FR3112017A1 - Electronic equipment including a distortion simulator - Google Patents

Abstract

Electronic equipment (11) integrating or arranged to be connected to a microphone (12) and to a transmission chain (13) comprising an amplifier (14) and a loudspeaker (15), the electronic equipment comprising: - a distortion simulator (18) arranged to acquire an audio signal to be transmitted, to simulate a distortion introduced into the sound signal transmitted by the transmission chain, and to introduce the distortion into the audio signal to be transmitted so as to produce a reference (Sref); - an echo canceller (16) arranged to acquire the reference signal and the received audio signal, to simulate and introduce linear disturbances into the reference signal, and to remove the echo signal from the received audio signal and thus reproduce the useful sound signal. FIGURE OF THE ABRIDGE: Fig. 2

Description

Electronic equipment including a distortion simulator

The present invention relates to the field of electronic equipment which is capable of transmitting and receiving sound simultaneously, such as a connected speaker comprising a voice assistant.

BACKGROUND OF THE INVENTION

Some connected speakers incorporate a voice assistant. Such a connected speaker is therefore capable of broadcasting an audio signal to be transmitted (for example music) and, simultaneously, of acquiring and interpreting a useful sound signal produced by a user (for example a voice command). The interpretation of the voice command is likely to be disturbed by the echo phenomenon: the speaker microphones receive both the voice command and the music emitted by the speaker.

This situation is illustrated in the . The connected speaker 1 comprises a microphone 2, a transmission chain 3 comprising an amplifier 4 and a loudspeaker 5, as well as an echo canceller component 6.

Transmit channel 3 broadcasts an audio signal to be transmitted Sae (the music) and thus generates a transmitted sound signal Sse. User 7 simultaneously emits a useful sound signal Ssu (the voice command). The microphone 2 picks up a received sound signal Ssr comprising the useful sound signal Ssu emitted by the user 7 and an echo signal Se resulting from the propagation of the emitted sound signal Sse produced by the transmission chain 3, and generates a signal audio received Sar.

The purpose of the echo canceller 6 is to suppress the echo signal Se from the received audio signal Sar. The echo canceller 6 acquires for this purpose the received audio signal Sar as well as a reference signal Sref comprising the audio signal to be transmitted Sae, and produces a processed signal St which has been “cleaned” and which is as close as possible of the useful sound signal Ssu, that is to say of the voice command.

If the sound signal emitted Sse as picked up by the microphone 2 were identical to the audio signal to be emitted Sae, the role of the echo canceller 6 would be limited to a simple subtraction. However, the sound signal emitted Sse has been disturbed by amplifier 4, loudspeaker 5 and the resonance of the room in which speaker 1 is located, and is therefore not identical to the audio signal to be emitted Sae.

There are two kinds of disturbances.

Linear disturbances are disturbances which modify the volume and the phase (or the delay) of the emitted sound signal Sse in a different way for each frequency. These disturbances, in a system, are independent between frequencies: the output signal of the system at a given frequency depends only on the input signal of said system at the same frequency and not on the input signal at other frequencies.

Nonlinear disturbances are disturbances affecting several frequencies simultaneously. The most common nonlinear disturbance is harmonic distortion which adds energy at frequencies multiple of those of the input signal. Thus, the output signal at a given frequency depends not only on the input signal at the same frequency, but also on the input signal at lower frequencies. These non-linear disturbances are particularly present when connected speaker 1 plays sound at high volume.

The echo canceller 6 acquires the reference signal Sref comprising the audio signal to be transmitted Sae, simulates linear disturbances present in the transmitted sound signal Sse and introduces said linear disturbances into the reference signal Sref, so as to remove them from the received audio signal Sar to reproduce the useful sound signal Ssu.

The echo canceller 6 is therefore capable of handling linear disturbances, including disturbances that vary over time (such as disturbances linked to the resonance of the room). On the other hand, this echo canceller 6 is not capable of managing non-linear disturbances.

There are equipment whose reference signal for the echo canceller comes from an additional microphone, called "reference microphone", located just in front of the loudspeaker. However, this kind of system is very expensive because the reference microphone must be able to absorb high sound pressure levels without introducing additional distortion.

In addition, it is necessary that the main microphones be located far enough from the loudspeaker so that the proportion of the useful sound signal they pick up is significantly higher than that picked up by the reference microphone.

Indeed, all the microphones, that is to say both the main microphones and the reference microphone, pick up a received sound signal which combines a part of useful sound signal (voice command) and a part of echo signal. . As the reference microphone acquires part of the useful sound signal, when the signal from the reference microphone is used to cancel the echo signal, we end up canceling this part of the useful sound signal as well. Therefore, if the part of the useful sound signal compared to the echo signal is the same in the reference microphone and in the main microphones, the equipment finds itself canceling the useful sound signal at the same time as the signal of echo.

Thus, mathematically, if U denotes the useful sound signal and E denotes the echo signal, then the main microphones receive a signal M _p such that:

M _p = a _p ×U + b _p ×E,

where a _p and b _p represent the response of the environment.

The reference microphone receives a signal M _r such that:

M _r = a _r ×U + b _r ×E.

The echo canceller works by calculating a gain g and an output signal O such that:

O = M _p - g×M _r ,

so as to minimize the share of the echo signal in the output signal. If we develop the formulas, we get:

O = (a _p -g · a _r )×U + (b _p -g · b _r )×E,

with g ≈ b _p /b _r ,

so that O ≈ (a _p -g·a _r )×U no longer contains an echo signal.

For such a system to work, it is necessary that a _p -g · a _r ≠ 0, that is to say that a _p /b _p ≠ a _r /b _r , or that the part of the useful sound signal compared to the echo signal in the main microphones is different from the share of useful sound signal compared to the echo signal in the reference microphone.

This distance constraint between the reference microphone and the main microphones can be difficult to implement on a product such as a connected speaker.

OBJECT OF THE INVENTION

The object of the invention is to improve echo cancellation in electronic equipment capable of transmitting and receiving sound signals simultaneously, without increasing the cost of the electronic equipment significantly and without bringing particular constraints to its design .

With a view to achieving this aim, an electronic equipment is proposed integrating or arranged to be connected to a microphone and to a transmission chain comprising an amplifier and a loudspeaker, the transmission chain being able to broadcast an audio signal to transmit so as to generate a transmitted sound signal, the microphone being capable, simultaneously, of receiving a received sound signal comprising a useful sound signal transmitted by an external entity and an echo signal resulting from a propagation of the transmitted sound signal, and producing a audio signal received from the sound signal received,

electronic equipment including:

- a distortion simulator arranged to acquire the audio signal to be transmitted, to simulate a distortion introduced into the sound signal transmitted by the transmission chain, and to introduce the distortion into the audio signal to be transmitted so as to produce a reference signal ;

- an echo canceller arranged to acquire the reference signal and the received audio signal, to simulate and introduce linear disturbances into the reference signal, and to remove the echo signal from the received audio signal and thus reproduce the sound signal useful.

Thus, in operation, the distortion simulator produces in real time a reference signal integrating the harmonic distortion, and transmits said reference signal to the echo canceller. The echo canceller, which is designed to simulate and correct (only) linear disturbances, therefore produces a processed signal free of both distortion (and therefore most of the non-linear disturbances) and linear disturbances . Echo cancellation is therefore very significantly improved compared to the prior art thanks to the taking into account of the distortion by the distortion simulator, upstream of the echo canceller. This improvement does not require a particular design of the electronic equipment and does not significantly increase the cost of the electronic equipment, because the echo canceller can be a "traditional" linear echo canceller, which it does not It is therefore not necessary to design specially for the implementation of the invention.

We also propose electronic equipment as previously described, in which the distortion simulator is arranged to use a model defined by:

where x(t) is the audio signal to be transmitted and where y(t) is the reference signal, where P , Q and R are polynomials of predetermined degrees, and where k, q and n are integers greater than or equal to 1.

We also propose electronic equipment as previously described, in which we have q=1, k=1, n=1.

We also propose electronic equipment as previously described, in which we have q=1, k>1, n=k.

We also propose electronic equipment as previously described, in which we have q=1, k>1, n=1.

We also propose electronic equipment as previously described, in which we have q>1, k≥1.

We also propose electronic equipment as previously described, in which we have: R =0.

We also propose electronic equipment as previously described, in which we have: Q =0.

We also propose electronic equipment as previously described, in which the polynomials P , Q and R are polynomials of degree 5.

In addition, electronic equipment is proposed as described above, the electronic equipment being a connected speaker integrating the transmission chain and the microphone, and being arranged to implement a voice assistant.

A method for adjusting electronic equipment as previously described is also proposed, implemented prior to commissioning of the electronic equipment, and comprising the steps, for determining coefficients of the polynomials P , Q and R , of :

- broadcast, at low volume, by the transmission channel, a first transmitted test audio signal, and record a first received test audio signal produced by the microphone;

- determining a linear response H of the transmission chain and of a test environment by comparing the first audio test signal transmitted and the first audio test signal received;

- calculate an inverse linear response H ^-1 ;

- broadcast, at high volume, by the transmission channel, a second transmitted test audio signal, and record a second received test audio signal produced by the microphone;

- calculating a convolution product of the inverse linear response H ^-1 and of the second test audio signal received to obtain a rectified signal;

- determining the coefficients of the polynomials from the second transmitted audio test signal and the rectified signal.

An adjustment method as described above is also proposed, in which the first test audio signal emitted x ₀ (t) is such that:

,

with :

And

where T is a duration of the first transmitted test audio signal x ₀ (t) , ω ₁ is a low limit frequency and ω ₂ is a high limit frequency of the loudspeaker (15).

We also propose an adjustment method as previously described, in which we have R=0 , in which the model is defined by:

,

the adjustment method comprising the step of solving the following system of equations by the method of least squares:

the values x(i ) and ŷ(i) being respectively the values of the second transmitted audio test signal and of the rectified signal, the unknowns of the system p ₁ , p ₂ , … p _N and q ₁ , q ₂ , … q _N being the coefficients of the polynomials P and Q.

We also propose an adjustment method as previously described, in which we have R ≠0, in which the model is defined by:

the adjustment method comprising the step of solving the following system of equations by the method of least squares:

,

the values x(i) and ŷ(i) being respectively the values of the second transmitted test audio signal and of the rectified signal, the unknowns of the system p ₁ , p ₂ , … p _N , q ₁ , q ₂ , … q _N , r ₁ , r ₂ ,…, r _N being the coefficients of the polynomials P , Q and R .

We also propose an adjustment method as previously described, further comprising the steps of improving the determination of the coefficients of the polynomials according to an iterative process by calculating a simulated signal ȳ such that:

then using the simulated signal to recalculate the coefficients of the polynomials by solving the system using the least squares method:

.

The invention will be better understood in the light of the following description of a particular non-limiting mode of implementation of the invention.

Reference will be made to the attached drawings, among which:

there represents a connected speaker of the prior art and a user;

there represents a connected speaker according to the invention and a user;

there is a graph comprising a curve of the sound signal received by the microphone and a curve of the reference signal, for an audio signal to be transmitted at 206Hz;

there is a graph comprising a curve of the sound signal received by the microphone and a curve of the reference signal, for an audio signal to be transmitted at 242Hz.

DETAILED DESCRIPTION OF THE INVENTION

With reference to the , the invention is here implemented in a connected enclosure 11 comprising at least one microphone 12, at least one transmission chain 13 comprising an amplifier 14 and a loudspeaker 15, an echo canceller 16 and a distortion 18.

The distortion simulator 18 is here implemented in at least one processing component which is adapted to execute instructions of a program to implement said distortion simulator 18. The program is stored in a memory connected or integrated in the processing component. The processing component is for example a processor, a DSP (for Digital Signal Processor ), a microcontroller, or else a programmable logic circuit such as an FPGA (for Field Programmable Gate Arrays ) or an ASIC (for Application Specific Integrated Circuit ) .

The transmission channel 13 broadcasts an audio signal to be transmitted Sae (for example music) and thus generates a transmitted sound signal Sse, and, at the same time, the user 17 transmits a useful sound signal Ssu (for example a command voice).

Simultaneously, the microphone 12 therefore picks up a received sound signal Ssr comprising the useful sound signal Ssu generated by the user 17 and an echo signal Se resulting from the propagation of the transmitted sound signal Sse generated by the transmission chain 13, and produces a received audio signal Sar. It is specified that the “audio” signals are digital or analog electrical signals.

The echo canceller 16 used is the same as that visible on the (reference 6). The echo canceller 16 is therefore designed to simulate and correct linear disturbances (only).

However, in the invention, the echo canceller 16 does not use as a reference signal a reference signal comprising only the audio signal to be transmitted Sae.

The distortion simulator 18 is in fact positioned "upstream" of the echo canceller 16 with respect to the acquisition of the audio signal to be transmitted Sae. The distortion simulator 18 acquires the audio signal to be transmitted Sae. The distortion simulator 18 simulates a harmonic distortion present in the transmitted sound signal Sse (mainly generated by the transmission chain 13), and introduces said distortion into the audio signal to be transmitted Sae so as to produce the reference signal Sref.

The echo canceller 16 acquires the reference signal Sref and the received audio signal Sar. The echo canceller 16 simulates the linear disturbances present in the transmitted sound signal Sse, introduces the linear disturbances into the reference signal Sref and thus produces a resulting reference signal integrating both the distortion and the linear disturbances. The echo canceller 16 then subtracts the resulting reference signal from the received audio signal Sar to remove both linear disturbances and distortion from the received audio signal Sar. The echo canceller 16 thus removes the echo signal Se from the received audio signal Sar and thus reproduces the useful sound signal Ssu.

The suppression of the echo signal is thus improved by the taking into account by the distortion simulator 18 of the distortion upstream of the echo canceller 16, without the echo canceller 16 in itself differing of a prior art linear echo canceller.

It is known to use the following prior art model to jointly model the harmonic distortion (nonlinear) and the linear response of a system:

where y(t) represents the output signal of said system, x(t ) represents the input signal of said system, ⊗ represents the convolution operation, and the h _i (t) represent the impulse responses of several linear filters. The values of h _i (t) constitute the parameters of the system.

This model is very expensive, because the impulse responses h _i (t) are quite long and the convolution operations are therefore computationally expensive.

In the invention, the echo canceller 16 used is capable of handling linear disturbances, so that the distortion simulator 18 must simulate only non-linear disturbances.

The distortion simulator 18 therefore uses a model defined by:

where x(t) is the system input signal, i.e. the audio signal to be emitted Sae and where y(t) is the simulator output signal, i.e. the reference signal Sref.

P , Q and R are polynomials of predetermined degrees, and k, q and n are integers greater than or equal to 1. For example, each of the polynomials P , Q and R is of degree 5.

In a first embodiment, we have q=1, k=1 and n=1.

The model used is therefore the following.

It is noted that, in the case where R =0, the above model is equivalent to the model of the prior art which has just been cited with impulse responses h _i (t) of length 2.

The parameters of the model are determined via an adjustment process comprising adjustment operations implemented prior to the commissioning of the connected speaker 11.

The adjustment operations take place, for example, in the factory during a calibration phase of the connected speaker 11, or else during the design of said connected speaker 11. In the first case, the parameters are specific to the connected speaker 11, whereas in the second case, the parameters are valid for a plurality of connected speakers 11 of the same type as the connected speaker 11 (by "of the same type", we mean for example the speakers having the same number number, or P/N, for Part Number ).

In order to determine the parameters of the model, that is to say the coefficients of the polynomials P , Q and R , the behavior of the transmission chain 13 is measured as perceived by the microphone 12 by broadcasting an audio test signal transmitted via the transmission channel 13 so as to produce a transmitted test sound signal, and by recording the received test audio signal produced by the microphone 12 during playback. The transmitted test audio signal and the recorded received test audio signal are then compared to determine the parameters of the model.

The main difficulty in determining the parameters of the model comes from the fact that the audio test signal received has undergone not only the nonlinear disturbances that one seeks to model but also the linear disturbances linked, among other things, to the test environment in which the connected enclosure 11 is located at the time of the adjustment process (deaf room or acoustic box).

We know, however, that nonlinear disturbances are especially present at high sound volume. The parameters of the model are therefore determined by implementing an adjustment process which includes the steps of:

- broadcast, at low volume, via the transmission channel 13, a first test audio signal transmitted x ₀ (t) , and record a first test audio signal received y ₀ (t) produced by the microphone 12;

- determining the linear response H of the transmission chain 13 and of the test environment by comparing the first audio test signal transmitted x ₀ (t) and the first audio test signal received y ₀ (t) ;

- calculate the inverse linear response H ^-1 ;

- broadcast, at high volume, via the transmission channel 13, a second audio test signal transmitted x ₁ (t) , and record a second audio test signal received y ₁ (t) produced by the microphone 12;

- calculate the convolution product of the inverse linear response H ^-1 and the second test audio signal received y ₁ (t) to obtain a rectified signal ŷ ₁ (t) :

ŷ ₁ (t)=y ₁ (t)⊗H ^-1 ;

- determining the coefficients of the polynomials P , Q , R from the second audio test signal emitted x ₁ (t) and from the rectified signal ŷ ₁ (t) .

The high volume is here for example the maximum volume of the connected speaker 11. The low volume is here equal to a predetermined percentage of the maximum volume. The predetermined percentage is for example equal to 25%.

The linear response H is determined as follows.

A first test audio signal transmitted x ₀ (t) is used which carries out a logarithmic sweep of the frequencies.

We have here:

with :

T is the duration of the first test audio signal emitted x ₀ (t) (for example 30s), ω ₁ is the minimum frequency limit and ω ₂ is the maximum frequency limit of the loudspeaker 15. For example, for a subwoofer bass, ω ₁ =20 Hz and ω ₂ =1 kHz.

The system response is then given by performing the convolution of the first test audio signal received y ₀ (t) with the inverse filter of x ₀ :

Note that the linear response H and its inverse H ^-1 depend on the test environment (in particular the anechoic chamber or the acoustic box where the connected speaker is placed) and are therefore only used when determining the parameters of the model, and not during normal operation of the connected speaker 11. Their calculation cost therefore does not pose a problem in normal operation.

It is also noted that the above adjustment method is only valid for frequencies between ω ₁ and ω ₂ . H and H ^-1 are therefore fixed at 1 for frequencies lower than ω ₁ or higher than ω ₂ .

Moreover, it can be observed that the quality of the filters H and H ^-1 deteriorates when approaching the frequencies ω ₁ and ω ₂ , even having taken a long duration T in order to have long filters and therefore of good quality. .

Therefore, it is advantageous to take a margin when choosing ω ₁ and ω ₂ . It can be considered that the H and H ^-1 filters are good between 2× ω ₁ and ω ₂ /2, it is therefore advisable to choose values of ω ₁ and ω ₂ sufficiently large with respect to the nominal operating frequencies of the device so that the H and H ^-1 filters are good over the entire useful range.

Indeed, it is interesting to use a value of ω ₁ lower than the nominal minimum limit frequency of the loudspeaker 15 (for example half) the time of the measurement to allow the filters to be good from the limit frequency nominal minimum. The same reasoning applies symmetrically for ω ₂ and the nominal maximum limit frequency. The second audio test signal emitted x ₁ (t) is here broadcast at the maximum volume of the connected speaker 11. The second audio test signal emitted x ₁ (t) comprises all the useful frequencies.

For example, a second test audio signal emitted x ₁ (t) is used such that:

x ₁ (t) = g× x ₀ (t) ,

where g is a gain allowing to reach the maximum volume,

and only the part of the signal whose frequency is between 2× ω ₁ and ω ₂ /2 is kept. The second test audio signal emitted x ₁ (t) therefore also carries out a logarithmic sweep of the frequencies.

In the simplest case, the model is non-recursive, ie we have chosen to force R =0. In this case, the distortion model is written:

If we apply this equation to all the samples of the second audio test signal emitted, we obtain the system of equations below.

The values x(i) and ŷ(i) are respectively the values of the second transmitted test audio signal x ₁ (t) and of the rectified signal ŷ ₁ (t) , the unknowns of the system p ₁ , p ₂ , … p _N and q ₁ , q ₂ , … q _N are the coefficients of the polynomials P and Q .

By solving this system by the method of least squares, we obtain the coefficients of the polynomials P and Q of the model.

We see on the the curve C1 of the received sound signal Ssr picked up by the microphone 12 and the curve C2 of the reference signal Sref, for an audio signal to be transmitted at 206Hz. We see on the the curve C3 of the received sound signal Ssr picked up by the microphone 12 and the curve C4 of the reference signal Sref, for an audio signal to be transmitted at 242Hz.

In the case of a recursive model, it is also necessary to determine the coefficients of R . Here the model is written:

As for the non-recursive model, the coefficients can be obtained by solving the system using the least squares method:

The values x(i) and ŷ(i) are respectively the values of the second transmitted test audio signal x ₁ (t) and of the rectified signal ŷ ₁ (t) , the unknowns of the system p ₁ , p ₂ , … p _N , q ₁ , q ₂ , … q _N , r ₁ , r ₂ , …, r _N are the coefficients of the polynomials P , Q and R .

We then improve the estimation of the coefficients according to an iterative process by calculating a simulated signal ȳ :

We use this simulated signal ȳ to recalculate the coefficients of the polynomials by solving the system by the method of least squares (note that we still use the rectified signal ŷ on the left of the equalities, and that we now use the simulated signal ȳ on the right ):

This operation is repeated if necessary, until the error stops decreasing. The coefficients of the polynomials are thus defined very precisely.

It has just been described that the model used by the distortion simulator 18 is the following:

We have seen that it is possible to force R =0. Similarly, the model can be further simplified by forcing Q =0.

When Q = 0, the model is able to simulate the distortion linked to the saturation of the amplifier 14, but cannot simulate the mechanical behavior of the loudspeaker 15.

Note that in audio, a sampling frequency of 48 kHz is generally used. However, the most important distortion often comes from the low frequencies. A model that just uses the previous sample, like the one described earlier, may struggle to handle low frequencies. We therefore seek to increase the depth of the model used.

It is for example possible to implement remote sampling.

As a reminder, the general model used is expressed in the form:

To overcome the problems related to low frequencies, we can define that:

q=1, k>1, n=k.

The model used therefore becomes:

We can also define that:

q=1, k>1, n=1.

The model used therefore becomes:

For example, we can choose k=12 for a signal sampled at 48 kHz, if we are only interested in the bass speaker and we are sure that the input signals do not contain frequencies higher than 2 kHz.

The determination of the parameters of the model then uses the same principle as previously by replacing x ( t -1) by x ( t- k ) and y ( t -1) by y ( t- n ) in the systems of equations to be solved .

Another solution to overcome the problems related to low frequencies consists in implementing an averaged sampling and therefore in replacing x ( t -1) by the average of the values of x between the instants t- k -q (with k≥1 and q>1) and t -k.

We therefore define that:

q>1, k≥1, and R =0.

The model used therefore becomes:

This solution is slightly more computationally expensive, but there are fast recursive averaging methods that can prevent the overhead from being too large.

Of course, the invention is not limited to the embodiment described but encompasses any variant falling within the scope of the invention as defined by the claims.

The electronic equipment in which the invention is implemented is not necessarily a connected speaker, but may be any equipment capable of transmitting and receiving sound simultaneously, and for example a sound bar or a television comprising a microphone to acquire commands, or a smartphone or tablet.

The microphone and/or the transmission chain (including the amplifier and the loudspeaker) are not necessarily integrated into the electronic equipment in which the invention is implemented, but can be connected to said electronic equipment.

The useful sound signal is not necessarily emitted by a human user, but could be emitted by another external entity, and in particular by other electronic equipment (separate from the electronic equipment in which the invention is implemented).

Claims (15)

Electronic equipment (11) integrating or arranged to be connected to a microphone (12) and to a transmission chain (13) comprising an amplifier (14) and a loudspeaker (15),
the transmission chain being able to broadcast an audio signal to be transmitted (Sae) so as to generate a transmitted sound signal (Sse),
the microphone being able, simultaneously, to receive a received sound signal (Ssr) comprising a useful sound signal (Ssu) emitted by an external entity (17) and an echo signal (Se) resulting from a propagation of the emitted sound signal, and producing a received audio signal (Sar) from the received sound signal,
electronic equipment including:
- a distortion simulator (18) arranged to acquire the audio signal to be transmitted, to simulate a distortion introduced into the sound signal transmitted by the transmission chain, and to introduce the distortion into the audio signal to be transmitted so as to produce a reference signal (Sref);
- an echo canceller (16) arranged to acquire the reference signal and the received audio signal, to simulate and introduce linear disturbances into the reference signal, and to remove the echo signal from the received audio signal and thus reproduce the useful sound signal. Electronic equipment according to claim 1, in which the distortion simulator (18) is arranged to use a model defined by:

where x(t) is the audio signal to be transmitted and where y(t) is the reference signal, where P , Q and R are polynomials of predetermined degrees, and where k, q and n are integers greater than or equal to 1. Electronic equipment according to claim 2, in which q=1, k=1, n=1. Electronic equipment according to claim 2, in which q=1, k>1, n=k. Electronic equipment according to claim 2, in which q=1, k>1, n=1. Electronic equipment according to claim 2, in which q>1, k≥1. Electronic equipment according to one of Claims 2 to 6, in which one has: R =0. Electronic equipment according to one of Claims 2 to 7, in which one has: Q =0. Electronic equipment according to one of Claims 2 to 8, in which the polynomials P , Q and R are polynomials of degree 5. Electronic equipment according to one of the preceding claims, the electronic equipment being a connected speaker (11) integrating the transmission chain (13) and the microphone (12), and being arranged to implement a voice assistant. Method for adjusting electronic equipment according to one of Claims 2 to 10, implemented prior to commissioning of the electronic equipment, and comprising the steps, for determining coefficients of the polynomials P , Q and R , of :
- broadcast, at low volume, by the transmission channel (13), a first transmitted test audio signal, and record a first received test audio signal produced by the microphone (12);
- determining a linear response H of the transmission chain and of a test environment by comparing the first audio test signal transmitted and the first audio test signal received;
- calculate an inverse linear response H ^-1 ;
- Broadcasting, at high volume, by the transmission channel, a second transmitted test audio signal, and recording a second received test audio signal produced by the microphone;
- calculating a convolution product of the inverse linear response H ^-1 and of the second test audio signal received to obtain a rectified signal;
- determining the coefficients of the polynomials from the second transmitted audio test signal and the rectified signal. Adjustment method according to claim 11, in which the first test audio signal transmitted x ₀ (t) is such that:
,
with :
And

where T is a duration of the first transmitted test audio signal x ₀ (t) , ω ₁ is a low limit frequency and ω ₂ is a high limit frequency of the loudspeaker (15). Adjustment method according to claim 11, in which one has R=0 , in which the model is defined by:
,
the adjustment method comprising the step of solving the following system of equations by the method of least squares:

the values x(i ) and ŷ(i) being respectively the values of the second transmitted audio test signal and of the rectified signal, the unknowns of the system p ₁ , p ₂ , … p _N and q ₁ , q ₂ , … q _N being the coefficients of the polynomials P and Q. Adjustment method according to claim 11, in which one has R ≠0, in which the model is defined by:

the adjustment method comprising the step of solving the following system of equations by the method of least squares:
,
the values x(i) and ŷ(i) being respectively the values of the second transmitted test audio signal and of the rectified signal, the unknowns of the system p ₁ , p ₂ , … p _N , q ₁ , q ₂ , … q _N , r ₁ , r ₂ ,…, r _N being the coefficients of the polynomials P , Q and R . Adjustment method according to claim 14, further comprising the steps of improving the determination of the coefficients of the polynomials according to an iterative process by calculating a simulated signal ȳ such that:

then using the simulated signal to recalculate the coefficients of the polynomials by solving the system using the least squares method:
.