The invention is directed to a method and a system for providing an acoustic signal, in particular a speech signal, with extended bandwidth.

Acoustic signals transmitted via an analog or digital signal path usually suffer from the drawback that the signal path only has a restricted bandwidth such that the transmitted acoustic signal differs considerably from the original signal. For example, in the case of conventional telephone connections, a sampling rate of 8 kHz is used resulting in a maximal signal bandwidth of 4 kHz. Compared to the case of audio CD's, the speech and audio quality is significantly reduced.

Furthermore, many kinds of transmissions show additional bandwidth restrictions. In the case of an analog telephone connection, only frequencies between 300 Hz and 3.4 kHz are transmitted. As a result, only 3.1 kHz bandwidth are available.

In principle, the bandwidth of telephone connections could be increased by using broadband or wideband digital coding and decoding methods (so-called broadband codecs). In such a case, however, both the transmitter and the receiver have to support corresponding coding and decoding methods which would require the implementation of a new standard.

As an alternative, systems for bandwidth extension can be used as described, for example, in P. Jax, Enhancement of Bandlimited Speech Signals: Algorithms and Theoretical Bounds, Dissertation, Aachen, Germany, 2002 or E. Larsen, R. M. Aarts, Audio Bandwidth Extension, Wiley, Hoboken, NJ, USA, 2004. These systems are to be implemented on the receiver's side only such that existing telephone connections do not have to be changed. In these systems, the missing frequency components of an input signal with small bandwidth are estimated and added to the input signal.

An example of the structure and the corresponding signal flow in such a state of the art bandwidth extension system is illustrated in Fig. 6. In general, both the lower and the upper frequency ranges are re-synthesized.

At block 601, an incoming or received acoustic signal x(n) in digitized form is processed by sub-sampling and block extraction so as to obtain signal vectors x(n). Here, the variable n denotes the time. In this Figure, it is assumed that the incoming signal x(n) has already been converted to the desired bandwidth by increasing the sampling rate. In this conversion step, no additional frequency components are to be generated which can be achieved, for example, by using appropriate anti-aliasing or anti-imaging filter elements. ln order to not amend the transmitted signal, the bandwidth extension is performed only within the missing frequency ranges. Depending on the transmission method, the extension concerns low frequency (for example from 0 to 300 Hz) and/or high frequency (for example 3400 Hz to half of the desired sampling rate) ranges.

In block 602, a narrowband spectral envelope is extracted from the narrowband signal, the narrowband signal being restricted by the bandwidth restrictions of the telephone channel. Via a non-linear mapping, a corresponding broadband envelope signal is estimated from the narrowband envelope. The mappings are based, for example, on codebook pairs (see J. Epps, W. H. Holmes, A New Technique for Wideband Enhancement of Coded Narrowband Speech, IEEE Workshop on Speech Coding, Conference proceedings, pages 174 to 176 June 1999) or on Neural Networks (see J.-M. Valin R. Lefebvre, Bandwidth Extension of Narrowband Speech for Low Bit-Rate Wideband Coding, IEEE Workshop on Speech Coding, Conference Proceedings, pages 130 to 132, September 2000). In these methods, the entries of the codebooks or the weights of the neural networks are generated using training methods requiring large processor and memory resources.

Furthermore, in block 603, a broadband or wideband excitation signal having a spectrally flat envelope is generated from the narrowband signal. This excitation signal corresponds to the signal which would be recorded directly behind the vocal cords, i.e. the excitation signal contains information about voicing and pitch, but not about form and structures or the spectral shaping in general. Thus, to retrieve a complete signal, such as a speech signal, the excitation signal has to be weighted with the spectral envelope. For the generation of excitation signals, non-linear characteristics (see U. Kornagel, Spectral Widening of the Excitation Signal for Telephone-Band Speech Enhancement, IWAENC 01, Conference Proceedings, pages 215 to 218, September 2001) such as two-ray rectifying or squaring, for example, may be used.

For bandwidth extension, the excitation signal x_exc(n) is spectrally colored using the envelope in block 604. After that, the spectral ranges used for the extension are extracted using a band stop filter in block 606 resulting in signal vectors y_ext(n). The band stop filter can be effective, for example, in the range from 200 to 3700 Hz.

The signal vectors x(n) of the received signal are passed through a complementary band pass filter in block 605. Then, the signal components y_ext (n) and y_tel(n) are added to obtain a signal vector y(n) with extended bandwidth. In block 607, the different signal vectors are assembled again and an over-sampling is performed resulting in a signal y(n).

A system and a method for bandwidth extension of bandlimited audio signals is known from EP 1 638 083. B. Iser et al "Bandwidth extension of telephoning speech", EURASIP NEWSLETTER, June 2005. pages 2 - 24 gives an introduction to this topic. EP 0 944 036 discloses a method and a device for detecting voice sections. A method for speech bandwidth extension is disclosed in US 2002/0138268. A frequency interpolating device and method is known from EP 1 298 643.

This problem is solved by the method according to claim 1 and the apparatus according to claim 13.

In accordance with the invention, a method for providing an acoustic signal with extended bandwidth is provided, comprising:

1. (a) automatically determining a current upper and a current lower bandwidth limit of received acoustic signal,
2. (b) automatically determining at least one complementary signal to complement the received acoustic signal between a predefined lower broadband bandwidth limit and the current lower bandwidth limit and/or between the current upper bandwidth limit and a predefined upper broadband bandwidth limit, wherein the predefined lower broadband bandwidth limit is smaller than the current bandwidth limit and the predefined upper broadband bandwidth limit is larger than the current upper bandwidth limit,
3. (c) automatically assembling the at least one complementary signal and the received acoustic signal to obtain an acoustic signal with extended bandwidth.

By determining current upper and lower bandwidth limits of a received acoustic signal and determining a complementary signal between the current bandwidth limits and the respective predefined broadband (or wideband) bandwidth limits, the method according to the invention allows an adaptation of the bandwidth extension to the acoustic signal actually received. For example, when the transmitter uses an ISDN telephone, a broader frequency range is used compared to the case of a mobile phone with a hands-free system. Therefore, the bandwidth of a received acoustic signal will be extended only in those ranges where it is necessary so that the quality of the resulting signal is very high.

In this way, on the one hand, no spectral gaps will occur even if the received signal covers only a very narrow frequency range. On the other hand, when receiving signals covering a relatively broad frequency range, no frequencies are cut-off when determining the complementary signal.

The received acoustic signal may be a digital signal or may be digitized. In the above method, steps (a) to (c) may be preceded by the step of converting the received acoustic signal to a predetermined sampling rate. Furthermore, steps (a) to (c) may be preceded by the step of extracting a signal vector from the acoustic signal, in particular, the converted acoustic signal. The signal vector may be obtained by sub-sampling the acoustic signal and may comprise a predefined number of entries. Then, subsequent (in time) signal vectors may overlap. The use of signal vectors simplifies further processing of the signals.

Steps (a) to (c) may be preceded by the step of determining a spectral vector of the received acoustic signal. In particular, a window function may be applied to signal vectors of the received acoustic signal. For example, a Hann or a Hamming window may be used (see K. D. Kammeyer, K. Kroschel, Digitale Signalverarbeitung, 4 th Edition, Teubner, Stuttgart, Germany 1997). Signal vectors, in particular the signal vectors weighted in this way, may be transformed into the Fourier domain using a discrete Fourier transform. The resulting vector is a short-term spectral vector. This allows for further processing in the Fourier domain.

In the above methods, step (b) comprises determining a broadband spectral envelope signal and a broadband excitation signal between the lower and upper broadband bandwidth limits such that the product of spectral envelope signal and excitation signal corresponds to the received acoustic signal according to a predetermined criterion.

Such a decomposition into an envelope signal and an excitation signal simplifies determining the current bandwidth limits and increases the accuracy when determining a complementary signal.

Step (a) comprises comparing a determined broadband spectral envelope signal and a spectrum of the received acoustic signal. It turned out that the spectrum is a suitable basis for determining current bandwidth limits of the acoustic signal.

Thus, if current bandwidth limits have been determined in step (a) in this way using a broadband spectral envelope signal of the received acoustic signal, determining a complementary signal in step (b) based on these current bandwidth limits and comprising determination of an envelope signal enables to iteratively adapt the current bandwidth limits by comparing again the (newly) determined envelope signal and a spectrum. In other words, determining current bandwidth limits in step (a) may use a spectral envelope signal determined according to step (b), particularly in a preceding step or in a preceding iteration of the method.

The comparing step may comprise selecting the minimal and maximal frequency for which the long-term power spectrum is larger than or equal to the determined broadband spectral envelope signal plus a predetermined constant.

This is a particularly simple and reliable way to determine the bandwidth limits. The predetermined constant can be chosen based on empirical or theoretical data. The predetermined constant may be negative.

In the above methods, determining a broadband spectral envelope signal may comprise selecting an envelope signal from a codebook according to a predetermined criterion.

By using codebooks, the required computing power can be reduced for determining an envelope signal. In principle, different kinds of criteria can be used when selecting an envelope signal from a codebook. In particular, using a predetermined distance criterion such as a cepstral distance can be used, particularly if the codebook entries have the form of cepstral vectors.

In particular, selecting an envelope signal may comprise equalizing the received acoustic signal and selecting an envelope signal from the codebook having minimal distance to the equalized acoustic signal according to a predetermined distance criterion, in particular, having a minimal cepstral distance.

Equalizing the acoustic signal allows to modify it such that a comparison with envelope signals from the codebook can be simplified. In particular, the received acoustic signal can be equalized in such a way that the resulting signal shows a long-term power spectrum corresponding to the long-term power spectrum of the signal used for training the codebook. Equalizing can be restricted to frequencies between the current upper and lower bandwidth limits of the received acoustic signal; outside these limits, the signal may remain unchanged. In particular, equalizing the received acoustic signal can be performed using a normalized long-term power spectrum of the signal used for training the codebooks, particularly using the normalized long-term power spectrum divided by the normalized long-term power spectrum of the received acoustic signal itself.

The codebook may comprise pairs of corresponding envelope signals, each pair comprising a broadband envelope signal between the lower and upper broadband bandwidth limits and a corresponding narrowband envelope signal between a lower narrowband bandwidth limit being larger than the lower broadband bandwidth limit and an upper narrowband bandwidth limit being smaller than the upper broadband bandwidth limit, and selecting an envelope signal may comprise determining a narrowband envelope signal having minimal distance to the equalized acoustic signal according to the predetermined distance criterion and selecting the corresponding broadband envelope signal of this pair.

In this way, a simple comparison between the received acoustic signal and the elements of the codebook can be performed as narrowband signals usually match a received acoustic signal with a narrow bandwidth more closely.

When using a cepstral distance to select an envelope signal, the received acoustic signal, particularly in its equalized form, has to be transformed into the cepstral domain. Thus, the step of selecting an envelope signal can further comprise the steps of determining the absolute value squared of the sub-band signals of the received acoustic signal, determining an auto-correlation in the time domain, particularly by performing an inverse discrete Fourier transform on the vector of the absolute value squared, determining prediction coefficients, particularly using the Levinson-Durbin algorithm, performing a recursion to obtain the cepstral coefficients.

In order to determine a spectral envelope from the cepstral vectors, the method may further comprise the steps of recursively transforming a cepstral vector into prediction error coefficients, augmenting the prediction error filter vector by adding a predetermined number of zeros and subsequently performing a discrete Fourier transform to obtain an inverse spectrum, determining the reciprocal of each sub-band component to obtain a spectral envelope vector.

In the above methods, the step of selecting an envelope signal may be preceded by providing adapted narrowband codebook envelope signals being adapted to the current lower and upper bandwidth limits.

Such an adaptation of the codebook entries allows for an improved selection of a corresponding envelope signal from the codebook. In particular, if the received acoustic signal shows a broader bandwidth than the original narrowband envelope signals of the codebook, the adaptation would result in envelope signals in the codebook having an extended bandwidth. In this way, particularly fricatives can be more reliably detected.

The providing step may comprise processing broadband codebook envelope signals using a long-term power spectrum of the received acoustic signal.

Due to the use of the power spectrum of the received acoustic signal, a suitable adaptation to the acoustic signal can be obtained. The long-term power spectrum may be normalized; furthermore, the long-term power spectrum of the received acoustic signal may be divided by a normalized long-term power spectrum of a broadband signal used for training of the codebook. The processing of the broadband codebook envelope signals may be performed only for frequencies outside the current bandwidth limits; within the bandwidth limits, the envelope signals may remain unchanged. Processing using the long-term power spectrum may comprise weighting broadband codebook envelope signal vectors using the long-term power spectrum of the received acoustic signal.

In particular, if the received acoustic signal has been transformed into the Fourier domain, determining a long-term power spectrum may comprise performing a first order recursive smoothing of the absolute values squared of the sub-band signals corresponding to the acoustic signal. This can be done, in particular, only if a wanted signal, such as a speech signal, has been detected in the received acoustic signal.

In addition, the long-term power spectrum may be normalized, particularly with respect to a long-term power spectrum within predetermined frequency limits.

Alternatively, the long-term power spectrum may be determined in the time domain. This can be done by determining the auto-correlation and performing an LPC analysis to obtain corresponding prediction coefficients.

In the above methods, determining a broadband excitation signal may be based on prediction error filtering and/or a non-linear characteristic. In this way, suitable excitation signals can be generated. Possible non-linear characteristics are disclosed, for example, in U. Kornagel, Spectral Widening of the Excitation Signal for Telephone-Band Speech Enhancement.

In the above methods, the at least one complementary signal may be based on a product of the determined broadband spectral envelope and the determined broadband excitation signal, and step (c) may comprise summing the received acoustic signal between the current lower and upper bandwidth limits and the at least one complementary signal being restricted to the band between the lower broadband bandwidth limit and a current lower bandwidth limit and/or to the band between the current upper bandwidth limit and the upper broadband bandwidth limit.

Thus, the complementary signal is based on spectrally coloring the excitation signal using the envelope signal. By adding a complementary signal only outside the current bandwidth limits of the received acoustic signal, artifacts are avoided in the resulting signal with extended bandwidth.

Step (c) may also comprise adapting the power of the complementary signal and/or the received acoustic signal. With this step, the power of the received acoustic signal can be maintained.

In the above-described methods, at least one of the steps may be performed in the cepstral domain. Particularly if the entries of the codebook are cepstral vectors, this allows for performing the method in a simpler way.

Steps (a) to (c) of the above methods may be repeated at predetermined time intervals. Then, the repeated adaptation to the currently received acoustic signal leads to a permanent high quality of the resulting broadband signal.

Steps (a) to (c) of the above methods may be repeated only if a wanted signal component, such as speech activity, is detected in the received acoustic signal. Particularly in the case of speech signals, an extension of the bandwidth of the received acoustic signal is advantageous. Thus, restricting the method to the case of detected speech activity reduces the required computing power and avoids the presence of artifacts due to mal-adaptation.

The invention also provides a computer program product comprising one or more computer-readable media having computer-executable instructions for performing the steps of the above-described methods when run on a computer.

Furthermore, an apparatus for providing an acoustic signal with extended bandwidth is provided, comprising:

• bandwidth determining means for automatically determining a current upper and a current lower bandwidth limit of a received acoustic signal,
• complementary signal means for automatically determining at least one complementary signal to complement the received acoustic signal between a predefined lower broadband bandwidth limit and the current lower bandwidth limit and/or between the current upper bandwidth limit and a predefined upper broadband bandwidth limit, wherein the predefined lower broadband bandwidth limit is smaller than
• the current bandwidth limit and the predefined upper broadband bandwidth limit is larger than the current upper bandwidth limit, and
• assembling means for automatically assembling the at least one complementary signal and the received acoustic signal to obtain an acoustic signal with extended bandwidth.

Analogous to the above-described method, such an apparatus provides an advantageous way to extend the bandwidth of a received acoustic signal. In particular, due to the determination of current upper and lower bandwidth limits of the received acoustic signal and a corresponding determination of a complementary signal, the quality of the resulting output signal is increased compared to the case of bandwidth extension systems with fixed parameters.

The complementary signal means comprises a means for determining a broadband spectral envelope signal and a broadband excitation signal between the lower and upper broadband bandwidth limits such that the product of spectral envelope signal and excitation signal corresponds to the received acoustic signal according to a predetermined criterion.

The bandwidth determining means is configured to compare a determined broadband spectral envelope signal and a spectrum of the received acoustic signal.

The bandwidth determining means may be configured to select the minimal and maximal frequency for which the spectrum is larger than or equal to the power spectrum of the determined broadband spectral envelope signal plus a predetermined constant.

In the above-described apparatus, the means for determining a broadband spectral envelope signal may comprise a means for selecting an envelope signal from a codebook according to a predetermined criterion.

The means for selecting an envelope signal may be configured to equalize the received acoustic signal and select an envelope signal from the codebook having minimal distance to the equalized acoustic signal according to a predetermined distance criterion, in particular, having a minimal cepstral distance.

In the above-described apparatus, the codebook may comprise pairs of corresponding envelope signals, each pair comprising a broadband envelope signal between the lower and upper broadband bandwidth limits and a corresponding narrowband envelope signal between a lower narrowband bandwidth limit being larger than the lower broadband bandwidth limit and an upper narrowband bandwidth limit being smaller than the upper broadband bandwidth limit, and the means for selecting an envelope signal may be configured to determine a narrowband envelope signal having minimal distance to the equalized acoustic signal according to the predetermined distance criterion and to select the corresponding broadband envelope signal of this pair.

The means for determining a broadband spectral envelope signal may comprise a means for providing adapted narrowband codebook envelope signals being adapted to the current lower and upper bandwidth limits.

The means for providing may be configured to process the broadband codebook envelope signal using a long-term power spectrum of the received acoustic signal.

In the above-described apparatus, the means for determining a broadband excitation signal may be configured to determine the broadband excitation signal based on prediction error filtering and/or a non-linear characteristic.

The at least one complementary signal may be based on a product of the determined broadband spectral envelope and the determined broadband excitation signal, and the assembling means may be configured to sum the received acoustic signal between the current lower and upper bandwidth limits and the at least one complementary signal being restricted to the band between the lower broadband bandwidth limit and a current lower bandwidth limit and/or to the band between the current upper bandwidth limit and the upper broadband bandwidth limit.

In the above-described apparatus, at least one of the means may be configured to perform at least part of its function in the cepstral domain.

The means of the above-described apparatus may be configured to perform their respective function repeatedly at predetermined time intervals.

The apparatus may further comprise a wanted signal detector, in particular, a speech detector, and the means may be configured to perform their respective function only if a wanted signal component is detected in the received acoustic signal.

Further features and advantages of the invention will be described in the following with reference to the figures.

Fig. 1

illustrates the structure of an example of an apparatus for providing an acoustic signal with extended bandwidth;

Fig. 2

is a flow diagram of an example of a method for providing an acoustic signal with extended bandwidth;

Fig. 3

illustrates an example of a normalized long-term power spectrum for training a codebook;

Fig 4

illustrates examples of codebook entries;

Fig. 5

illustrates the determination of current bandwidth limits;

Fig. 6

illustrates the structure of a prior art system.

Fig. 1 shows the structure of the signal flow in an apparatus for providing an acoustic signal with extended bandwidth. Fig. 2 is a flow diagram illustrating an example of a method for providing an acoustic signal with extended bandwidth which could be performed by the apparatus corresponding to Fig. 1. In view of this, Fig.'s 1 and 2 will be described in the following simultaneously.

According to step 201, an acoustic signal, such as a speech signal, is received via a telephone line. Because of the restricted bandwidth of the telephone line, an extension of the bandwidth is desired to improve the signal quality. Thus, the signal is to be augmented so as to obtain a predetermined broader bandwidth. It is to be understood that the method described in the following can be used for bandwidth extension independent of the type of incoming signal and independent of the type of transmission line, i.e., it need not be a telephone line.

The acoustic signal x(n) received by block 101 has already been pre-processed by increasing the sampling rate up to the predetermined broadband or wideband bandwidth. In this way, however, no additional frequency components are generated. This can be achieved, for example, by using suitable anti-aliasing or anti-imaging filters. This kind of bandwidth extension, preferably, is performed only for the "missing" frequency ranges; in the case of an analog telephone line, these ranges may be between 0 and 300 Hz and 3400 Hz up to half of the desired sampling rate, for example, up to 3700 Hz.

From the resulting signal x(n), n denoting the time variable, signal vectors x(n) are generated (step 202). This can be achieved by taking every r sampling values up to a certain length. Thus, a signal vector with N_ana elements has the form: $$\mathbf{x}\left(n\right)=[x\left(\mathit{nr}\right),x\left(\mathit{nr}-1\right),\dots ,x\left(\mathit{nr}-N_{\mathit{ana}}+1\right){]}^T\mathrm{.}$$

It is to be noted that an overlap may exist between neighboring signal vectors. For a desired or final sampling rate of 11.025 kHz, one may take the following values: $$r=64,$$ $$N_{\mathit{ana}}=256.$$

After that (step 203), a windowing procedure is performed on the signal vector so as to obtain a windowed signal vector x_w(n) : $${\mathbf{x}}_w\left(n\right)=\mathbf{Fx}\left(n\right)\mathrm{.}$$

The window matrix F is a diagonal matrix of the form $$\mathbf{F}=\left[\begin{array}{ccccc}{h}_0& 0& 0& \dots & 0\\ 0& h_1& 0& \dots & 0\\ 0& 0& h_2& \dots & 0\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ 0& 0& 0& \dots & h_{N_{\mathit{ana}}-1}\end{array}\right]$$

The elements of this matrix can be chosen corresponding to different kinds of windows. Typical windows are the Hann or Hamming window. The weighted signal vectors are transformed into the Fourier domain using a discrete Fourier transform: $${\mathbf{X}}_n\left(n\right)=\mathit{DFT}\left\{{\mathbf{x}}_w\left(n\right)\right\}\mathrm{.}$$

The resulting short-term spectral vector has the form: $$X_w\left(n\right)[X\left(e^{{j\Omega }_0}n\right),X\left(e^{{j\Omega }_1}n\right),\dots ,X\left(e^{{j\Omega }_{\mu }}n\right),\dots ,X\left(e^{{j\Omega }_{N_{{\mathit{DFT}}^{-1}}}}n\right){]}^T,$$
wherein Ω_µ denotes the frequency variable.

Based on the spectral vectors, a long-term power spectrum of the received acoustic signal is determined in block 102 (step 204). There are different possibilities to estimate such a long-term power spectrum. According to one alternative, a first order recursive smoothing is performed on the absolute value squared of the sub-band signals X(e^jΩµ, n) : $${\hat{S}}_{\mathit{xx}}\left({\mathrm{\Omega }}_{\mu }n\right)=\{\begin{array}{ll}{\mathit{\beta }}_{\mathit{fre}}{\hat{S}}_{\mathit{xx}}\left({\mathrm{\Omega }}_{\mu },n-1\right)+\left(1-{\mathit{\beta }}_{\mathit{fre}}\right)|X_w\left(e^{{j\Omega }_{\mu }}n\right){|}^2,& \mathrm{diring\; speech\; activity}\\ {\hat{S}}_{\mathit{xx}}\left({\mathrm{\Omega }}_{\mu },n-1\right),& \mathrm{else}\mathrm{.}\end{array}$$

Preferably, the time constant β_fre is chosen to be close to 1 (0 << β_fre < 1) so as to obtain a sufficiently large averaging time.

In principle, the recursive smoothing according to the first line of the above equation may be performed continuously. However, in order to avoid any artefacts, it may be performed only if a wanted signal component is present in the received acoustic signal, for example, if speech activity is detected. For this purpose, a speech detector may be provided as described, for example, in E. Hänsler, G. Schmidt, Acoustic Echo and Noise Control - A Practical Approach, Wiley, Hoboken, NJ, USA, 2004.

In order to simplify the further processing, the long-term power spectrum may be normalized to the long-term power within a predefined frequency band: $${\hat{S}}_{\mathit{xx},\mathit{norm}}\left({\mathrm{\Omega }}_{\mu }n\right)=\frac{{\hat{S}}_{\mathit{xx}}\left({\mathrm{\Omega }}_{\mu }n\right)}{\sum _{\mu ={\mu }_l}^{{\mu }_{\mu }}{\hat{S}}_{\mathit{xx}}\left({\mathrm{\Omega }}_{\mu }n\right)}$$

The band limits Ω_µl and Ω_µu denote the lower and upper limits of a predefined frequency band. For example, this frequency band may correspond to a telephone band with minimal bandwidth for which the present method is to be used, for example, the limits may be 400 Hz and 3300 Hz. Preferably, the limits correspond to a band which is smaller or at most equal to the frequency band of the narrow frequency band within which the codebook described below has been trained; these limits being denoted by Ω_l and Ω_u.

Alternatively, to determine the long-term power spectrum in the frequency domain, an estimation can be performed in the time domain as well. For this purpose, an auto-correlation is estimated for about 10 to 20 sampling cycles of offset. Afterwards, prediction coefficients can be determined using an LPC (linear predictive coding) analysis. The long-term power spectrum is obtained via a discrete Fourier transform and a division.

In block 103 (step 205), the acoustic signal is equalized. The equalizing is performed on the spectral vector determined above: $${\mathbf{X}}_{\mathit{eq}}\left(n\right)={\mathbf{H}}_{\mathit{eq}}\left(n\right){\mathbf{X}}_w\left(n\right)\mathrm{.}$$

The equalizing matrix H_eq(n) is a diagonal matrix of the form $${\mathbf{H}}_{\mathit{eq}}\left(n\right)=\left[\begin{array}{cccc}{H}_{\mathit{eq}}\left(e^{j{\mathrm{\Omega }}_{\mathit{0}}}n\right)& \mathit{0}& \dots & \mathit{0}\\ \mathit{0}& H_{\mathit{eq}}\left(e^{j{\mathrm{\Omega }}_{\mathit{1}}}n\right)& \dots & \mathit{0}\\ ⋮& ⋮& \ddots & ⋮\\ \mathit{0}& \mathit{0}& \dots & H_{\mathit{eq}}\left(e^{j{\mathrm{\Omega }}_{N_{{\mathit{DFT}}^{-1}}}}n\right)\end{array}\right]$$ with the entries $${\stackrel{}{\mathit{H}}}_{\mathit{eq}}\left(e^{j{\mathrm{\Omega }}_{\mu }}n\right)=\{\begin{array}{ll}1& \mathrm{if}\left(\left({\mathrm{\Omega }}_{\mu }<{\stackrel{}{\mathrm{\Omega }}}_l\left(n-1\right)\right)\mathrm{or}\left({\mathrm{\Omega }}_{\mu }<{\stackrel{}{\mathrm{\Omega }}}_u\left(n-1\right)\right)\right)\\ \frac{{\hat{S}}_{\mathit{xx},\mathit{norm}}\left({\mathrm{\Omega }}_{\mu }n\right)}{{\hat{S}}_{\mathit{xx},\mathit{norm}}\left({\mathrm{\Omega }}_{\mu }n\right)},& \mathrm{else}\end{array}$$ and $$H_{\mathit{eq}}\left(e^{j{\mathrm{\Omega }}_{\mu }},\mathrm{n}\right)=\{\begin{array}{ll}{H}_{\mathit{eq}},\max ,& \mathrm{if}\left({\stackrel{}{H}}_{\mathit{eq}}\left(e^{j{\mathrm{\Omega }}_{\mu }},\mathrm{n}\right)>H_{\mathit{eq}},\max \right),\\ H_{\mathit{eq}},\min ,& \mathrm{if}\left({\stackrel{}{H}}_{\mathit{eq}}\left(e^{j{\mathrm{\Omega }}_{\mu }},\mathrm{n}\right)>H_{\mathit{eq}},\min \right),\\ H_{\mathit{eq}}\left(e^{j{\mathrm{\Omega }}_{\mu }},\mathrm{n}\right),& \mathrm{else},\end{array}$$

In the equations above, Ω_l (n -1) and Ω_u (n -1) denote the current lower and upper bandwidth limits of the received acoustic signal. Thus, for obtaining an updated equalized signal, the bandwidth limits at time (n-1) are taken as the current bandwidth limits. Furthermore, S_{x̃ x̃,norm}(Ω_µ, n) denotes the normalized long-term power spectrum of the broadband signal which has been used for training the codebook. Normalizing of such a power spectrum is performed analogously to the case of the long-term power spectrum of the received acoustic signal described above. An example for such a normalized long-term power spectrum used for training a codebook is shown in Figure 3.

The equalizing is restricted to minimal and maximum values, for example, to $$H_{\mathit{eq},\min }=-12\mathrm{dB},$$ $$H_{\mathit{eq},\max }=12\mathrm{dB}\mathrm{.}$$

As can be seen from the above, the acoustic signal is equalized only within the current bandwidth limits one time step before. Outside these bandwidth limits, no equalizing takes place.

In the following, determining a broadband spectrum envelope will be described in more detail. An envelope signal corresponding to the received acoustic signal will be determined using a codebook. The used codebook comprises a number of pairs of corresponding narrowband and broadband envelope signals. The codebook has been obtained by training with a large database on the basis of a starting long-term power spectrum (see Y. Linde, A. Buzo, R. M. Gray, An Algorithm for Vector Quantizer Design, IEEE Trans. Comm., vol. COM-28, no. 1, pages 84 - 95, Jan. 1980).

As indicated in Figure 2, the codebook entries are adapted in step 206 (block 104). In particular, the narrowband codebook entries c_i,s(n) are adapted.

This is achieved by starting with the broadband entries of the codebook. If the broadband envelope signals are provided as cepstral vectors c_i,b(n), the corresponding spectra C_i,b (n) are determined. Based on these broadband spectral envelopes, the adapted or optimized narrowband spectra are determined by a multiplication with a weighting matrix: $${\mathbf{C}}_{i,s}\left(n\right)={\mathbf{H}}_{\mathrm{mod}}\left(n\right){\mathbf{C}}_{i,b}\left(n\right)\mathrm{.}$$

The weighting matrix is a diagonal matrix of the form: $${\mathbf{H}}_{\mathrm{mod}}\left(n\right)=\left[\begin{array}{cccc}{H}_{\mathit{mod}}\left(e^{j{\mathrm{\Omega }}_{\mathit{0}}}n\right)& 0& \dots & 0\\ 0& H_{\mathit{mod}}\left(e^{j{\mathrm{\Omega }}_{\mathit{1}}}n\right)& \dots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \dots & H_{\mathit{mod}}\left(e^{j{\mathrm{\Omega }}_{N_{{\mathit{DFT}}^{-1}}}}n\right)\end{array}\right]$$ with the entries $$H_{\mathit{mod}}\left(e^{j{\mathrm{\Omega }}_{\mu }}n\right)=\{\begin{array}{ll}1,& \mathrm{if}\left({\stackrel{}{\mathrm{\Omega }}}_l\left(n-1\right)<{\mathrm{\Omega }}_{\mu }<{\stackrel{}{\mathrm{\Omega }}}_u\left(n-1\right)\right),\\ \frac{{\hat{S}}_{\mathit{xx},\mathit{norm}}\left({\mathrm{\Omega }}_{\mu }n\right)}{{\hat{S}}_{\stackrel{}{\mathit{x}}\stackrel{}{\mathit{x}},\mathit{norm}}\left({\mathrm{\Omega }}_{\mu }n\right)},& \mathrm{else}\mathrm{.}\end{array}$$

Afterwards, cepstral vectors are determined from the resulting spectral narrowband envelopes.

The conversion from spectral vectors to cepstral vectors and vice versa will be described in the following with respect to step 207 in which broadband spectral envelopes are determined (block 105).

A broadband spectral envelope from the codebook matching the acoustic signal best is determined by comparing the narrowband codebook entries with the spectral envelope of the spectrum of the acoustic signal (after equalizing). The narrowband codebook entry is selected that has the smallness distance to the acoustic signal spectrum. In principle, different distance criteria can be used. The cepstral distance is particularly useful as the codebook entries are provided in the form of cepstral vectors.

When an optimal narrowband codebook entry has been selected, the corresponding broadband codebook entry is determined as the optimal broadband spectral envelope for the received acoustic signal. Due to the adaptation of the narrowband codebook entries as described above, an optimal narrowband envelope can be selected in a very reliable way.

Converting a spectral vector, particularly of the received acoustic signal, to a cepstral vector can be achieved by:

1. 1. Determining the absolute value squared of each sub-band signal X_eq (e^jΩµ, n).
2. 2. Applying an inverse discrete Fourier transform on this vector results in an estimation of the auto-correlation in the time domain.
3. 3. Using the Levinson-Durbin algorithm, prediction coefficients (with an order of about 10 to 20) can be determined from the auto-correlation.
4. 4. By performing a recursion with respect to the order, the prediction coefficients are used to determine the cepstral coefficients. Usually, the order corresponds to one and a half of the prediction order.

The optimal cepstral vector of the broadband codebook is designated by c_opt,b(n). The resulting broadband spectral envelope has the form: $${\mathbf{C}}_{\mathit{opt},b}\left(n\right)=[C_{\mathit{opt},b}\left(e^{{j\Omega }_0}n\right),C_{\mathit{opt},b}\left(e^{{j\Omega }_1}n\right),\dots ,C_{\mathit{opt},b}\left(e^{{j\Omega }_{N_{{\mathit{DFT}}^{-1}}}}n\right){]}^T\mathrm{.}$$

Conversion of cepstral vectors into spectral vectors is achieved by:

1. 1. Converting the cepstral vectors using a recursion with respect to the order (as above) to obtain prediction error filter coefficients.
2. 2. By augmenting the prediction error filter vector by a predetermined number of zeros and subsequent performing of a discrete Fourier transform, an inverse spectrum is obtained.
3. 3. By determining the reciprocal of each sub-band component, the vector C_opt,b(n) is generated. Divisions by zero have to be treated separately, for example by adding a suitable constant.

Fig. 4 illustrates an example of a codebook with four pairs of entries. In each diagram, a corresponding original narrowband envelope, and a corresponding adapted narrowband envelope are shown. The original broadband and narrowband codebook entries have been obtained on the basis of a large database for an ISDN telephone connection. As can be seen in this figure, after the adaptation, the resulting optimized entries have a higher upper limit frequency. This allows for an improved detection of fricatives.

In step 208 (block 103), an excitation signal corresponding to the received acoustic signal is generated. This broadband excitation signal shows a spectrally flat envelope. It corresponds to a signal which would be recorded directly behind the vocal cords.

For determining a broadband excitation signal, first of all, the spectral envelope of the equalized short-term spectrum X_eq (n) is estimated in the form of prediction error filter coefficients. Applying an inverse discrete Fourier transform on this spectral vector allows to determine the corresponding time signal. After that, the vector in the time domain is filtered by a prediction error filter. The corresponding filter coefficients are those that have been determined previously.

Then, a non-linear characteristic, such as a two-way rectification or squaring, is applied to the filtered time domain vector. This generates the missing low frequency and high frequency signal components. A transformation in the Fourier domain provides, then, the spectrum of the extended excitation signal X_exc(n).

Alternatively, determining an excitation signal can be performed in the time sub-band or Fourier domain as well. Examples for this alternative can be found in B. Iser, G. Schmidt, Bandwidth Extension of Telephony Speech, Eurasip Newsletter, Volume 16, Number 2, pages 2 to 24, June 2005.

In the following step 209 (block 107), the broadband spectral envelope and the excitation signal are used for spectrally coloring the excitation signal. This can be achieved by multiplication in the sub-band or Fourier domain: $${\stackrel{}{\mathbf{Y}}}_{\mathit{ext}}\left(n\right)=\mathrm{diag}\left\{{\mathbf{C}}_{\mathrm{opt},p}\left(n\right)\right\}{\mathbf{X}}_{\mathit{exc}}\left(n\right)\mathrm{.}$$

The diagonal matrix diag {C_opt,b(n)} has the form: $$\mathrm{diag}\left\{{\mathbf{C}}_{\mathit{opt},b}\left(n\right)\right\}=\left[\begin{array}{cccc}{C}_{\mathit{opt}\mathit{,}\mathit{b}}\left(e^{j{\mathrm{\Omega }}_0}n\right)& 0& \dots & 0\\ 0& C_{\mathit{opt}\mathit{,}\mathit{b}}\left(e^{j{\mathrm{\Omega }}_1}n\right)& \dots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \dots & C_{\mathit{opt}\mathit{,}\mathit{b}}\left(e^{j{\mathrm{\Omega }}_{N_{{\mathit{DFT}}^{-1}}}}n\right)\end{array}\right]$$

Because of the non-linearity or the prediction error filtering when generating the excitation signal, the power of the acoustic signal need not be maintained. Therefore, a power adaptation may be performed: $${\mathbf{Y}}_{\mathit{ext}}\left(n\right)=K\left(n\right){\stackrel{}{\mathbf{Y}}}_{\mathit{ext}}\left(n\right)\mathrm{.}$$

The correction factor K can be chosen to be $$K\left(n\right)=\frac{{\displaystyle \sum _{\mu ={\mu }_l}^{{\mu }_u}}|X_w\left(e^{j\Omega }n\right){|}^2}{{\displaystyle \sum _{\mu ={\mu }_l}^{{\mu }_u}}{\stackrel{}{Y}}_{\mathit{erw}}(e^{j{\Omega }_{\mu }},n{)}^2}$$
wherein Ω_µl and Ω_µu denote the same bandwidth limits as in the estimation of the long-term power spectrum above.

The current bandwidth limits are adapted in step 210 (block 108). According to one possibility, the bandwidth limits are determined starting with a comparison of the spectrum of the received acoustic signal and the broadband spectral envelope being reduced by a predefined constant: $${\stackrel{}{\mathrm{\Omega }}}_l\left(n\right)=\min \left\{{\mathrm{\Omega }}_{\mu }\in \left\{|X_w\left(e^{{j\Omega }_{\mu ,n}}\right){|}^2\ge \left|C_{\mathit{opt},b}{\left(e^{{j\Omega }_{\mu ,n}}\right)}^2\right|+K_C\right\}\right\},$$ $${\stackrel{}{\mathrm{\Omega }}}_u\left(n\right)=\min \left\{{\mathrm{\Omega }}_{\mu }\in \left\{|X_w\left(e^{{j\Omega }_{\mu ,n}}\right){|}^2\ge \left|C_{\mathit{opt},b}{\left(e^{{j\Omega }_{\mu ,n}}\right)}^2\right|+K_C\right\}\right\}\mathrm{.}$$

The parameter K_c can have the value: $$K_C=-12\mathrm{dB}\mathrm{.}$$

In Fig. 5, an example for determining the bandwidth limits is illustrated. The above, intermediate limit values are given by the points of intersection between the lowered broadband spectral envelope and the spectrum of the received acoustic signal.

These intermediate limit values may be recursively smoothed to eliminate temporary mal-estimations. In this case, preferably, smoothing is performed only if speech activity is detected in the current signal frame. $${\stackrel{}{\mathrm{\Omega }}}_l\left(n\right)=\{\begin{array}{ll}{\mathit{\beta }}_{\mathit{bandl}}{\stackrel{}{\mathrm{\Omega }}}_l\left(n-1\right)+\left(1-{\mathit{\beta }}_{\mathit{bandl}}\right){\stackrel{}{\mathrm{\Omega }}}_l\left(n\right),& \mathrm{during\; speech\; activity},\\ {\stackrel{}{\mathrm{\Omega }}}_l\left(n-1\right),& \mathrm{else},\end{array}$$ $${\stackrel{}{\mathrm{\Omega }}}_u\left(n\right)=\{\begin{array}{ll}{\mathit{\beta }}_{\mathit{bandl}}{\stackrel{}{\mathrm{\Omega }}}_u\left(n-1\right)+\left(1-{\mathit{\beta }}_{\mathit{bandl}}\right){\stackrel{}{\mathrm{\Omega }}}_u\left(n\right),& \mathrm{during\; speech\; activity},\\ {\stackrel{}{\mathrm{\Omega }}}_l\left(n-1\right),& \mathrm{else}\mathrm{.}\end{array}$$

Then, the received acoustic signal is passed through an adaptive band pass filter to retain only components within the current bandwidth limits (block 109) to obtain a spectral vector Y_tel(n). Similarly, the spectrally colored excitation signal is passed through a complementary adaptive band stop filter (block 110) so as to obtain a vector Y_ext(n).

An output signal with a standard bandwidth is generated (step 211) by starting with summing these two spectral vectors: $$\mathbf{Y}\left(n\right)={\mathbf{Y}}_{\mathit{tel}}\left(n\right)+{\mathbf{Y}}_{\mathit{ext}}\left(n\right)\mathrm{.}$$

The components of these vectors are generated as: $${\mathbf{Y}}_{\mathit{tel}}\left(n\right)={\mathbf{G}}_{\mathit{tel}}\left(n\right){\mathbf{X}}_{\mathit{w}}\left(n\right),$$ $${\mathbf{Y}}_{\mathit{ext}}\left(n\right)={\mathbf{G}}_{\mathit{ext}}\left(n\right){\mathbf{X}}_{\mathit{ext}}\left(n\right),$$ wherein the weighting matrices G_tel(n) and G_ext(n) are diagonal matrices: $${\mathbf{G}}_{\mathit{tel}}\left(n\right)=\left[\begin{array}{cccc}{G}_{\mathit{tel}}\left(e^{j{\mathrm{\Omega }}_0}n\right)& 0& \dots & 0\\ 0& G_{\mathit{tel}}\left(e^{j{\mathrm{\Omega }}_1}n\right)& \dots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \dots & G_{\mathit{tel}}\left(e^{j{\mathrm{\Omega }}_{N_{{\mathit{DFT}}^{-1}}}}n\right)\end{array}\right],$$ $${\mathbf{G}}_{\mathit{ext}}\left(n\right)=\left[\begin{array}{cccc}{G}_{\mathit{ext}}\left(e^{j{\mathrm{\Omega }}_0}n\right)& 0& \dots & 0\\ 0& G_{\mathit{tel}}\left(e^{j{\mathrm{\Omega }}_1}n\right)& \dots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \dots & G_{\mathit{tel}}\left(e^{j{\mathrm{\Omega }}_{N_{{\mathit{DFT}}^{-1}}}}n\right)\end{array}\right]\mathrm{.}$$

The elements of the matrix G_tel(n) are determined as: $$\begin{array}{c}{G}_{\mathit{tel}}\left(e^{j{\mathrm{\Omega }}_{\mu }}n\right)=\end{array}\{\begin{array}{ll}1,& \mathrm{if}{\stackrel{}{\Omega }}_l\left(n\right)\le {\mathrm{\Omega }}_{\mu }\le {\stackrel{}{\Omega }}_u\left(n\right),\\ 0,& \mathrm{else}\mathrm{.}\end{array}$$

The weights of the complementary weighting matrix are determined so as to yield the unity matrix when summed: $$G_{\mathit{ext}}\left(e^{j{\mathrm{\Omega }}_{\mu }},\mathrm{n}\right)=1-G_{\mathit{tel}}\left(e^{j{\mathrm{\Omega }}_{\mu }},\mathrm{n}\right)\mathrm{.}$$

Alternatively, the transitions at the bandwidth limits can be realized in a smoother way.

The resulting output spectrum Y(n), then, is transformed into the time domain via an inverse Fourier transform: $$\mathbf{y}\left(n\right)=\mathrm{IDFT}\left\{\mathbf{Y}\left(n\right)\right\},$$ followed by windowing the resulting vector. Particularly when using the above-indicated values for N_ana and r and a Hann window, this window function can be used again to obtain windowed time domain vectors: $${\mathbf{y}}_w\left(n\right)=\mathbf{Fy}\left(n\right)\mathrm{.}$$

The resulting time domain vectors are, then, assembled using an overlap add method (as described in K. D. Kammeyer, K. Kroschel, Digitale Signalverarbeitung) to obtain the final output signal y(n).

In the above-described steps of the method, more complex filter bank systems may be used instead of the conventional discrete Fourier transform and inverse discrete Fourier transform (see, for example, P. P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice Hall, Englewood Cliffs, NJ, USA, 1992).

Further alternatives to the above-described variants are possible as well. For example, the steps performed in the Fourier domain may also be performed in the time domain. Furthermore, equalizing the acoustic signal may be performed when adapting the narrowband codebook entries. Also, the above-described equalizing step may be augmented. For example, if an amplification or an attenuation is detected at particular frequencies, it may be adjusted within the bandwidth limits as well. In this case, the output vector Y_tel(n) is modified with the weighting matrix H_mod(n).

In addition to the above-described codebook analysis for estimating the broadband spectral envelopes, a so-called linear mapping (see B. Iser, G. Schmidt, Bandwidth Extension of Telephony Speech) may be used additionally.

Further modifications and variations of the present invention will be apparent to those skilled in the art in view of this description. Accordingly, the description is to be construed as illustrated only and is for the purpose of teaching those skilled in the art the general manner of carrying out the present invention. It is to be understood that the forms of the invention shown and described herein are to be taken as the presently preferred embodiments.