Optimized scale factor for frequency band extension in an audio frequency signal decoder

Abstract

A method and device are provided for determining an optimized scale factor to be applied to an excitation signal or a filter during a process for frequency band extension of an audio frequency signal. The band extension process includes decoding or extracting, in a first frequency band, an excitation signal and parameters of the first frequency band including coefficients of a linear prediction filter, generating an excitation signal extending over at least one second frequency band, filtering using a linear prediction filter for the second frequency band. The determination method includes determining an additional linear prediction filter, of a lower order than that of the linear prediction filter of the first frequency band, the coefficients of the additional filter being obtained from the parameters decoded or extracted from the first frequency and calculating the optimized scale factor as a function of at least the coefficients of the additional filter.

Claims

1. A scale factor determination method for determining an optimized scale factor to be applied to an excitation signal or to a filter in a band extension method, the scale factor determination method comprising: computing a first frequency response (R) of a first linear prediction filter, wherein the first linear prediction filter is applied to a first frequency band; smoothing a value of the first frequency response (R) so as to obtain a smoothed frequency response (R.sub.smoothed) using a smoothing method, wherein the smoothing method is selected from a set of at least two smoothing methods, wherein at least one of the set of at least two smoothing methods is a function of a plurality of parameters, wherein the plurality of parameters include a value of spectral slope or tilt, wherein the smoothing method comprises an adaptive smoothing method, wherein the adaptive smoothing method is adaptive over time; applying the smoothed frequency response (R.sub.smoothed) to the excitation signal, or to the filter so as to extend a frequency band of an audio frequency signal; determining the optimized scale factor based on the smoothed frequency response (R.sub.smoothed), wherein the smoothed frequency response (R.sub.smoothed) is a frequency response of the first linear prediction filter over a second frequency band, wherein the second frequency band is higher than the first frequency band, wherein a frequency response of a second filter is obtained from a polynomial of the first linear prediction filter; and applying the optimized scale factor to the excitation signal or to the filter so as to reduce artifacts during a rendering of the audio frequency signal.

2. The method of claim 1, wherein the adaptive smoothing method provides stronger smoothing for smaller values of the first frequency response (R).

3. The method of claim 1, wherein the adaptive smoothing is:
R.sub.smoothed=(1)R.sub.precomputed+R.sub.prev, wherein =1R.sub.precomputed{circumflex over ()}2, wherein R.sub.prev corresponds to a value of the smoothed frequency response (R.sub.smoothed) in a previous subframe, wherein R.sub.precomputed corresponds to the first frequency response (R).

4. The method of claim 1, wherein the set of smoothing methods further comprises an exponential smoothing with a factor, wherein the factor is fixed over time.

5. The method of claim 4, wherein the exponential smoothing is of the type:
R.sub.smoothed=0.5 R.sub.precomputed+0.5 R.sub.prev, wherein R.sub.prev corresponds to a value of the smoothed frequency response (R.sub.smoothed) in a previous subframe, wherein R.sub.precomputed corresponds to the first frequency response (R).

6. The method of claim 1, wherein the second filter has an order lower than an order of the first linear prediction filter.

7. The method of claim 1, further comprising obtaining the second filter by truncating a polynomial of the first linear prediction filter.

8. A scale factor determination method for determining an optimized scale factor to be applied to an excitation signal or to a filter in a band extension method the scale factor determination method comprising: computing a first frequency response (R) of a first linear prediction filter, wherein the first linear prediction filter is applied to a first frequency band; smoothing of a value of the frequency response R so as to obtain a smoothed frequency response (R.sub.smoothed) using a smoothing method, wherein the smoothing method is selected from a set of at least two smoothing methods, wherein at least one of the set of at least two smoothing methods is a function of a plurality of parameters, wherein the plurality of parameters include a value of spectral slope or tilt, wherein the smoothing method comprises an adaptive smoothing method, wherein the adaptive smoothing method is adaptive over time; applying the smoothed frequency response (R.sub.smoothed) to the excitation signal, or to the filter so as to extend a frequency band of an audio frequency signal; and determining the optimized scale factor, wherein the determining of the optimized scale factor comprises a computation of max(Min(R.sub.smoothed, Q), P)/P, wherein P is a frequency response of the first linear prediction filter over a second frequency band, wherein the second frequency band is higher than the first frequency band, wherein Q is a frequency response of a second filter, wherein the second filter is obtained by truncating a polynomial of the first linear prediction filter.

9. A scale factor determination method for determining an optimized scale factor to be applied to an excitation signal or to a filter in a band extension method, the scale factor determination method comprising: computing a first frequency response (R) of a first linear prediction filter, wherein the first linear prediction filter is applied to a first frequency band; smoothing of a value of the frequency response R so as to obtain a smoothed frequency response (R.sub.smoothed) using a smoothing method, wherein the smoothing method is selected from a set of at least two smoothing methods, wherein at least one of the set of at least two smoothing methods is a function of a plurality of parameters, wherein the plurality of parameters include a value of spectral slope or tilt, wherein the smoothing method comprises an adaptive smoothing method, wherein the adaptive smoothing method is adaptive over time; and applying the smoothed frequency response (R.sub.smoothed) to the excitation signal, or to the filter so as to extend a frequency band of an audio frequency signal, wherein the adaptive smoothing is:
R.sub.smoothed=(1)R.sub.precomputed+R.sub.prev, wherein =1R.sub.precomputed{circumflex over ()}2, wherein R.sub.prev corresponds to a value of the smoothed frequency response (R.sub.smoothed) in a previous subframe, wherein R.sub.precomputed corresponds to the first frequency response (R), wherein $R_{\mathrm{precomputed}}=\frac{1}{.Math.\underset{i=0}{\overset{M}{.Math.}}{\hat{a}}_i{e}^{-ji}.Math.}$ wherein M=16 is the order of the first linear prediction filter, wherein corresponds to the frequency of 6,000 Hz normalized for a sampling rate of 12.8 kHz, wherein coefficients .sub.i are the coefficients of a polynomial of the first linear prediction filter.

10. A scale factor determining apparatus for determining an optimized scale factor to be applied to an excitation signal or to a filter in an apparatus, the determining apparatus comprising: a processor circuit, wherein the processor circuit is arranged to compute a first frequency response (R) of a first linear prediction filter, wherein the first linear prediction filter is applied to a first frequency band; a smoothing circuit, wherein the smoothing circuit is arranged to select a smoothing method, wherein the smoothing method is arranged to smooth a value of the frequency response R so as to obtain a smoothed frequency response (R.sub.smoothed), wherein the smoothing method is selected from a set of at least two smoothing methods, wherein at least one of the set of at least two smoothing methods is a function of a plurality of parameters, wherein the plurality of parameters include a value of spectral slope or tilt, wherein the smoothing method comprises an adaptive smoothing method, wherein the adaptive smoothing method is adaptive over time; and an output circuit, wherein the output circuit is arranged to apply the smoothed frequency response (R.sub.smoothed) to the excitation signal, or to the filter so as to extend a frequency band of an audio frequency signal, wherein the processor circuit is arranged to determine the optimized scale factor based on the smoothed frequency response (R.sub.smoothed), wherein the smoothed frequency response (R.sub.smoothed) is a frequency response of the first linear prediction filter over a second frequency band, wherein the second frequency band is higher than the first frequency band, wherein a frequency response of a second filter is obtained from a polynomial of the first linear prediction filter, wherein the processor circuit is arranged to apply the optimized scale factor to the excitation signal or to the filter during a rendering of the audio frequency signal.

11. The scale factor determining apparatus of claim 10, wherein the second filter has an order lower than an order of the first linear prediction filter.

12. The scale factor determining apparatus of claim 10, wherein the second filter is obtained by truncating a polynomial of the first linear prediction filter.

13. The scale factor determining apparatus of claim 10, wherein the adaptive smoothing method provides stronger smoothing for smaller values of the first frequency response (R).

14. The scale factor determining apparatus of claim 10, wherein the adaptive smoothing is of a form of:
R.sub.smoothed=(1)R.sub.precomputed+R.sub.prev, wherein =1R.sub.precomputed{circumflex over ()}2, wherein R.sub.prev corresponds to a value of the smoothed frequency response (R.sub.smoothed) in a previous subframe, wherein R.sub.precomputed corresponds to the first frequency response (R).

15. A scale factor determination method for determining an optimized scale factor to be applied to an excitation signal or to a filter in a band extension method, the scale factor determination method comprising: computing a first frequency response (R) of a first linear prediction filter, wherein the first linear prediction filter is applied to a first frequency band; smoothing of a value of the frequency response R so as to obtain a smoothed frequency response (R.sub.smoothed) using a smoothing method, wherein the smoothing method is selected from a set of at least two smoothing methods, wherein at least one of the set of at least two smoothing methods is a function of a plurality of parameters, wherein the plurality of parameters include a value of spectral slope or tilt, wherein the smoothing method comprises an exponential smoothing with a factor, wherein the factor is variable over time; applying the smoothed frequency response (R.sub.smoothed) to the excitation signal, or to the filter so as to extend a frequency band of an audio frequency signal; determining the optimized scale factor based on the smoothed frequency response (R.sub.smoothed), wherein the smoothed frequency response (R.sub.smoothed) is a frequency response of the first linear prediction filter over a second frequency band, wherein the second frequency band is higher than the first frequency band, wherein a frequency response of a second filter is obtained from a polynomial of the first linear prediction filter; and applying the optimized scale factor to the excitation signal or to the filter during a rendering of the audio frequency signal.

16. A scale factor determining apparatus for determining an optimized scale factor to be applied to an excitation signal or to a filter in an apparatus, the determining apparatus comprising: a processor circuit, wherein the processor circuit is arranged to compute a first frequency response (R) of a first linear prediction filter, wherein the first linear prediction filter is applied to a first frequency band; a smoothing circuit, wherein the smoothing circuit is arranged to select a smoothing method, wherein the smoothing method is arranged to smooth a value of the frequency response R so as to obtain a smoothed frequency response (R.sub.smoothed), wherein the smoothing method is selected from a set of at least two smoothing methods, wherein at least one of the set of at least two smoothing methods is a function of a plurality of parameters, wherein the plurality of parameters include a value of spectral slope or tilt, wherein the smoothing method comprises an exponential smoothing with a factor, wherein the factor is variable over time; and an output circuit, wherein the output circuit is arranged to apply the smoothed frequency response (R.sub.smoothed) to the excitation signal, or to the filter so as to extend a frequency band of an audio frequency signal, wherein the processor circuit is arranged to determine the optimized scale factor based on the smoothed frequency response (R.sub.smoothed), wherein the smoothed frequency response (R.sub.smoothed) is a frequency response a frequency response of the first linear prediction filter over a second frequency band, wherein the second frequency band is higher than the first frequency band, wherein a frequency response of a second filter is obtained from a polynomial of the first linear prediction filter, wherein the processor circuit is arranged to apply the optimized scale factor to the excitation signal or to the filter during a rendering of the audio frequency signal.

Description

(1) Other features and advantages of the invention will become more clearly apparent on reading the following description, given purely as a nonlimiting example and with reference to the attached drawings, in which:

(2) FIG. 1 illustrates a part of a decoder of AMR-WB type implementing frequency band extension steps of the prior art and as described previously;

(3) FIGS. 2a and 2b present the coding of the high band in the AMR-WB+ codec according to the prior art and as described previously;

(4) FIG. 3 illustrates a decoder that can interwork with the AMR-WB coding, incorporating a band extension device used according to an embodiment of the invention;

(5) FIG. 4 illustrates a device for determining a scale factor optimized by a subframe as a function of the bit rate, according to an embodiment of the invention; and

(6) FIGS. 5a and 5b illustrate the frequency responses of the filters used for the computation of the optimized scale factor according to an embodiment of the invention;

(7) FIG. 6 illustrates, in flow diagram form, the main steps of a method for determining an optimized scale factor according to an embodiment of the invention;

(8) FIG. 7 illustrates an embodiment in the frequency domain of a device for determining an optimized scale factor as part of a band extension;

(9) FIG. 8 illustrates a hardware implementation of an optimized scale factor determination device in a band extension according to the invention.

(10) FIG. 3 illustrates an exemplary decoder, compatible with the AMR-WB/G.722.2 standard in which there is a band extension comprising a determination of an optimized scale factor according to an embodiment of the method of the invention, implemented by the band extension device illustrated by the block 309.

(11) Unlike the AMR-WB decoding which operates with an output sampling frequency of 16 kHz, a decoder is considered here which can operate with an output signal (synthesis) at the frequency fs=8, 16, 32 or 48 kHz. It should be noted that it is assumed here that the coding has been performed according to the AMR-WB algorithm with an internal frequency of 12.8 kHz for the CELP coding in low band and at 23.85 kbit/s a gain coding per subframe at the frequency of 16 kHz; even though the invention is described here at the decoding level, it is assumed here that the coding can also operate with an input signal at the frequency fs=8, 16, 32 or 48 kHz and suitable resampling operations, beyond the context of the invention, are implemented in coding as a function of the value of fs. It can be noted that, when fs=8 kHz, in the case of a decoding compatible with AMR-WB, it is not necessary to extend the 0-6.4 kHz low band, because the audio band reconstructed at the frequency fs is limited to 0-4000 Hz.

(12) In FIG. 3, the CELP decoding (LF for low frequencies) still operates at the internal frequency of 12.8 kHz, as in AMR-WB, and the band extension (HF for high frequencies) used for the invention operates at the frequency of 16 kHz, and the LF and HF syntheses are combined (block 312) at the frequency fs after suitable resampling (block 306 and internal processing in the block 311). In the variant embodiments, the combining of the low and high bands can be done at 16 kHz, after having resampled the low band from 12.8 to 16 kHz, before resampling the combined signal at the frequency fs.

(13) The decoding according to FIG. 3 depends on the AMR-WB mode (or bit rate) associated with the current frame received. As an indication, and without affecting the block 309, the decoding of the CELP part in low band comprises the following steps: demultiplexing of the coded parameters (block 300) in the case of a frame correctly received (bfi=0 where bfi is the bad frame indicator with a value 0 for a frame received and 1 for a frame lost); decoding of the ISF parameters with interpolation and conversion into LPC coefficients (block 301) as described in clause 6.1 of the standard G.722.2; decoding of the CELP excitation (block 302), with an adaptive and fixed part for reconstructing the excitation (exc or u(n)) in each subframe of length 64 at 12.8 kHz:
u(n)=.sub.pv(n)+.sub.cc(n),n=0,L,63
by following the notations of clause 7.1.2.1 of ITU-T recommendation G.718 of a decoder interoperable with the AMR-WB coder/decoder, concerning the CELP decoding, where v(n) and c(n) are respectively the code words of the adaptive and fixed dictionaries, and .sub.p and .sub.c are the associated decoded gains. This excitation u(n) is used in the adaptive dictionary of the next subframe; it is then post-processed and, as in G.718, the excitation u(n) (also denoted exc) is distinguished from its modified post-processed version u(n) (also denoted exc2) which serves as input for the synthesis filter, 1/(z), in the block 303; synthesis filtering by 1/(z) (block 303) where the decoded LPC filter (z) is of the order 16; narrow-band post-processing (block 304) according to clause 7.3 of G.718 if fs=8 kHz; de-emphasis (block 305) by the filter 1/(10.68z.sup.1); post-processing of the low frequencies (called bass posfilter) (block 306) attenuating the cross-harmonics noise at low frequencies as described in clause 7.14.1.1 of G.718. This processing introduces a delay which is taken into account in the decoding of the high band (>6.4 kHz); resampling of the internal frequency of 12.8 kHz at the output frequency fs (block 307). A number of embodiments are possible. Without losing generality, it is considered here, by way of example, that if fs=8 or 16 kHz, the resampling described in clause 7.6 of G.718 is repeated here, and if fs=32 or 48 kHz, additional finite impulse response (FIR) filters are used; computation of the parameters of the noise gate (block 308) preferentially performed as described in clause 7.14.3 of G.718 to enhance the quality of the silences by level reduction.
In variants which can be implemented for the invention, the post-processing operations applied to the excitation can be modified (for example, the phase dispersion can be enhanced) or these post-processing operations can be extended (for example, a reduction of the cross-harmonics noise can be implemented), without affecting the nature of the band extension.
It can be noted that the use of blocks 306, 308, 314 is optional.
It will also be noted that the decoding of the low band described above assumes a so-called active current frame with a bit rate between 6.6 and 23.85 kbit/s. In fact, when the DTX mode is activated, certain frames can be coded as inactive and in this case it is possible to either transmit a silence descriptor (on 35 bits) or transmit nothing. In particular, it will be recalled that the SID frame describes a number of parameters: ISF parameters averaged over 8 frames, average energy over 8 frames, dithering flag for the reconstruction of non-stationary noise. In all cases, in the decoder, there is the same decoding model as for an active frame, with a reconstruction of the excitation and of an LPC filter for the current frame, which makes it possible to apply the band extension even to inactive frames. The same observation applies for the decoding of lost frames (or FEC, PLC) in which the LPC model is applied.

(14) In the embodiment described here and with reference to FIG. 7, the decoder makes it possible to extend the decoded low band (50-6400 Hz taking into account the 50 Hz high-pass filtering on the decoder, 0-6400 Hz in the general case) to an extended band, the width of which varies, ranging approximately from 50-6900 Hz to 50-7700 Hz depending on the mode implemented in the current frame. It is thus possible to refer to a first frequency band of 0 to 6400 Hz and to a second frequency band of 6400 to 8000 Hz. In reality, in the preferred embodiment, the extension of the excitation is performed in the frequency domain in a 5000 to 8000 Hz band, to allow a bandpass filtering of 6000 to 6900 or 7700 Hz width.

(15) At 23.85 kbit/s, the HF gain correction information (0.8 kbit/s) transmitted at 23.85 kbit/s is here decoded. Its use is detailed later, with reference to FIG. 4. The high-band synthesis part is produced in the block 309 representing the band extension device used for the invention and which is detailed in FIG. 7 in an embodiment.

(16) In order to align the decoded low and high bands, a delay (block 310) is introduced to synchronize the outputs of the blocks 306 and 307 and the high band synthesized at 16 kHz is resampled from 16 kHz to the frequency fs (output of block 311). The value of the delay T depends on how the high band signal is synthesized, and on the frequency fs as in the post-processing of the low frequencies. Thus, generally, the value of T in the block 310 will have to be adjusted according to the specific implementation.

(17) The low and high bands are then combined (added) in the block 312 and the synthesis obtained is post-processed by 50 Hz high-pass filtering (of IIR type) of order 2, the coefficients of which depend on the frequency fs (block 313) and output post-processing with optional application of the noise gate in a manner similar to G.718 (block 314).

(18) Referring to FIG. 3, an embodiment of a device for determining an optimized scale factor to be applied to an excitation signal in a frequency band extension process is now described. This device is included in the band extension block 309 described previously.

(19) Thus, the block 400, from an excitation signal decoded in a first frequency band u (n), performs a band extension to obtain an extended excitation signal u.sub.HB(n) on at least one second frequency band.

(20) It will be noted here that the optimized scale factor estimation according to the invention is independent of how the signal u.sub.HB(n) is obtained. One condition concerning its energy is, however, important. Indeed, the energy of the high band from 6000 to 8000 Hz must be at a level similar to the energy of the band from 4000 to 6000 Hz of the decoded excitation signal at the output of the block 302. Furthermore, since the low-band signal is de-emphasized (block 305), the de-emphasis must also be applied to the high-band excitation signal, either by using a specific de-emphasis filter, or by multiplying by a constant factor which corresponds to an average attenuation of the filter mentioned. This condition does not apply to the case of the 23.85 kbit/s bit rate which uses the additional information transmitted by the coder. In this case, the energy of the high-band excitation signal must be consistent with the energy of the signal corresponding to the coder, as explained later.

(21) The frequency band extension can, for example, be implemented in the same way as for the decoder of AMR-WB type described with reference to FIG. 1 in the blocks 100 to 102, from a white noise.

(22) In another embodiment, this band extension can be performed from a combination of a white noise and of a decoded excitation signal as illustrated and described later for the blocks 700 to 707 in FIG. 7.

(23) Other frequency band extension methods with conservation of the energy level between the decoded excitation signal and the extended excitation signal as described below, can of course be envisaged for the block 400.

(24) Furthermore, the band extension module can also be independent of the decoder and can perform a band extension for an existing audio signal stored or transmitted to the extension module, with an analysis of the audio signal to extract an excitation and an LPC filter therefrom. In this case, the excitation signal at the input of the extension module is no longer a decoded signal but a signal extracted after analysis, like the coefficients of the linear prediction filter of the first frequency band used in the method for determining the optimized scale factor in an implementation of the invention.

(25) In the example illustrated in FIG. 4, the case of the bit rates<23.85 kbit/s, for which the determination of the optimized scale factor is limited to the block 401, is considered first.

(26) In this case, an optimized scale factor denoted g.sub.HB2(m) is computed. In one embodiment, this computation is performed preferentially for each subframe and it consists in equalizing the levels of the frequency responses of the LPC filters 1/(z) and 1/(z/) used in low and high frequencies, as described later with reference to FIG. 7, with additional precautions to avoid the cases of overestimations which can result in an excessive energy of the synthesized high band and therefore generate audible artifacts.

(27) In an alternative embodiment, it will be possible to keep the extrapolated HF synthesis filter 1/.sup.ext(z/) as implemented in the AMR-WB decoder or a decoder that can interwork with the AMR-WB coder/decoder, for example according to the ITU-T recommendation G.718, in place of the filter 1/(z/). The compensation according to the invention is then performed from the filters 1/(z) and 1/.sup.ext(z/).

(28) The determination of the optimized scale factor is also performed by the determination (in 401a) of a linear prediction filter called additional filter, of lower order than the linear prediction filter of the first frequency band 1/(z), the coefficients of the additional filter being obtained from the parameters decoded or extracted from the first frequency band. The optimized scale factor is then computed (in 401b) as a function at least of these coefficients to be applied to the extended excitation signal u.sub.HB(n).

(29) The principle of the determination of the optimized scale factor, implemented in the block 401, is illustrated in FIGS. 5a and 5b with concrete examples obtained from signals sampled at 16 kHz; the frequency response amplitude values, denoted R, P, Q below, of 3 filters are computed at the common frequency of 6000 Hz (vertical dotted line) in the current subframe, of which the index m is not recalled here in the notations of the LPC filters interpolated by subframe to lighten the text. The value of 6000 Hz is chosen such that it is close to the Nyquist frequency of the low band, that is 6400 Hz. It is preferable not to take this Nyquist frequency to determine the optimized scale factor. Indeed, the energy of the decoded signal in low frequencies is typically already attenuated at 6400 Hz. Furthermore, the band extension described here is performed on a second frequency band, called high band, which ranges from 6000 to 8000 Hz. It should be noted that, in variants of the invention, a frequency other than 6000 Hz will be able to be chosen, with no loss of generality for determining the optimized scale factor. It will also be possible to consider the case where the two LPC filters are defined for the separate bands (as in AMR-WB+). In this case, R, P and Q will be computed at the separation frequency.

(30) FIGS. 5a and 5b illustrate how the quantities R, P, Q are defined.

(31) The first step consists in computing the frequency responses R and P respectively of the linear prediction filter of the first frequency band (low band) and of the second frequency band (high band) at the frequency of 6000 Hz. The following is first computed:

(32) $R=\frac{1}{.Math.\hat{A}\left(e^j\right).Math.}=\frac{1}{.Math.\underset{i=0}{\overset{M}{.Math.}}{\hat{a}}_i{e}^{-\mathrm{ji}}.Math.}$
in which M=16 is the order of the decoded LPC filter, 1/(z), and corresponds to the frequency of 6000 Hz normalized for the sampling frequency of 12.8 kHz, that is:

(33) $=2\frac{6000}{12800}.$
Then, similarly, the following is computed:

(34) $P=\frac{1}{.Math.\hat{A}\left(e^{j{}^{}}/\right).Math.}=\frac{1}{.Math.\underset{i=0}{\overset{M}{.Math.}}{\hat{a}}_i{}^i{e}^{-\mathrm{ji}{}^{}}.Math.}$
in which

(35) ${}^{}=2\frac{6000}{16000}.$
In a preferred embodiment, the quantities P and R are computed according to the following pseudo-code:

(36) TABLE-US-00001 px = py = 0 rx = ry = 0 for i=0 to 16 px = px + Ap[i]*exp_tab_p[i] py = py + Ap[i]*exp_tab_p[33-i] rx = rx + Aq[i]*exp_tab_q[i] ry = ry + Aq[i]*exp_tab_q[33-i] end for P = 1/sqrt(px*px+py*py) R = 1/sqrt(rx*rx+ry*ry)
in which Aq[i]=.sub.i corresponds to the coefficients of (z) (of order 16), Ap[i]=.sup.i.sub.i corresponds to the coefficient of (z/), sqrt( ) corresponds to the square root operation and the tables exp_tab_p and exp_tab_q of size 34 contain the real and imaginary parts of the complex exponentials associated with the frequency of 6000 Hz, with

(37) $\mathrm{exp\_tab}\mathrm{\_p}\left[i\right]=\{\begin{array}{cc}\cos \left(2\frac{6000}{12800}i\right)& i=0,L,16\\ -\sin \left(2\frac{6000}{12800}\left(33-i\right)\right)& i=17,L,33\end{array}\mathrm{exp\_tab}\mathrm{\_q}\left[i\right]=\{\begin{array}{cc}\cos \left(2\frac{6000}{16000}i\right)& i=0,L,16\\ -\sin \left(2\frac{6000}{16000}\left(33-i\right)\right)& i=17,L,33\end{array}$
The additional prediction filter is obtained for example by suitably truncating the polynomial (z) to the order 2.
In fact, the direct truncation to the order leads to the filter 1+.sub.1+.sub.2, which can pose a problem because there is generally nothing to guarantee that this filter of order 2 is stable. In a preferred embodiment, the stability of the filter 1+.sub.1+.sub.2 is therefore detected and a filter 1+.sup.1+.sub.2 is used, the coefficients of which are drawn from 1+.sub.1+.sub.2 as a function of the instability detection. More specifically, the following are initialized:
.sub.1=.sub.i,i=1,2
The stability of the filter 1+.sub.1+.sub.2 can be verified differently; here, a conversion is used in the PARCOR coefficients (or reflection coefficients) domain by computing:
k.sub.1=.sub.1/(1+.sub.2)
k.sub.2=.sub.2

(38) The stability is verified if |k.sub.i|<1, i=1, 2. The value of k.sub.i is therefore conditionally modified before ensuring the stability of the filter, with the following steps:

(39) $k_2\{\begin{array}{cc}\min \left(0.6,k_2\right)& k_2>0\\ \max \left(-0.6,k_2\right)& k_2<0\end{array}{k}_1\{\begin{array}{cc}\min \left(0.99,k_2\right)& k_1>0\\ \max \left(-0.99,k_2\right)& k_1<0\end{array}$
in which min(.,.) and max(.,.) respectively give the minimum and the maximum of 2 operands.
It should be noted that the threshold values, 0.99 for k.sub.1 and 0.6 for k.sub.2, will be able to be adjusted in variants of the invention. It will be recalled that the first reflection coefficient, k.sub.1, characterizes the spectral slope (or tilt) of the signal modeled to the order 1; in the invention the value of k.sub.1 is saturated at a value close to the stability limit, in order to preserve this slope and retain a tilt similar to that of 1/(z). It will also be recalled that the second reflection coefficient, k.sub.2, characterizes the resonance level of the signal modeled to the order 2; since the use of a filter of order 2 aims to eliminate the influence of such resonances around the frequency of 6000 Hz, the value of k.sub.2 is more strongly limited; this limit is set at 0.6.

(40) The coefficients of 1+.sub.1+.sub.2 are then obtained by:
.sub.1=(1+k.sub.2)k.sub.1
.sub.2=k.sub.2
The frequency response of the additional filter is therefore finally computed:

(41) 0$Q=\frac{1}{.Math.\underset{k=0}{\overset{2}{.Math.}}{\hat{a}}_k^{}{e}^{-\mathrm{jk}}.Math.}$$\mathrm{with}=2\frac{6000}{12800}.$
This quantity is computed preferentially according to the following pseudo-code:

(42) TABLE-US-00002 qx = qy = 0 for i=0 to 2 qx = qx + As[i]*exp_tab_q[i]; qy = qy + As[i]*exp_tab_q[33-i]; end for Q = 1/sqrt(qx*qx+qy*qy)
in which As[i]=.sub.i.

(43) With no loss of generality, it will be possible to compute the coefficients of the filter of order 2 otherwise, for example by applying to the LPC filter (z) of order 16 the reduction procedure of the LPC order called STEP DOWN described in J. D. Markel and A. H. Gray, Linear Prediction of Speech, Springer Verlag, 1976 or by performing two Levinson-Durbin (or STEP-UP) algorithm iterations from the self-correlations computed on the signal synthesized (decoded) at 12.8 kHz and windowed.

(44) For some signals, the quantity Q, computed from the first 3 LPC coefficients decoded, better takes account of the influence of the spectral slope (or tilt) in the spectrum and avoids the influence of spurious peaks or troughs close to 6000 Hz which can skew or raise the value of the quantity R, computed from all the LPC coefficients.
In a preferred embodiment, the optimized scale factor is deduced from the pre-computed quantities R, P, Q conditionally, as follows:
If the tilt (computed as in AMR-WB in the block 104, by normalized self-correlation in the form r(1)/r(0) in which r(i) is the self-correlation) is negative (tilt<0 as represented in FIG. 5b), the computation of the scale factor is done as follows:

(45) to avoid artifacts due to excessively abrupt variations of energy of the high band, a smoothing is applied to the value of R. In a preferred embodiment, an exponential smoothing is performed with a fixed factor in time (0.5) in the form of:
R=0.5R+0.5R.sub.Prev
R.sub.prev=R
in which R.sub.prev corresponds to the value of R in the preceding subframe and the factor 0.5 is optimized empirically obviously, the factor 0.5 will be able to be changed for another value and other smoothing methods are also possible. It should be noted that the smoothing makes it possible to reduce the temporal variants and therefore avoid artifacts.
The optimized scale factor is then given by:
g.sub.HB2(m)=Max(Min(R,Q),P)/P
In an alternative embodiment, it will be possible to replace the smoothing of R with a smoothing of g.sub.HB2(m) such that:
g.sub.HB2(m)0.5g.sub.HB2(m)+0.5g.sub.HB2(m1)
If the tilt (computed as in AMR-WB in the block 104) is positive (tilt>0 as in FIG. 5a), the computation of the scale factor is done as follows:

(46) the quantity R is smoothed adaptively in time, with a stronger smoothing when R is low as in the preceding case, this smoothing makes it possible to reduce the temporal variants and therefore avoids artifacts:
R=(1)R+R.sub.prev with =1R.sup.2
R.sub.prev=R
Then, the optimized scale factor is given by:
g.sub.HB2=min(R,P,Q)/P
In an alternative embodiment, it will be possible to replace the smoothing of R with a smoothing of g.sub.HB2(m) as computed above.
g.sub.HB(m)=(1)g.sub.HB(m)+g.sub.HB(m1),m=0, . . . ,3,=1g.sub.HB.sup.2(m)
where g.sub.HB(1) is the scale or gain factor computed for the last subframe of the preceding frame.
The minimum of R, P, Q is taken here in order to avoid overestimating the scale factor.
In a variant, the above condition depending only on the tilt will be able to be extended to take account not only of the tilt parameter but also of other parameters in order to refine the decision. Furthermore, the computation of g.sub.HB2 (m) will be able to be adjusted according to these said additional parameters.
An example of additional parameter is the number of zero crossings (ZCR, zero crossing rate) which can be defined as:

(47) ${\mathrm{zcr}}_s=\frac{1}{2}\underset{n=1}{\overset{N-1}{.Math.}}.Math.\mathrm{sgn}\left[s\left(n\right)\right]-\mathrm{sgn}\left[s\left(n-1\right)\right].Math.$
in which

(48) $\mathrm{sgn}\left(x\right)=\{\begin{array}{cc}1& \mathrm{if}x0\\ -1& \mathrm{if}x<0\end{array}$
The parameter zcr generally gives results similar to the tilt. A good classification criterion is the ratio between zcr.sub.s computed for the synthesized signal s(n) and zcr.sub.u computed for the excitation signal u(n) at 12 800 Hz. This ratio is between 0 and 1, where 0 means that the signal has a decreasing spectrum, 1 that the spectrum is increasing (which corresponds to (1tilt)/2. In this case, a ratio zcr.sub.s/zcr.sub.u>0.5 corresponds to the case tilt<0, a ratio zcr.sub.s/zcr.sub.u<0.5 corresponds to tilt>0.
In a variant, it will be possible to use a function of a parameter tilt.sub.hp where tilt.sub.hp is the tilt computed for the synthesized signal s(n) filtered by a high-pass filter with a cut-off frequency for example at 4800 Hz; in this case, the response 1/(z/) from 6 to 8 kHz (applied at 16 kHz) corresponds to the weighted response of 1/(z) from 4.8 to 6.4 kHz. Since 1/(z/) has a more flattened response, it is necessary to compensate this change of tilt. The scale factor function according to tilt.sub.hp is then given in an embodiment by: (1tilt.sub.hp).sup.2+0.6. Q and R are therefore multiplied by min (1,(1tilt.sub.hp).sup.2+0.6) when tilt>0 or by max (1, (1tilt.sub.hp).sup.2+0.6) when tilt<0.

(49) The case of the 23.85 kbit/s bit rate is now considered, for which a gain correction is performed by the blocks 403 to 408. This gain correction could moreover be the subject of a separate invention. In this particular embodiment according to the invention, the gain correction information, denoted g.sub.HBcorr(m), transmitted by the AMR-WB (compatible) coding with a bit rate of 0.8 kbit/s, is used to improve the quality at 23.85 kbit/s.

(50) It is assumed here that the AMR-WB (compatible) coding has performed a correction gain quantization on 4 bits as described in ITU-T clause G.722.2/5.11 or, equivalently, in the 3GPP clause TS 26.190/5.11.

(51) In the AMR-WB coder, the correction gain is computed by comparing the energy of the original signal sampled at 16 kHz and filtered by a 6-7 kHz bandpass filter, s.sub.HB(n), with the energy of the white noise at 16 kHz filtered by a synthesis filter 1/(z/) and a 6-7 kHz bandpass filter (before the filtering, the energy of the noise is set to a level similar to that of the excitation at 12.8 kHz), s.sub.HB2(n). The gain is the root of the ratio of energy of the original signal to the energy of the noise divided by two. In one possible embodiment, it will be possible to change the bandpass filter for a filter with a wider band (for example from 6 to 7.6 kHz).

(52) $g_{\mathrm{HBcorr}}\left(m\right)=\sqrt{\frac{\underset{n=80m}{\overset{80\left(m+1\right)-1}{.Math.}}{s_{\mathrm{HB}}\left(n\right)}^2}{\underset{n=80m}{\overset{80\left(m+1\right)-1}{.Math.}}{s_{\mathrm{HB}2}\left(n\right)}^2}},m=0,\mathrm{.Math.},3$
To be able to apply the gain information received at 23.85 kbit/s (in the block 407), it is important to bring the excitation to a level similar to that expected of the AMR-WB (compatible) coding. Thus, the block 404 performs the scaling of the excitation signal according to the following equation:
u.sub.HB1(n)=g.sub.HB3(m)u.sub.HB(n),n=80m,L,80(m+1)1
in which g.sub.HB3(m) is a gain per subframe computed in the block 403 in the form:

(53) $g_{\mathrm{HB}3}\left(m\right)=\sqrt{\frac{\underset{n=0}{\overset{63}{.Math.}}{u\left(n\right)}^2}{5.Math.\underset{n=0}{\overset{79}{.Math.}}{u_{\mathrm{HB}}\left(n\right)}^2}}$
in which the factor 5 in the denominator serves to compensate the bandwidth difference between the signal u(n) and the signal u.sub.HB(n), given that, in the AMR-WB coding, the HF excitation is a white noise over the 0-8000 Hz band.
The index of 4 bits per subframe, denoted index.sub.HF_gain(m), sent at 23.85 kbit/s is demultiplexed from the bit stream (block 405) and decoded by the block 406 as follows:
g.sub.HBcorr(m)=2.Math.HP_gain(index.sub.HF_gain(m))
in which HP_gain(.) is the HF gain quantization dictionary defined in the AMR-WB coding and recalled below:

(54) TABLE-US-00003 TABLE 1 (gain dictionary at 23.85 kbit/s) i HP_gain(i) I HP_gain(i) 0 0.110595703125000 8 0.342102050781250 1 0.142608642578125 9 0.372497558593750 2 0.170806884765625 10 0.408660888671875 3 0.197723388671875 11 0.453002929687500 4 0.226593017578125 12 0.511779785156250 5 0.255676269531250 13 0.599822998046875f 6 0.284545898437500 14 0.741241455078125 7 0.313232421875000 15 0.998779296875000
The block 407 performs the scaling of the excitation signal according to the following equation:
u.sub.HB2(n)=g.sub.HBcorr(m)u.sub.HB1(n),n=80m,L,80(m+1)1
Finally, the energy of the excitation is adjusted to the level of the current subframe with the following conditions (block 408). The following is computed:

(55) $\mathrm{fac}\left(m\right)=\sqrt{\frac{\underset{n=0}{\overset{79}{.Math.}}{\left(g\left(m\right)g_{\mathrm{HB}2}\left(m\right)u_{\mathrm{HB}}\left(n\right)\right)}^2}{\underset{n=0}{\overset{79}{.Math.}}{u_{\mathrm{HB}2}\left(n\right)}^2}}$
The numerator here represents the high-band signal energy which would be obtained in the mode 23.05. As explained before, for the bit rates<23.85 kbit/s, it is necessary to retain the level of energy between the decoded excitation signal and the extended excitation signal u.sub.HB(n), but this constraint is not necessary in the case of the 23.85 kbit/s bit rate, since u.sub.HB(n) is in this case scaled by the gain g.sub.HB3(m). To avoid double multiplications, certain multiplication operations applied to the signal in the block 400 are applied in the block 402 by multiplying by g(m). The value of g(m) depends on the u.sub.HB(n) synthesis algorithm and must be adjusted such that the energy level between the decoded excitation signal in low band and the signal g(m)u.sub.HB(n) is retained.
In a particular embodiment, which will be described in detail later with reference to FIG. 7, g(m)=0.6g.sub.HB1(m), where g.sub.HB1(m) is a gain which ensures, for the signal u.sub.HB, the same ratio between energy per subframe and energy per frame as for the signal u (n) and 0.6 corresponds to the average frequency response amplitude value of the de-emphasis filter from 5000 to 6400 Hz.
It is assumed that, in the block 408, there is information on the tilt of the low-band signal in a preferred embodiment, this tilt is computed as in the AMR-WB codec according to the blocks 103 and 104, but other methods for estimating the tilt are possible without changing the principle of the invention.
If fac(m)>1 or tilt<0, the following is assumed:
u.sub.HB(n)=u.sub.HB2(n)n=80m,L,80(m+1)1
Otherwise:
u.sub.HB(n)=max({square root over (1tilt)},fac(m)).Math.u.sub.HB2(n),n=80m,L,80(m+1)1
It will be noted that the optimized scale factor computation described here, notably in the blocks 401 and 402, is distinguished from the abovementioned equalization of filter levels performed in the AMR-WB+ codec by a number of aspects: The optimized scale factor is computed directly from the transfer functions of the LPC filters without involving any temporal filtering. This simplifies the method. The equalization is done preferentially at a frequency different from the Nyquist frequency (6400 Hz) associated with the low band. Indeed, the LPC modeling implicitly represents the attenuation of the signal typically caused by the resampling operations and therefore the frequency response of an LPC filter may be subject at the Nyquist frequency to a decrease which is not at the chosen common frequency. The equalization here relies on a filter of lower order (here of order 2) in addition to the 2 filters to be equalized. This additional filter makes it possible to avoid the effects of local spectral fluctuations (peaks or troughs) which may be present at the common frequency for the computation of the frequency response of the prediction filters.
For the blocks 403 to 408, the advantage of the invention is that the quality of the signal decoded at 23.85 kbit/s according to the invention is improved relative to a signal decoded at 23.05 kbit/s, which is not the case in an AMR-WB decoder. In fact, this aspect of the invention makes it possible to use the additional information (0.8 kbit/s) received at 23.85 kbit/s, but in a controlled manner (block 408), to improve the quality of the extended excitation signal at the bit rate of 23.85.
The device for determining the optimized scale factor as illustrated by the blocks 401 to 408 of FIG. 4 implements a method for determining the optimized scale factor now described with reference to FIG. 6.

(56) The main steps are implemented by the block 401.

(57) Thus, an extended excitation signal u.sub.HB(n) is obtained in a frequency band extension method E601 which comprises a step of decoding or of extraction, in a first frequency band called low band, of an excitation signal and of parameters of the first frequency band such as, for example, the coefficients of the linear prediction filter of the first frequency band.

(58) A step E602 determines a linear prediction filter called additional filter, of lower order than that of the first frequency band. To determine this filter, the parameters of the first frequency band decoded or extracted are used.

(59) In one embodiment, this step is performed by truncation of the transfer function of the linear prediction filter of the low band to obtain a lower filter order, for example 2. These coefficients can then be modified as a function of a stability criterion as explained previously with reference to FIG. 4.

(60) From the coefficients of the additional filter thus determined, a step E603 is implemented to compute the optimized scale factor to be applied to the extended excitation signal. This optimized scale factor is, for example, computed from the frequency response of the additional filter at a common frequency between the low band (first frequency band) and the high band (second frequency band). A minimum value can be chosen between the frequency response of this filter and those of the low-band and high-band filters.

(61) This therefore avoids the overestimations of energy which could exist in the methods of the prior art.

(62) This step of computation of the optimized scale factor is, for example, described previously with reference to FIG. 4 and FIGS. 5a and 5b.

(63) The step E604 performed by the block 402 or 409 (depending on the decoding bit rate) for the band extension, applies the duly computed optimized scale factor to the extended excitation signal so as to obtain an optimized extended extension signal u.sub.HB(n).

(64) In a particular embodiment, the device for determining the optimized scale factor 708 is incorporated in a band extension device now described with reference to FIG. 7. This device for determining the optimized scale factor illustrated by the block 708 implements the method for determining the optimized scale factor described previously with reference to FIG. 6.

(65) In this embodiment, the band extension block 400 of FIG. 4 comprises the blocks 700 to 707 of FIG. 7 that is now described.

(66) Thus, at the input of the band extension device, a low-band excitation signal decoded or estimated by analysis is received (u(n)). The band extension here uses the excitation decoded at 12.8 kHz (exc2 or u(n)) at the output of the block 302 of FIG. 3.

(67) It will be noted that, in this embodiment, the generation of the oversampled and extended excitation is performed in a frequency band ranging from 5 to 8 kHz therefore including a second frequency band (6.4-8 kHz) above the first frequency band (0-6.4 kHz).

(68) Thus, the generation of an extended excitation signal is performed at least over the second frequency band but also over a part of the first frequency band.

(69) Obviously, the values defining these frequency bands can be different depending on the decoder or the processing device in which the invention is applied.

(70) For this exemplary embodiment, this signal is transformed to obtain an excitation signal spectrum U(k) by the time-frequency transformation module 500. In a particular embodiment, the transform uses a DCT-IV (for Discrete Cosine Transformtype IV) (block 700) on the current frame of 20 ms (256 samples), without windowing, which amounts to directly transforming u(n) with n=0,L, 255 according to the following formula:

(71) $U\left(k\right)=\underset{n=0}{\overset{N-1}{.Math.}}u\left(n\right)\cos \left(\frac{}{N}\left(n+\frac{1}{2}\right)\left(k+\frac{1}{2}\right)\right)$
in which N=256 and k=0,L, 255.
It should be noted here that the transformation without windowing (or, equivalently, with an implicit rectangular window of the length of the frame) is possible because the processing is performed in the excitation domain, and not the signal domain so that no artifact (block effects) is audible, which constitutes an important advantage of this embodiment of the invention.

(72) In this embodiment, the DCT-IV transformation is implemented by FFT according to the so-called Evolved DCT (EDCT) algorithm described in the article by D. M. Zhang, H. T. Li, A Low Complexity TransformEvolved DCT, IEEE 14th International Conference on Computational Science and Engineering (CSE), August 2011, pp. 144-149, and implemented in the ITU-T standards G.718 Annex B and G.729.1 Annex E.

(73) In variants of the invention, and without loss of generality, the DCT-IV transformation will be able to be replaced by other short-term time-frequency transformations of the same length and in the excitation domain, such as an FFT (for Fast Fourier Transform) or a DCT-II (Discrete Cosine Transformtype II). Alternatively, it will be possible to replace the DCT-IV on the frame by a transformation with overlap-addition and windowing of length greater than the length of the current frame, for example by using an MDCT (for Modified Discrete Cosine Transform). In this case, the delay T in the block 310 of FIG. 3 will have to be adjusted (reduced) appropriately as a function of the additional delay due to the analysis/synthesis by this transform.

(74) The DCT spectrum, U(k), of 256 samples covering the 0-6400 Hz band (at 12.8 kHz), is then extended (block 701) into a spectrum of 320 samples covering the 0-8000 Hz band (at 16 kHz) in the following form:

(75) $U_{\mathrm{HB}1}\left(k\right)=\{\begin{array}{cc}0& k=0,L,199\\ U\left(k\right)& k=200,L,239\\ U\left(k+\mathrm{start\_band}-240\right)& k=240,L,319\end{array}$
in which it is preferentially taken that start_band=160.

(76) The block 701 operates as module for generating an oversampled and extended excitation signal and performs a resampling from 12.8 to 16 kHz in the frequency domain, by adding of samples (k=240,L,319) to the spectrum, the ratio between 16 and 12.8 being 5/4.

(77) Furthermore, the block 701 performs an implicit high-pass filtering in the 0-5000 Hz band since the first 200 samples of U.sub.HB1(k) are set to zero; as explained later, this high-pass filtering is also complemented by a part of progressive attenuation of the spectral values of indices k=200,L, 255 in the 5000-6400 Hz band; this progressive attenuation is implemented in the block 704 but could be performed separately outside of the block 704. Equivalently, and in variants of the invention, the implementation of the high-pass filtering separated into blocks of coefficients of index k=0,L,199 set to zero, of attenuated coefficients k=200,L, 255 in the transformed domain, will therefore be able to be performed in a single step.

(78) In this exemplary embodiment and according to the definition of U.sub.HB1(k), it will be noted that the 5000-6000 Hz band of U.sub.HB1(k) (which corresponds to the indices k=200,L, 239) is copied from the 5000-6000 Hz band of U(k). This approach makes it possible to retain the original spectrum in this band and avoids introducing distortions in the 5000-6000 Hz band upon the addition of the HF synthesis with the LF synthesisin particular the phase of the signal (implicitly represented in the DCT-IV domain) in this band is preserved.

(79) The 6000-8000 Hz band of U.sub.HB1(k) is here defined by copying the 4000-6000 Hz band of U(k) since the value of start_band is preferentially set at 160.

(80) In a variant of the embodiment, the value of start_band will be able to be made adaptive around the value of 160. The details of the adaptation of the start_band value are not described here because they go beyond the framework of the invention without changing its scope.

(81) For certain wide-band signals (sampled at 16 kHz), the high band (>6 kHz) may be noisy, harmonic or comprise a mixture of noise and harmonics. Furthermore, the level of harmonicity in the 6000-8000 Hz band is generally correlated with that of the lower frequency bands. Thus, the noise generation block 702 performs a noise generation in the frequency domain, U.sub.HBN(k) for k=240,L,319 (80 samples) corresponding to a second frequency band called high frequency in order to then combine this noise with the spectrum U.sub.HB1(k) in the block 703.

(82) In a particular embodiment, the noise (in the 6000-8000 Hz band) is generated pseudo-randomly with a linear congruential generator on 16 bits:

(83) $U_{\mathrm{HBN}}\left(k\right)=\{\begin{array}{cc}0& k=0,L,239\\ 31821U_{\mathrm{HBN}}\left(k-1\right)+13849& k=240,L,319\end{array}$
with the convention that U.sub.HBN (239) in the current frame corresponds to the value U.sub.HBN (319) of the preceding frame. In variants of the invention, it will be possible to replace this noise generation by other methods.

(84) The combination block 703 can be produced in different ways. Preferentially, an adaptive additive mixing of the following form is considered:
U.sub.HB2(k)U.sub.HB1(k)G.sub.HBNU.sub.HBN(k),k=240,L,319
in which G.sub.HBN is a normalization factor serving to equalize the level of energy between the two signals,

(85) $G_{\mathrm{HBN}}=\sqrt{\frac{\underset{k=240}{\overset{319}{.Math.}}{U_{\mathrm{HB}1}\left(k\right)}^2+\mathrm{.Math.}}{\underset{k=240}{\overset{319}{.Math.}}{U_{\mathrm{HBN}}\left(k\right)}^2+\mathrm{.Math.}}}$
with =0.01, and the coefficient (between 0 and 1) is adjusted as a function of parameters estimated from the decoded low band and the coefficient between 0 and 1) depends on .

(86) In a preferred embodiment, the energy of the noise is computed in three bands: 2000-4000 Hz, 4000-6000 Hz and 6000-8000 Hz, with

(87) 0$E_{N2\text{-}4}=\underset{kN\left(80,159\right)}{.Math.}{U}^2\left(k\right)$$E_{N4\text{-}6}=\underset{kN\left(160,239\right)}{.Math.}{U}^2\left(k\right)$$E_{N4\text{-}6}=\underset{kN\left(240,319\right)}{.Math.}{U}^2\left(k\right)$
in which

(88) $U^{}\left(k\right)=\{\begin{array}{cc}\sqrt{\frac{\underset{k=160}{\overset{239}{.Math.}}{U}^2\left(k\right)}{\stackrel{159}{\underset{k=80}{.Math.}}{U}^2\left(k\right)}U\left(k\right)}& k=80,\mathrm{.Math.},159\\ U\left(k\right)& k=160,\mathrm{.Math.},239\\ \sqrt{\frac{\underset{k=160}{\overset{239}{.Math.}}{U}^2\left(k\right)}{\stackrel{319}{\underset{k=240}{.Math.}}{U}_{\mathrm{HB}1}^2\left(k\right)}{U}_{\mathrm{HB}1}\left(k\right)}& k=240,\mathrm{.Math.},319\end{array}$
and N(k.sub.1, k.sub.2) is the set of the indices k for which the coefficient of index k is classified as being associated with the noise. This set can, for example be obtained by detecting the local peaks in U(k) that verify and by |U(k)||U(k1)| and |U(k)||U(k+1)| considering that these rays are not associated with the noise, i.e. (by applying the negation of the preceding condition):
N(a,b)={akbU(k)|<|U(k1)| or |U(k)|<|U(k+1)|}
It can be noted that other methods for computing the energy of the noise are possible, for example by taking the median value of the spectrum on the band considered or by applying a smoothing to each frequency ray before computing the energy per band. is set such that the ratio between the energy of the noise in the 4-6 kHz and 6-8 kHz bands is the same as between the 2-4 kHz and 4-6 kHz bands:

(89) $=\sqrt{\frac{-E_{N6\text{-}8}}{\underset{k=160}{\overset{239}{.Math.}}{U}^2\left(k\right)-E_{N6\text{-}8}}}$
in which

(90) $E_{N4\text{-}6}=\max \left(E_{N4\text{-}6},E_{N2\text{-}4}\right),=\frac{E_{N4\text{-}6}^2}{E_{N2\text{-}4}},=\max \left(,E_{N6\text{-}8}\right)$
In variants of the invention, the computation of will be able to be replaced by other methods. For example, in a variant, it will be possible to extract (compute) different parameters (or features) characterizing the signal in low band, including a tilt parameter similar to that computed in the AMR-WB codec, and the factor will be estimated as a function of a linear regression from these different parameters by limiting its value between 0 and 1. The linear regression will, for example, be able to be estimated in a supervised manner by estimating the factor by exchanging the original high band in a learning base. It will be noted that the way in which is computed does not limit the nature of the invention.

(91) In a preferred embodiment, the following is taken
={square root over (1.sup.2)}
in order to preserve the energy of the extended signal after mixing.
In a variant, the factors and will be able to be adapted to take account of the fact that a noise injected into a given band of the signal is generally perceived as stronger than a harmonic signal with the same energy in the same band. Thus, it will be possible to modify the factors and as follows:
.Math.f()
.Math.f()
in which f() is a decreasing function of , for example f()=ba{square root over ()}, b=1.1, a=1.2, f() limited from 0.3 to 1. It must be noted that, after multiplication by f(), .sup.2+.sup.2<1 so that the energy of the signal U.sub.HB2(k)=U.sub.HB1(k)+G.sub.HBN(k) is lower than the energy of U.sub.HB1(k) (the energy difference depends on , the more noise is added, the more the energy is attenuated).
In other variants of the invention, it will be possible to take:
=1
which makes it possible to preserve the amplitude level (when the combined signals are of the same sign); however, this variant has the disadvantage of resulting in an overall energy (at the level of U.sub.HB2(k)) which is not monotonous as a function of .
It should therefore be noted here that the block 703 performs the equivalent of the block 101 of FIG. 1 to normalize the white noise as a function of an excitation which is, by contrast here, in the frequency domain, already extended to the rate of 16 kHz; furthermore, the mixing is limited to the 6000-8000 Hz band.

(92) In a simple variant, it is possible to consider an implementation of the block 703, in which the spectra, U.sub.HB1(k) or G.sub.HBNU.sub.HBN(k), are selected (switched) adaptively, which amounts to allow only the values 0 or 1 for ; this approach amounts to classifying the type of excitation to be generated in the 6000-8000 Hz band.

(93) The block 704 optionally performs a double operation of application of bandpass filter frequency response and of de-emphasis filtering in the frequency domain.

(94) In a variant of the invention, the de-emphasis filtering will be able to be performed in the time domain, after the block 705, even before the block 700; however, in this case, the bandpass filtering performed in the block 704 may leave certain low-frequency components of very low levels which are amplified by de-emphasis, which can modify, in a slightly perceptible manner, the decoded low band. For this reason, it is preferred here to perform the de-emphasis in the frequency domain. In the preferred embodiment, the coefficients of index k=0,L,199 are set to zero, so the de-emphasis is limited to the higher coefficients.

(95) The excitation is first de-emphasized according to the following equation:

(96) $U_{\mathrm{HB}2}^{}\left(k\right)=\{\begin{array}{cc}0& k=0,L,199\\ G_{\mathrm{deemph}}\left(k\right)U_{\mathrm{HB}2}\left(k\right)& k=200,L,255\\ G_{\mathrm{deemph}}\left(255\right)U_{\mathrm{HB}2}\left(k\right)& k=256,L,319\end{array}$
in which G.sub.deemph(k) is the frequency response of the filter 1/(10.68z.sup.1) over a restricted discrete frequency band. By taking into account the discrete (odd) frequencies of the DCT-IV, G.sub.deemph(k) is defined here as:

(97) $G_{\mathrm{deemph}}\left(k\right)=\frac{1}{.Math.e^{j{}_k}-0.68.Math.},k=0,L,255$
in which

(98) ${}_k=\frac{256-80+k+\frac{1}{2}}{256}.$
In the case where a transformation other than DCT-IV is used, the definition of .sub.k will be able to be adjusted (for example for even frequencies).
It should be noted that the de-emphasis is applied in two phases for k=200,L, 255 corresponding to the 5000-6400 Hz frequency band, where the response 1/(10.68z.sup.1) is applied as at 12.8 kHz, and for k=256,L,319 corresponding to the 6400-8000 Hz frequency band, where the response is extended from 16 kHz here to a constant value in the 6.4-8 kHz band.

(99) It can be noted that, in the AMR-WB codec, the HF synthesis is not de-emphasized.

(100) In the embodiment presented here, the high frequency signal is, on the contrary, de-emphasized so as to bring it into a domain consistent with the low frequency signal (0-6.4 kHz) which leaves the block 305 of FIG. 3. This is important for the estimation and the subsequent adjustment of the energy of the HF synthesis.

(101) In a variant of the embodiment, in order to reduce the complexity, it will be ossible to set G.sub.deemph (k) at a constant value independent of k, by taking for example G.sub.deemph (k)=0.6 which corresponds approximately to the average value of G.sub.deemph (k) for k=200,L,319 in the conditions of the embodiment described above.

(102) In another variant of the embodiment of the extension device, the de-emphasis will be able to be performed in an equivalent manner in the time domain after inverse DCT.

(103) In addition to the de-emphasis, a bandpass filtering is applied with two separate parts: one, high-pass, fixed, the other, low-pass, adaptive (function of the bit rate).

(104) This filtering is performed in the frequency domain.

(105) In the preferred embodiment, the low-pass filter partial response is computed in the frequency domain as follows:

(106) $G_{\mathrm{lp}}\left(k\right)=1-0.999\frac{k}{N_{\mathrm{lp}}-1}$
in which N.sub.lp=60 at 6.6 kbit/s, 40 at 8.85 kbit/s, and 20 at the bit rates>8.85 bit/s. Then, a bandpass filter is applied in the form:

(107) $U_{\mathrm{HB}3}\left(k\right)=\{\begin{array}{cc}0& k=0,L,199\\ G_{hp}\left(k-200\right)U_{\mathrm{HB}2}^{}\left(k\right)& k=200,L,255\\ U_{\mathrm{HB}2}^{}\left(k\right)& k=256,L,319-N_{\mathrm{lp}}\\ G_{\mathrm{lp}}\left(k-320-N_{\mathrm{lp}}\right)U_{\mathrm{HB}2}^{}\left(k\right)& k=320-N_{\mathrm{lp}},L,319\end{array}$
The definition of G.sub.hp(k), k=0,L,55, is given, for example, in table 1 below.

(108) TABLE-US-00004 TABLE 2 K g.sub.hp(k) 0 0.001622428 1 0.004717458 2 0.008410494 3 0.012747280 4 0.017772424 5 0.023528982 6 0.030058032 7 0.037398264 8 0.045585564 9 0.054652620 10 0.064628539 11 0.075538482 12 0.087403328 13 0.100239356 14 0.114057967 15 0.128865425 16 0.144662643 17 0.161445005 18 0.179202219 19 0.197918220 20 0.217571104 21 0.238133114 22 0.259570657 23 0.281844373 24 0.304909235 25 0.328714699 26 0.353204886 27 0.378318805 28 0.403990611 29 0.430149896 30 0.456722014 31 0.483628433 32 0.510787115 33 0.538112915 34 0.565518011 35 0.592912340 36 0.620204057 37 0.647300005 38 0.674106188 39 0.700528260 40 0.726472003 41 0.751843820 42 0.776551214 43 0.800503267 44 0.823611104 45 0.845788355 46 0.866951597 47 0.887020781 48 0.905919644 49 0.923576092 50 0.939922577 51 0.954896429 52 0.968440179 53 0.980501849 54 0.991035206 55 1.000000000
It will be noted that, in variants of the invention, the values of G.sub.hp (k) will be able to be modified while keeping a progressive attenuation. Similarly, the low-pass filtering with variable bandwidth, G.sub.lp(k), will be able to be adjusted with values or a frequency medium that are different, without changing the principle of this filtering step.

(109) It will also be noted that the bandpass filtering will be able to be adapted by defining a single filtering step combining the high-pass and low-pass filtering.

(110) In another embodiment, the bandpass filtering will be able to be performed in an equivalent manner in the time domain (as in the block 112 of FIG. 1) with different filter coefficients according to the bit rate, after an inverse DCT step. However, it will be noted that it is advantageous to perform this step directly in the frequency domain because the filtering is performed in the domain of the LPC excitation and therefore the problems of circular convolution and of edge effects are very limited in this domain.

(111) It will also be noted that, in the case of the 23.85 kbit/s bit rate, the de-emphasis of the excitation U.sub.HB2(k) is not performed to remain in agreement with the way in which the correction gain is computed in the AMR-WB coder and to avoid double multiplications. In this case, block 704 performs only the low-pass filtering.

(112) The inverse transform block 705 performs an inverse DCT on 320 samples to find the high-frequency excitation sampled at 16 kHz. Its implementation is identical to the block 700, because the DCT-IV is orthonormal, except that the length of the transform is 320 instead of 256, and the following is obtained:

(113) $u_{\mathrm{HB}0}\left(n\right)=\underset{k=0}{\overset{N_{16k}-1}{.Math.}}{U}_{\mathrm{HB}3}\left(k\right)\cos \left(\frac{}{N_{16k}}\left(k+\frac{1}{2}\right)\left(n+\frac{1}{2}\right)\right)$
in which N.sub.16k=320 and k=0,L,319.

(114) This excitation sampled at 16 kHz is then, optionally, scaled by gains defined per subframe of 80 samples (block 707).

(115) In a preferred embodiment, a gain g.sub.HB1(m) is first computed (block 706) per subframe by energy ratios of the subframes such that, in each subframe of index m=0, 1, 2 or 3 of the current frame:

(116) 0$g_{\mathrm{HB}1}\left(m\right)=\sqrt{\frac{e_3\left(m\right)}{e_2\left(m\right)}}$
in which

(117) $e_1\left(m\right)=\underset{n=0}{\overset{63}{.Math.}}{u\left(n+64m\right)}^2+\mathrm{.Math.}$$e_2\left(m\right)=\underset{n=0}{\overset{79}{.Math.}}{u_{\mathrm{HB}0}\left(n+80m\right)}^2+\mathrm{.Math.}$$e_3\left(m\right)=e_1\left(m\right)\frac{\underset{n=0}{\overset{319}{.Math.}}{u_{\mathrm{HB}0}\left(n\right)}^2+\mathrm{.Math.}}{\underset{n=0}{\overset{255}{.Math.}}{u\left(n\right)}^2+\mathrm{.Math.}}$
with =0.01. The gain per subframe g.sub.HB1(m) can be written in the form:

(118) $g_{\mathrm{HB}1}\left(m\right)=\sqrt{\frac{\frac{\underset{n=0}{\overset{63}{.Math.}}{u\left(n+64m\right)}^2+\mathrm{.Math.}}{\underset{n=0}{\overset{255}{.Math.}}{u\left(n\right)}^2+\mathrm{.Math.}}}{\frac{\underset{n=0}{\overset{79}{.Math.}}{u_{\mathrm{HB}0}\left(n+80m\right)}^2+\mathrm{.Math.}}{\underset{n=0}{\overset{319}{.Math.}}{u_{\mathrm{HB}0}\left(n\right)}^2+\mathrm{.Math.}}}}$
which shows that, in the signal u.sub.HB, the same ratio between energy per subframe and energy per frame as in the signal u(n) is assured.
The block 707 performs the scaling of the combined signal according to the following equation:
u.sub.HB(n)=g.sub.HB1(m)u.sub.HB0(n),n=80m,L,80(m+1)1

(119) It will be noted that the implementation of the block 706 differs from that of the block 101 of FIG. 1, because the energy at the current frame level is taken into account in addition to that of the subframe. This makes it possible to have the ratio of the energy of each subframe in relation to the energy of the frame. The energy ratios (or relative energies) are therefore compared rather than the absolute energies between low band and high band.

(120) Thus, this scaling step makes it possible to retain, in the high band, the energy ratio between the subframe and the frame in the same way as in the low band.

(121) It will be noted here that, in the case of the 23.85 kbit/s bit rate, the gains g.sub.H1B(m) are computed but applied in the next step, as explained with reference to FIG. 4, to avoid the double multiplications. In this case u.sub.HB(n)=u.sub.HB0(n).

(122) According to the invention, the block 708 then performs a scale factor computation per subframe of the signal (steps E602 to E603 of FIG. 6), as described previously with reference to FIG. 6 and detailed in FIGS. 4 and 5.

(123) Finally, the corrected excitation u.sub.HB(n) is filtered by the filtering module 710 which can be performed here by taking as transfer function 1/(z/), in which =0.9 at 6.6 kbit/s and =0.6 at the other bit rates, which limits the order of the filter to the order 16.

(124) In a variant, this filtering will be able to be performed in the same way as is described for the block 111 of FIG. 1 of the AMR-WB decoder, but the order of the filter changes to 20 at the 6.6 bit rate, which does not significantly change the quality of the synthesized signal. In another variant, it will be possible to perform the LPC synthesis filtering in the frequency domain, after having computed the frequency response of the filter implemented in the block 710.

(125) In a variant embodiment, the step of filtering by a linear prediction filter 710 for the second frequency band is combined with the application of the optimized scale factor, which makes it possible to reduce the processing complexity. Thus, the steps of filtering 1/(z/) and of application of the optimized scale factor g.sub.HB2 are combined in a single step of filtering g.sub.HB2/(z/) to reduce the processing complexity.

(126) In variant embodiments of the invention, the coding of the low band (0-6.4 kHz) will be able to be replaced by a CELP coder other than that used in AMR-WB, such as, for example, the CELP coder in G.718 at 8 kbit/s. With no loss of generality, other wide-band coders or coders operating at frequencies above 16 kHz, in which the coding of the low band operates with an internal frequency at 12.8 kHz, could be used. Moreover, the invention can obviously be adapted to sampling frequencies other than 12.8 kHz, when a low-frequency coder operates with a sampling frequency lower than 3.0 that of the original or reconstructed signal. When the low-band decoding does not use linear prediction, there is no excitation signal to be extended, in which case it will be possible to perform an LPC analysis of the signal reconstructed in the current frame and an LPC excitation will be computed so as to be able to apply the invention.

(127) Finally, in another variant of the invention, the excitation (u(n)) is resampled, or example by linear interpolation or cubic spline, from 12.8 to 16 kHz before transformation (for example DCT-IV) of length 320. This variant has the defect of being more complex, because the transform (DCT-IV) of the excitation is then computed over a greater length and the resampling is not performed in the transform domain.

(128) Furthermore, in variants of the invention, all the computations necessary for the estimation of the gains (G.sub.HBN, g.sub.HB1(m), g.sub.HB2(m), g.sub.HBN, . . . ) will be able to be performed in a logarithmic domain.

(129) In variants of the band extension, the excitation in low band u(n) and the LPC filter 1/(z) will be estimated per frame, by LPC analysis of a low-band signal for which the band has to be extended. The low-band excitation signal is then extracted by analysis of the audio signal.

(130) In a possible embodiment of this variant, the low-band audio signal is resampled before the step of extracting the excitation, so that the excitation extracted from the audio signal (by linear prediction) is already resampled.

(131) The band extension illustrated in FIG. 7 is applied in this case to a low band which is not decoded but analyzed.

(132) FIG. 8 represents an exemplary physical embodiment of a device for determining an optimized scale factor 800 according to the invention. The latter can form an integral part of an audio frequency signal decoder or of an equipment item receiving audio frequency signals, decoded or not.

(133) This type of device comprises a processor PROC cooperating with a memory block BM comprising a storage and/or working memory MEM.

(134) Such a device comprises an input module E suitable for receiving an excitation audio signal decoded or extracted in a first frequency band called low band (u(n) or U(k)) and the parameters of a linear prediction synthesis filter ((z)). It comprises an output module S suitable for transmitting the synthesized and optimized high-frequency signal (u.sub.HB(n)) for example to a filtering module like the block 710 of FIG. 7 or to a resampling module like the module 311 of FIG. 3.

(135) The memory block can advantageously comprise a computer program comprising code instructions for implementing the steps of the method for determining an optimized scale factor to be applied to an excitation signal or to a filter within the meaning of the invention, when these instructions are executed by the processor PROC, 3.5 and notably the steps of determination (E602) of a linear prediction filter, called additional filter, of lower order than the linear prediction filter of the first frequency band, the coefficients of the additional filter being obtained from parameters decoded or extracted from the first frequency band, and of computation (E603) of an optimized scale factor as a function at least of the coefficients of the additional filter.

(136) Typically, the description of FIG. 6 reprises the steps of an algorithm of such a computer program. The computer program can also be stored on a memory medium that can be read by a reader of the device or that can be downloaded into the memory space thereof.

(137) The memory MEM stores, generally, all the data necessary for the implementation of the method.

(138) In a possible embodiment, the device thus described can also comprise functions for application of the optimized scale factor to the extended excitation signal, of frequency band extension, of low-band decoding and other processing functions described for example in FIGS. 3 and 4 in addition to the optimized scale factor determination functions according to the invention.