The signal has a fundamental frequency <NUM> and its magnitude spectrum in the considered target range of <NUM> to <NUM> is depicted in <FIG>. A filter bank of N = <NUM> subbands is used at a sampling frequency of <NUM> to implement the transpositions. The magnitude spectrum of the output of a third order direct transposer (T=<NUM>) is depicted in <FIG>. As can be seen, every third harmonic is reproduced with high fidelity as predicted by the theory outlined above, and the perceived pitch will be <NUM>, three times the original one. <FIG> shows the output of a transposer applying cross term products. All harmonics have been recreated up to imperfections due to the approximative aspects of the theory. For this case, the side lobes are about <NUM> dB below the signal level and this is more than sufficient for regeneration of high frequency content which is perceptually indistinguishable from the original harmonic signal.

In the following, reference is made to <FIG> and <FIG> which illustrate an exemplary encoder <NUM> and an exemplary decoder <NUM>, respectively, for unified speech and audio coding (USAC). The general structure of the USAC encoder <NUM> and decoder <NUM> 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 processing and an enhanced SBR (eSBR) unit <NUM> and <NUM>, respectively, which handles the parametric representation of the higher audio frequencies in the input signal and which may make use of the harmonic transposition methods outlined in the present document. Then there are two branches, one consisting of a modified Advanced Audio Coding (AAC) tool path and the other consisting of a linear prediction coding (LP or LPC domain) based path, which in turn features either a frequency domain representation or a time domain representation of the LPC residual. All transmitted spectra for both, AAC and LPC, may be represented in MDCT domain following quantization and arithmetic coding. The time domain representation uses an ACELP excitation coding scheme.

The enhanced Spectral Band Replication (eSBR) unit <NUM> of the encoder <NUM> may comprise the high frequency reconstruction systems outlined in the present document. In particular, the eSBR unit <NUM> may comprise an analysis filter bank <NUM> in order to generate a plurality of analysis subband signals.

This analysis subband signals may then be transposed in a non-linear processing unit <NUM> to generate a plurality of synthesis subband signals, which may then be inputted to a synthsis filter bank <NUM> in order to generate a high frequency component. In the eSBR unit <NUM>, on the encoding side, a set of information may be determined on how to generate a high frequency component from the low frequency component which best matches the high frequency component of the original signal. This set of information may comprise information on signal characteristics, such as a predominant fundamental frequency Ω, on the spectral envelope of the high frequency component, and it may comprise information on how to best combine analysis subband signals, i.e. information such as a limited set of index shift pairs (p<NUM>,p<NUM>). Encoded data related to this set of information is merged with the other encoded information in a bitstream multiplexer and forwarded as an encoded audio stream to a corresponding decoder <NUM>.

The decoder <NUM> shown in <FIG> also comprises an enhanced Spectral Bandwidth Replication (eSBR) unit <NUM>. This eSBR unit <NUM> receives the encoded audio bitstream or the encoded signal from the encoder <NUM> and uses the methods outlined in the present document to generate a high frequency component of the signal, which is merged with the decoded low frequency component to yield a decoded signal. The eSBR unit <NUM> may comprise the different components outlined in the present document. In particular, it may comprise an analysis filter bank <NUM>, a non-linear processing unit <NUM> and a synthesis filter bank <NUM>. The eSBR unit <NUM> may use information on the high frequency component provided by the encoder <NUM> in order to perform the high frequency reconstruction. Such information may be a fundamental frequency Ω of the signal, the spectral envelope of the original high frequency component and/or information on the analysis subbands which are to be used in order to generate the synthesis subband signals and ultimately the high frequency component of the decoded signal.

Furthermore, <FIG> and <FIG> illustrate possible additional components of a USAC encoder/decoder, such as:.

<FIG> illustrates an embodiment of the eSBR units shown in <FIG> and <FIG>. The eSBR unit <NUM> will be described in the following in the context of a decoder, where the input to the eSBR unit <NUM> is the low frequency component, also known as the lowband, of a signal and possible additional information regarding specific signal characteristics, such as a fundamental frequency Ω, and/or possible index shift values (p<NUM>,p<NUM>). On the encoder side, the input to the eSBR unit will typically be the complete signal, whereas the output will be additional information regarding the signal characteristics and/or index shift values.

In <FIG> the low frequency component <NUM> is fed into a QMF filter bank, in order to generate QMF frequency bands. These QMF frequency bands are not 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 component of the signal in the frequency domain, rather than in the time domain. The low frequency component <NUM> is fed into the transposition unit <NUM> which corresponds to the systems for high frequency reconstruction outlined in the present document. The transposition unit <NUM> may also receive additional information <NUM>, such as the fundamental frequency Ω of the encoded signal and/or possible index shift pairs (p<NUM>,p<NUM>) for subband selection. The transposition unit <NUM> generates a high frequency component <NUM>, also known as highband, of the signal, which is transformed into the frequency domain by a QMF filter bank <NUM>. Both, the QMF transformed low frequency component and the QMF transformed high frequency component are fed into a manipulation and merging unit <NUM>. This unit <NUM> may perform an envelope adjustment of the high frequency component and combines the adjusted high frequency component and the low frequency component. The combined output signal is re-transformed into the time domain by an inverse QMF filter bank <NUM>.

Typically the QMF filter banks comprise <NUM> QMF frequency bands. It should be noted, however, that it may be beneficial to down-sample the low frequency component <NUM>, such that the QMF filter bank <NUM> only requires <NUM> QMF frequency bands. In such cases, the low frequency component <NUM> has a bandwidth of fs / <NUM>, where fs is the sampling frequency of the signal. On the other hand, the high frequency component <NUM> has a bandwidth of fs / <NUM>.

The method and system 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 as random access memory or optical storage media. They may be transferred via networks, such as radio networks, satellite networks, wireless networks or wireline networks, 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 broadcasting stations, e.g. in video headend systems.

Claim 1:
A system for decoding an audio signal, the system comprising:
a core decoder (<NUM>) for decoding a low frequency component of the audio signal;
an analysis filter bank (<NUM>) for providing a plurality of analysis subband signals of the low frequency component of the audio signal;
a subband selection reception unit for receiving information associated with a fundamental frequency Ω of the audio signal, and for selecting, in response to the information, a first (<NUM>) and a second (<NUM>) analysis subband signal from the plurality of analysis subband signals, from which a synthesis subband signal (<NUM>) is generated;
a non-linear processing unit (<NUM>) to generate the synthesis subband signal with a synthesis frequency, a magnitude and a phase by:
determining the magnitude of the synthesis subband signal from a generalized mean value of the magnitudes of the first and the second analysis subband signals, and
determining the phase of the synthesis subband signal from a weighted sum of the phases of the first and the second analysis subband signals, wherein a first weight applied to the phase of the first analysis subband signal corresponds to a first transposition factor T-r, and wherein a second weight applied to the phase of the second analysis subband signal corresponds to a second transposition factor r, wherein T and r are positive integers, T><NUM>, and <NUM>≤r<T; and
a synthesis filter bank (<NUM>) for generating a high frequency component of the audio signal from the synthesis subband signal.