EP2113913B1 - Method and system for reconstituting low frequencies in an audio signal - Google Patents

Abstract

The method involves generating a harmonic signal (S-harm) associated with a fundamental frequency to be reconstituted in an audio signal (S-in), and reinjecting the harmonic signal in a phase in the audio signal. The audio signal is filtered at a cut-off frequency using a lowpass filter (101), where the cut-off frequency is obviously equal to a cut-off frequency of a sound reproducing device. The fundamental frequency is determined by detecting zero-crossings of the filtered audio signal. The harmonic signal is synthesized by summation of two sinusoidal frequency components. An independent claim is also included for a module for reconstituting a low frequency of an audio signal in an output of a sound reproducing device presenting a cut-off frequency for low frequencies.

Description

The invention relates to a method and system for reconstructing low frequencies of an audio signal that can be used at the output of a sound reproducing device having a cut-off frequency for low frequencies.

The invention finds a particularly advantageous application in the field of electro-acoustic equipment, including stereo speakers for the reproduction of musical works or even the speakers of personal computers (PC) for reproducing the soundtrack of video files.

It is known that any acoustic speaker has a cutoff frequency for low frequencies below which it is no longer able to radiate energy. This cutoff frequency is directly related to the dimensions of the speaker, and more precisely to the size of the membrane. The smaller the speaker, the higher the cutoff frequency in the spectrum. Thus, a small enclosure will impose a natural attenuation to the low frequency content of a piece of music, and this to the detriment of the listener who can not benefit from this information and will therefore feel an unpleasant effect related to the loss serious sounds.

A first solution to this difficulty consists in applying a filter to amplify the low frequencies attenuated by the acoustic enclosure, by mechanically forcing the speaker diaphragm to radiate these low frequencies. However, this solution presents real risks for the integrity of the loudspeaker. Indeed, the excursion of the membrane, that is to say the amplitude of its displacement relative to its equilibrium position, would become too important, to the point of damaging or even breaking it. Another solution is based on a psychoacoustic property of the human ear that makes it possible to perceive low frequencies even if they are not actually transmitted by a device belonging to the sound reproduction system, a loudspeaker speaker. for example. This residual pitch perception effect, generally known by the Anglo-Saxon term Missing-Fundamental Effect, results from the fact that the perception of the "pitch" of a sound signal is not only related to the presence of the fundamental frequency in the signal but also to that of higher harmonics of this frequency. In other words, if the fundamental frequency, of 100 Hz for example, is eliminated from a signal while preserving its higher harmonics, at 200, 300, 400 Hz, ... the perceived "pitch" will be the same, because in this case it is in fact the frequency difference, here of 100 Hz, between the higher harmonics which fixes the "pitch" and gives the listener the impression of hearing a "pitch" signal 100 Hz. Of course, this truncation of the signal, thus deprived of its fundamental frequency, results in a different timbre, the latter being determined in particular by the relative amplitudes of the set of harmonics.

It is therefore possible to remedy the attenuation, in whole or in part, of the fundamental frequencies of the audio signals below the cutoff frequency, by generating in real time a harmonic signal synthesized from harmonics associated with each of the attenuated fundamental frequencies, and re-injecting this harmonic signal into the original audio signal. One understands that, even if the fundamental frequency of a sound is attenuated or completely absorbed, the higher harmonics, located above the cutoff frequency of the sound reproduction device, can be transmitted and reconstruct the "pitch" sound by the residual tone effect explained above.

This method of virtually extending the bandwidth of an electro-acoustic system to the bottom of the spectrum is referred to as "virtual bass generation".

In this context, the US 5,930,373 A1 discloses such a method of generating harmonics relating to the low frequencies of the audio signal by means of a modulation system. The reference signal is multiplied by itself to obtain a double frequency signal, then again multiplied by itself to obtain a triple frequency signal, and so on. This known system has the advantage of being fast, because without significant delay, and not requiring frequency information. However, it has the disadvantage of being non-linear. Indeed, if the original audio signal contains a sum of frequencies, will be generated not only the harmonics of each of these frequencies but also harmonics intermodulation terms that may severely degrade the audio performance of the system.

It is also known from the US 6 134 330 A1 a method in which the signal containing the low frequencies passes through a series of nonlinear filters consisting of a rectifier and an integrator. This treatment gives rise to a series of higher harmonics associated with each fundamental frequency. However, as the foregoing, this method has the disadvantages of a non-linear system, namely the generation of intermodulation artifacts that can affect the resulting signal.

Another technique is described in the WO 97/42789 A1 , which provides for filtering the audio signal by means of a low-pass filter of cut-off frequency substantially equal to the cut-off frequency of the sound reproduction device, and then determining the fundamental frequencies to be reconstructed by detection of zero crossings of the sound reproduction device. filtered audio signal. Since the fundamental frequencies to be reconstructed at the output are determined by detection of zero crossings, the values of higher harmonic frequencies are very simply deduced so as to synthesize the harmonic signals associated with each fundamental frequency which serve as a basis for the implementation of the "pitch" rendering effect explained above. However, the presence of the low-pass filter introduces a variable phase shift which negatively interferes with the signal obtained at the output because the harmonic signal will not be reinjected in phase in the original audio signal. This produces unequal harmonic levels depending on the frequencies, as they are potentially lower for frequencies that are not in phase with those of the original signal.

Another problem is that the synthesized signal has time variations that do not faithfully follow those of the original signal, which has the effect of altering the nuances.

The US 2003/223588 A1 proposes in this regard a bass enhancement device where the envelope of the synthetic signal is adjusted by a compression / expansion system in which the slope and an offset are adjustable. The slope and the offset are adjusted simultaneously so that the average energy of the envelope is compensated, this simultaneous control being adjustable by a potentiometer or other means of manual adjustment.

This system has the disadvantage of not being suitable for all types of input signals, especially if the aim is to obtain the most natural rendering possible tones, not to produce acoustic effects by generating components frequencies not contained in the original signal, as in the case of the US 2003/223588 A1 which essentially seeks to artificially expand the stereo field, increase the "brilliance" of the sound or introduce a distortion reminding the particular sound of tube amplifiers.

Indeed, if one applied the lessons of this document to the reconstitution of the "pitch" of the sound by the effect of residual tonality explained above, a line of bass of moderate level would be amplified of the same value as bass line very strong, and the effect would be perceived negatively by the user.

Another problem, common to all the techniques described in the documents presented above, is that these techniques do not take into account the variations of the human auditory perception with the frequency (effect of the "perception of the loudness ") . Indeed, according to the sound level and according to the frequency, the same variation of an acoustic signal will not produce the same variation of perceived intensity. For example, to change the perceived intensity from 40 to 50 phones, the acoustic signal needs to be increased by almost 10 dB at 100 Hz, while it takes only 5 or 6 dB more at 50 Hz.

Also, an object of the invention is to propose a method of reconstituting low frequencies of an audio signal at the output of a sound reproduction device which respects the temporal variations of the original signal so as to preserve the nuances, and which also takes into account variations in human auditory perception with frequency.

• filtrage du signal audio au moyen d'un filtre passe-bas de fréquence de coupure sensiblement égale à ladite fréquence de coupure du dispositif de reproduction du son ;
• détermination d'une fréquence fondamentale à reconstituer à partir du signal audio filtré passe-bas ;
• génération d'un signal harmonique associé à ladite fréquence fondamentale à reconstituer,
• détection d'une enveloppe temporelle du signal audio filtré passe-bas ; et
• réinjection en phase dudit signal harmonique dans ledit signal audio par addition après multiplication de ce signal harmonique avec l'enve-loppe temporelle adaptée.

The method of the invention is of the type disclosed by the WO 97/42789 A1 aforesaid corresponding to the preamble of claim 1, that is to say a method of reconstituting low frequencies of an audio signal at the output of a sound reproducing device having a low cutoff frequency (F ₀ ), and comprising steps of:

• filtering the audio signal by means of a low-pass filter of cutoff frequency substantially equal to said cutoff frequency of the sound reproduction device;
• determining a fundamental frequency to be reconstructed from the filtered low pass audio signal;
• generating a harmonic signal associated with said fundamental frequency to be reconstructed,
• detecting a temporal envelope of the filtered low-pass audio signal; and
• phase reinjection of said harmonic signal in said audio signal by addition after multiplication of this harmonic signal with the adapted temporal envelope.

The invention provides for a dynamic adaptation of said time envelope as a function of the frequency band considered.

The dynamic adaptation of the temporal envelope according to the frequency band makes it possible, in particular, to take into account the variations of the human auditory perception with the frequency, and the detection of the temporal envelope and its taking into account by multiplication with the signal generated harmonic allows to modulate the signal synthesized according to the temporal variations of the envelope.

According to the invention, the adaptation step of the temporal envelope is performed by compression / expansion of the temporal envelope.

In particular, it has been found that it is preferable to amplify the gain of the envelope when the bass line is weak or moderate, so that the proposed effect is always perceived positively by the user.

Thus, unlike the compression / expansion process proposed by the US 2003/223588 A1 above, which provided for adjusting the offset once and for all by manual adjustment, the invention proposes to dynamically automate the adjustment of the offset of the envelope by a feedback loop on the value of the envelope (advantageously with different time constants on ascent and descent). Thus, the offset will automatically adjust, based on the average energy of the input signal, to a value that maximizes this energy within a defined limit.

Still according to the invention, the control of the compression / expansion step is performed conditionally after comparing the level of the compressed / expanded signal with respect to a predetermined threshold.

• ce contrôle comprend la modification dynamique d'au moins un paramètre de la caractéristique de compression/expansion en fonction du niveau du signal comprimé/expansé ;
• cette modification dynamique est opérée de manière itérative, par pas successifs, le pas de modification dudit paramètre en cas de niveaux forts, supérieurs à un seuil donné, du niveau du signal comprimé/expansé étant supérieur au pas de modification de ce même paramètre en cas de niveaux faibles, supérieurs à un seuil donné, du signal comprimé/expansé ;
• le paramètre en question est la position du point invariant de la caractéristique de compression/expansion ;
• la caractéristique de compression/expansion est une caractéristique linéaire, pour des entrées/sorties exprimées en échelle logarithmique ;
• la pente de la caractéristique de compression/expansion est maintenue constante lors de la modification du paramètre ;
• la modification de la position du point invariant de la caractéristique de compression/expansion est opérée par modification de l'ordonnée à l'origine de ladite caractéristique linéaire, cette modification étant de préférence limitée par des valeurs minimale et maximale.

According to various advantageous subsidiary features:

• this control comprises dynamically modifying at least one parameter of the compression / expansion characteristic as a function of the level of the compressed / expanded signal;
• this dynamic modification is performed iteratively, in successive steps, the step of modifying said parameter in case of strong levels, greater than a given threshold, the level of the compressed / expanded signal being greater than the step of modifying this parameter in case low levels, above a given threshold, of the compressed / expanded signal;
• the parameter in question is the position of the invariant point of the compression / expansion characteristic;
• the compression / expansion characteristic is a linear characteristic, for inputs / outputs expressed in logarithmic scale;
• the slope of the compression / expansion characteristic is kept constant when the parameter is changed;
• the modification of the position of the invariant point of the compression / expansion characteristic is effected by modifying the ordinate at the origin of said linear characteristic, this modification being preferably limited by minimum and maximum values.

The invention also relates, according to claim 10, to a module for reconstituting low frequencies of an audio signal for implementing the aforementioned method.

• La figure 1 est un schéma de l'architecture générale d'un système de reconstitution de basses fréquences conforme à l'invention.
• La figure 2 représente l'extension de bande-passante réalisée par le système de la figure 1.
• La figure 3 est un schéma détaillé du module de reconstitution de basses fréquences du système de la figure 1.
• La figure 4 est un bloc-diagramme du détecteur d'enveloppe temporelle du module de la figure 3.
• La figure 5 est un schéma du compresseur/expanseur du circuit d'adaptation d'enveloppe du module de la figure 3.
• La figure 6 est un diagramme de réponse du compresseur/expanseur de
• la figure 5.
• La figure 7 illustre la manière dont évolue l'ordonnée à l'origine β du compresseur/expanseur de la figure 5, de façon différenciée dans le sens de l'augmentation et de la diminution, et avec application de seuils minimum et maximum.
• Les figures 8a et 8b sont des diagrammes de réponse du compresseur/expanseur de la figure 5, respectivement dans une configuration de gain minimal et de gain maximal, montrant la manière dont la caractéristique est modifiée en fonction du niveau du gain appliqué par le compresseur/expanseur.

An embodiment of the device of the invention will now be described with reference to the appended drawings in which the same reference numerals designate identical or functionally similar elements from one figure to another.

• The figure 1 is a diagram of the general architecture of a low frequency reconstruction system according to the invention.
• The figure 2 represents the bandwidth extension achieved by the system of the figure 1 .
• The figure 3 is a detailed diagram of the low frequency reconstitution module of the system of the figure 1 .
• The figure 4 is a block diagram of the time envelope detector of the module of the figure 3 .
• The figure 5 is a diagram of the compressor / expander of the envelope adaptation circuit of the module of the figure 3 .
• The figure 6 is a response chart of the compressor / expander of
• the figure 5 .
• The figure 7 illustrates the way in which the ordinate β of the compressor / expander of the figure 5 , in a differentiated way in the sense of increase and decrease, and with application of minimum and maximum thresholds.
• The Figures 8a and 8b are compressor / expander response diagrams from the figure 5 in a configuration of minimum gain and maximum gain, respectively, showing how the characteristic is changed according to the gain level applied by the compressor / expander.

The following description with reference to the accompanying drawings, given by way of non-limiting example, will make it clear what the invention is and how it can be achieved.

General principle of implementation

On the figure 1 is shown an architecture of a system 10 for reconstituting low frequencies in an audio signal, a stereo signal for example, said low frequencies to be reconstructed at the output of a sound reproducing device constituted by two loudspeakers 11, 12 , associated with each stereo output signal L _out and R _out , said speakers having a cutoff frequency F ₀ low frequency of 120 Hz for example.

The system of reconstitution of the figure 1 comprises a reconstitution module 100, also referred to as a module for generating "virtual basses", operating according to the "pitch" rendering principle explained above which consists, in essence, in processing an input signal S _in resulting from the average of the input stereo signals L _in and R _in order to generate an output harmonic signal S _out associated with at least one fundamental frequency lower than the cutoff frequency F ₀ that is to be reconstructed at the output of the loudspeakers 11, 12 by rendering effect of "pitch". The harmonic output signal S _out thus generated is fed back into phase at the output of the virtual bass generation module 100 in the original stereo signals L _in and R _in to form the stereo output signals L _out and R _out .

In the remainder of this description, it will be chosen to generate said output harmonic signal S _out by summation of three sinusoidal components of frequencies respectively equal to the first three harmonics of the low frequency signal to be reconstructed, namely the fundamental frequency, or first harmonic, and the next two higher harmonics, that is to say the double and triple harmonics of the fundamental frequency. Of course, other choices are possible, such as, for example, the use of the first four harmonics, the essential in all cases being that the generated harmonic signal contains at least two consecutive harmonics in order to perceive their difference, which is equal to the pitch.

Consequently, in the case envisaged here, if the cut-off frequency F ₀ is 120 Hz, the range of low frequencies that can benefit from a "pitch" reconstitution extends between 60 and 120 Hz. For a frequency fundamental to be reconstituted by 60 Hz, the harmonics to be considered are those at 60, 120, 180 Hz. The bandwidth of the system 100 is thus "virtually" extended downwards to a new cut-off frequency F ' ₀ equal to 60 Hz, as shown in figure 2 . The range of frequencies in the range [F ' ₀ , F ₀ ] is called FFR ( Fundamental Frequency Range ).

Reconstitution of low frequencies

The reconstitution module 100 will now be described in detail with reference to the figure 3 .

The module 100 comprises as input a first low-pass filter 101 whose cutoff frequency is substantially equal to the cut-off frequency F ₀ . This filter 101 is intended to perform a first partition of the FFR within all the frequencies contained in the input signal S _in , and to limit the distortion phenomenon by aliasing . Then, the signal S _in thus filtered is subsampled by the block 102, in order to reduce the complexity of the filtering while maintaining a sufficient resolution for the future estimation of the fundamental frequencies to be reconstructed.

The signal S _in thus filtered low-pass and under-sampled is then processed in parallel in two branches 110, 120, of the module 100.

The first branch 110 aims to generate a harmonic signal S _harm resulting from the synthesis of three sinusoidal components of respective frequencies equal to a fundamental frequency contained in the FFR and its first two higher harmonics.

The second branch 120 is intended to construct a time envelope env _adapt (t) for modulating the harmonic signal S _harm so that the output signal S _out reproduces the temporal variations of the original signal. The output signal S _out therefore results, in particular, from the multiplication by the multiplier circuit 103 of the harmonic signal S _harm by the env envelope _adapt (t): $${\mathrm{S}}_{\mathrm{out}}\mathrm{=}{\mathrm{S}}_{\mathrm{harm}}{\mathrm{ca.}}_{\mathrm{Customized}}\left(\mathrm{t}\right)$$

As shown in figure 3 the first processing branch 110 comprises a second low-pass filter 111 designed to delimit the FFR again and to eliminate from the original signal the frequencies extending outside the FFR.

This filter 111 advantageously incorporates an all-pass stage making it possible to linearize the phase of the signal, by neutralizing the variable phase shift effect introduced by the low-pass filtering. The phase effect introduced by this linearization is corrected by a delay τ introduced ( figure 1 ) on the original signal L _in or R _in before it is combined with the output harmonic signal S _out synthesized by the module 100 and reinjected in phase with the original signal to form the output signals L _out and R _out .

The fundamental frequencies, contained in the FFR and which one seeks to reconstitute by "pitch" effect, are determined by means of a block of zero crossings of the signal coming from the second low-pass filter 111. More precisely, block 112 determines the duration of the fundamental periods between two zero crossings and deduces the corresponding fundamental frequencies.

For each fundamental frequency determined by the block 112, a harmonic generator 113 then supplies three sinusoidal components at the fundamental frequency itself (n = 1), as well as to the two harmonics higher (n = 2, n = 3). These three sinusoidal components are built from the same table, called "sine table" or wavetable, stored in memory, which gives the values of a sinusoidal period. For more details on this technique, we can refer to the article Laroche J. Synthesis of Sinusoids via Non-Overlapping Inverse Fourier Transform, IEEE Transactions on Speech and Audio Processing, IEEE Service Center, New York, NY, USA, vol. 8, No. 4, July 2000, pp. 471-477 .

In practice, the generator 113 builds, from the fundamental period, the sinusoidal components from sample to sample while progressing in a regular step in the table. Based on the detected period, the generator 113 calculates a certain step to build the fundamental frequency component (n = 1) and, starting from the first sample, it increments the index of this step in order to determine the next sample. The sampling step is chosen so as to be compatible with the computing power of the microprocessor of the system 10, it being understood that the method implemented by the invention is a real-time method and that consequently it must not introduce delay between the signals. For example, the sine table can have 4096 points over an entire period.

The two higher harmonics (n = 2, n = 3) are generated in the same way, taking for each step the double and triple of the pitch corresponding to the fundamental frequency.

We can see on the figure 3 that the sinusoidal components supplied by the generator 113 are then subjected to a weighting operation performed by a circuit 114 consisting in assigning to each component an experimentally determined patch matching coefficient, in order to give the output signal S _out a stamp close to that of the original signal. The value of these coefficients depends essentially on the order of the harmonic considered, that is to say first harmonic (n = 1), or fundamental frequency, second (n = 2) and third (n = 3) harmonics (We have seen above that the timbre of a sound signal is determined by the energy ratio between its different frequency components). More precisely, the circuit 114 receives from the block 112 a frequency information and operates the weighting of the harmonics, which depends on the frequency instantaneous, from coefficient tables indexed by the frequency detected. Thus, for example, the weighting applied to the 60 Hz, 120 Hz and 180 Hz sinusoids will be different from that applied to 100 Hz, 200 Hz and 300 Hz sinusoids.

The weighted sinusoidal components are summed at the output of the weighting circuit 114 by an adder circuit 115 to form the synthesized harmonic signal S _harm containing the first three harmonics of the fundamental frequency to be reconstituted.

Determination and adaptation of the temporal envelope

In parallel with the generation of the harmonics in the first branch 110, the second branch 120 of the process extracts the temporal envelope env (t) from the filtered low-pass and subsampled signal coming from the block 102, by means of a detector of envelope 121 shown in figure 4 which, for this purpose, conventionally performs a least squared RMS ( Root Mean Square ) calculation consisting in raising the signal squared by the block 121a, filtering it through a low-pass filter 121b, and then taking the square root by block 121c.

Moreover, it should be noted that the synthesized harmonic signal S _harm does not have the same spectral composition as the original low frequency signal since it is composed not only of the fundamental frequency but also of the first two higher harmonics. However, the human ear does not perceive all the frequencies with the same intensity, and the temporal variations of two sound signals are not perceived in the same way if their spectral content is different. To take account of this constraint, the variations of the envelope env (t) must be adapted according to the FFR.

In accordance with the figure 3 this adaptation is made on the second branch 120 of processing by a circuit 122 capable of performing a compression / expansion operation according to the input / output response curve given on the figure 6 . The envelope env (t) being previously calculated in decibels, the lowest levels of the envelope below a given threshold -N dB for example -27 dB in the example illustrated, are attenuated, while the higher levels , greater than -N dB, are further increased. This adaptation, based on a perceptual scale, makes it possible to give the signal thus generated temporal variations which will be perceived as similar to the temporal variations of the original signal, thus making it possible to guarantee that the generated timbre will be faithful to the original timbre. As shown in the schematic representation of the figure 5 the matching circuit 122 is controlled by a feedback loop 122b as follows.

• le taux d'expansion, c'est-à-dire le facteur par lequel il faut multiplier une variation x donnée sur le signal original, exprimée en décibels, pour obtenir la même variation d'intensité perçue sur le signal harmonique, exprimée en phones, est constant pour une harmonique considérée ; et
• le taux d'expansion ne dépend pas non plus de l'ordre de l'harmonique considérée (alors que, théoriquement, il augmenterait avec l'ordre de l'harmonique).

To simplify the realization of the circuit, and without this having a significant impact on the results obtained, it is possible to make, in the frequency range analyzed (typically 40-120 Hz) the following double approximation:

• the rate of expansion, that is to say the factor by which it is necessary to multiply a given variation x on the original signal, expressed in decibels, to obtain the same variation of intensity perceived on the harmonic signal, expressed in phones is constant for a considered harmonic; and
• the rate of expansion does not depend either on the order of the harmonic considered (whereas, theoretically, it would increase with the order of the harmonic).

One will choose for the value of the rate of expansion an average of the rates of expansion for all the frequencies, amplitudes and orders of harmonic considered.

The compression / expansion process, schematized at 122a, will be applied to the detected envelope determined by the envelope detector 121, then this expanded envelope will be used to modulate the sum of the synthesized harmonics (since the rate of expansion is the same for all harmonics).

The rate of expansion, designated subsequently α, corresponds to the slope of the line D shown figure 6 (as indicated above, after studying the curves of isophony one can consider that this slope will be constant). The ordinate at the origin of this line D will be designated β, and will be a function of the desired invariant point I, which in the illustrated example figure 6 is located at (-27 dB, - 27 dB). The transfer function of block 122a can be expressed as: $$\mathit{exit}\left(\mathrm{dB}\right)=\mathrm{\alpha \; x}\mathit{Entrance}\left(\mathrm{dB}\right)+\mathrm{\beta }\left(\mathrm{dB}\right)$$

If it is desired that the system amplify in all cases the perceived loudness of the bass sounds (that is, even when the level of the time envelope is less than ^- -N dB (-27 dB in the illustrated example), and since α is fixed, it is necessary to increase β by a certain value so that the characteristic D of compression / expansion passes above the line y = x of unit slope for this low level of l Conversely, in the case of a significant bass level on the original signal, care should be taken not to over-amplify the envelope.

To achieve this result, the invention proposes to use an envelope level matching system, based on a feedback loop.

The principle of this loop, illustrated figure 5 , is to compare at a threshold S the instantaneous level of the expanded envelope delivered at the output of the compression / expansion module 122a. If this level is below the threshold, the parameter β is increased by a fixed step for the adaptation of the next sample. Conversely, if the instantaneous level of the expanded envelope is greater than the threshold S, β is reduced by a fixed step.

The step of increase or decrease will not be the same in one case and in the other. Indeed, if the instantaneous level of the expanded envelope suddenly becomes very large - in the case of a percussion for example - it is necessary that the decrease of β intervenes very quickly, to avoid reaching excessively high levels. On the other hand, if the instantaneous level is weak, it is possible to increase β more gradually, all the more since the nuances of the original piece must be respected: the natural attenuation of the bass notes must be respected because, if β increased as fast as it decreased, the notes would never stop.

The figure 7 illustrates how the parameter β varies in increase and decrease in the case of a piece of music having a sudden increase of level, followed by a fast decrease of this same level. It should also be noted that the variation of the parameter β is limited to a minimum value (for example β = 0) and to a maximum value (for example β = +12 dB).

x₀ étant choisi en fonction du rapport souhaité entre l'augmentation et le pas de diminution de β, et coeff étant choisi en fonction de la vitesse d'adaptation souhaitée (si coeff est petit, β évoluera doucement alors qu'il évoluera rapidement avec coeff grand).The principle of incrementation / decrementation of β is as follows: a flag variable takes the value 0 or 1 according to the result of the comparison between the instantaneous level of the expanded envelope and the threshold S, and the adaptation step of β is calculated according to the formula: $$\mathit{not}=\mathit{coefficient}x\left(x_{\mathit{0}}-\mathit{flag}\right),\mathrm{with}0<x_{\mathit{0}}<1,$$

x ₀ being chosen according to the desired ratio between the increase and the decrease step of β, and coeff being chosen as a function of the desired adaptation speed (if coeff is small, β will evolve slowly while it will evolve rapidly with coeff great).

The variations of β will result in a displacement of the invariant point I of the compression / expansion characteristic D.

The Figures 8a and 8b illustrate the characteristic D obtained for the two extreme values of β, respectively β = 0 dB and β = +12 dB (when β varies, the line D oscillates vertically between the two extreme positions represented Figures 8a and 8b ).

The effective compression zone (i.e., the area where the output signal is attenuated with respect to the input signal) and the effective expansion area (i.e., the area where the signal output is amplified with respect to the input signal) are separated by the invariant point I, the sectors between the characteristic D and the unit slope line y = x defining the compression regions (below point I) and expansion (beyond point I).

The feedback loop thus makes it possible to compress or expand the envelope according to its instantaneous level, in order to homogenize the level of the low components reinjected into the original signal whatever the musical genre of the piece in question (time constants of the enslavement being chosen sufficiently weak not to affect the natural decay of the notes). This makes it possible to generate harmonic signals of relatively constant amplitude regardless of the original signal. Thus, a low-frequency low-frequency sound signal at low frequencies will still be significantly enhanced by the system, while a sound signal with a high-energy bass line will be boosted to a limited level, to maintain a natural look. .

This method of adapting the envelope, combining a compression / expansion module with a feedback control loop, makes it possible to generate a signal that will be perceived as similar to the original signal if it was produced by one more acoustic speaker. large dimensions.

Final reconstitution of the output signal

If we go back to figure 3 once the adaptation of the envelope made by the circuit 122, the harmonic signal S _harm synthesized in the first branch 110 is modulated by the adapted envelope env _adapt (t) from the second branch 120, by multiplication effected at means of the circuit 103, then the signal is oversampled by a factor 10 by the block 105 to return to the initial sampling frequency. It may be advantageous to introduce at this stage a low-pass filter in the oversampling process, since this filter is linear phase, it does not introduce phase distortion that would defeat the objective sought signal reinjection signal synthesized in phase in the original signal.

Since the reinjection of the output signal S _out filtered high-pass and oversampled presents risks of exceeding the dynamic range, a limiter is used at the output of the reconstitution system 10, so that the signal sent back to the loudspeakers 11, 12 remains content on a 16-bit dynamic.

Claims (10)

1. Method for reconstituting low frequencies of an audio signal output from a sound reproduction device (11, 12) having a low cut-off frequency (F₀), comprising steps for:

   - filtering the audio signal by means of a low-pass filter (101) with a cut-off frequency substantially equal to said cut-off frequency (F₀) of the sound reproduction device;

   - determining a fundamental frequency to be reconstituted from the low-pass filtered audio signal;

   - generating a harmonic signal (S_harm) associated with said fundamental frequency to be reconstituted;

   - detecting a time envelope (env(t)) of the low-pass filtered audio signal; and

   - reinjecting said harmonic signal into said audio signal by addition after multiplication of this harmonic signal (S_harm) with the adapted time envelope (env_adapt(t)),

   characterized by a step for dynamic adaptation of said time envelope (env(t)) according to the frequency band concerned, performed by compression/expansion (122a) of the time envelope (env(t)) with a control by feedback loop (122b) of said compression/expansion step applied conditionally after comparison of the level of the compressed/expanded signal with a predetermined threshold (S), and in that the harmonic signal is reinjected in phase into said audio signal.
2. Method according to Claim 1, in which said control by feedback loop of the compression/expansion step comprises the dynamic modification of at least one parameter of the compression/expansion characteristic (D) according to the level of the compressed/expanded signal.
3. Method according to Claim 2, in which said dynamic modification of said parameter is a modification applied iteratively, by successive steps.
4. Method according to Claim 3, in which the modification step of said parameter in case of high levels, above a given threshold, of the level of the compressed/expanded signal is greater than the modification step of this same parameter in case of low levels, above a given threshold, of the compressed/expanded signal.
5. Method according to Claim 2, in which said at least one parameter is the position of the invariant point (I) of the compression/expansion characteristic.
6. Method according to Claim 5, in which said compression/expansion characteristic is a linear characteristic (D), for inputs/outputs expressed in logarithmic scale.
7. Method according to Claim 6, in which the slope (•) of said compression/expansion characteristic is kept constant during the modification of said parameter.
8. Method according to Claims 5 and 6 taken in combination, in which the modification of the position of said invariant point (I) is done by modifying the ordinate at the origin (•) of said linear characteristic.
9. Method according to Claim 8, in which said modification of the ordinate at the origin of the linear characteristic is a modification limited by minimum and maximum values.
10. Module for reconstituting low frequencies of an audio signal (S_in), at the output of a sound reproduction device (11, 12) having a cut-off frequency (F₀) for said low frequencies, for implementing the method according to one of the preceding claims, this module comprising:

    - a low-pass filter (101) suitable for filtering said audio signal (S_in) with a cut-off frequency substantially equal to the cut-off frequency (F₀) of said sound reproduction device (11, 12);

    - a first branch (110) for processing the low-pass filtered audio signal intended to generate a harmonic signal (S_harm) associated with at least one fundamental frequency to be reconstituted in the audio signal, said first branch (110) comprising a block (112) suitable for determining said fundamental frequency;

    - a second branch (120) for processing the low-pass filtered audio signal comprising a detector (121) for detecting the time envelope of said signal; and

    - a circuit suitable for reinjecting in phase said harmonic signal into said audio signal by addition after multiplication of this harmonic signal (S_harm) with the adapted time envelope (env_adapt(t)),

    module being characterized in that:

    - the second branch (120) also comprises a circuit (122) for adapting said time envelope according to its instantaneous level, comprising a compressor/expander (122a) for the time envelope and a control loop (122b) for said compressor/expander (122a) based on feedback according to the level of the compressed/expanded signal;

    - the control by the feedback loop is applied conditionally after comparison of the level of the compressed/expanded signal with a predetermined threshold (S); and

    - the harmonic signal is reinjected in phase into said audio signal.

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