CN107864444B - A method for calibrating the frequency response of a microphone array - Google Patents

Abstract

The invention discloses a microphone array frequency response calibration method, which comprises the following steps: s1: the electric audio signal w (n) reaches a microphone array through a loudspeaker and an acoustic propagation channel, and the input acoustic signal of the microphone array is x (n); s2: the sound signal x (n) passes through k different microphones and preamplifiers to obtain different electric signals x₁(n)～x_k(n); s3: electric signal x₁(n)～x_k(n) using the signal as the input signal of each calibration filter to adjust the filter coefficient of each calibration filter; s4: and according to the adjustment mode, calculating the filter coefficient of each calibration filter to finish the frequency response calibration of the microphone array. The method enables the frequency responses of different microphones in the same array to be close to the same, thereby improving the signal processing capacity of the microphone array.

Description

A method for calibrating the frequency response of a microphone array

technical field

The invention relates to the technical field of signal processing, in particular to a microphone array frequency response calibration method.

Background technique

Sound is an information carrier widely used by human beings, and audio signal is an important research object of signal processing technology. As a sound sensor, a microphone plays an important role in sound signal processing. Because a single microphone has a limited sound pickup range and weak noise suppression ability, it cannot meet the increasing audio signal quality requirements, and people have proposed a microphone array technology. Because it also introduces information in the space domain in addition to the time domain and frequency domain, the processing ability of the sound signal is enhanced, and it has become the first choice for many high-quality audio processing applications. As a sound information collection tool, the microphone array plays an important role in the field of array audio processing. The process of picking up sound by a microphone generally consists of the following two parts: (1) the acoustic signal is converted into an electrical signal; (2) the electrical signal is then passed through a preamplifier to obtain a sufficiently large electrical signal. Due to the discreteness of the acoustic-electrical parameters of the microphone or the discreteness of the component parameters in the amplifier, there are some differences between different microphones, whether it is an acoustic/electrical signal conversion module or a preamplifier module. These differences are more pronounced between cheap microphones or between different brands of microphones. This difference results in frequency responses that vary from microphone to microphone in the same array. The specific performance is: when different microphones at the same position pick up the same segment of sound signal, there are certain differences among the obtained electrical signals. The difference in frequency response between microphones will directly affect the subsequent audio signal processing results, such as the performance of algorithms such as sound field perception and speech enhancement. However, due to reasons such as hardware circuits, there are often some differences between the frequency responses of microphones in the same array. Some applications of microphone arrays such as sound field perception, speech enhancement, etc. will be affected by the above differences, resulting in reduced processing performance. Therefore, calibrating the frequency response of each microphone in the same array to make them close to the same becomes a practical technical requirement in the microphone array. In the gain calibration technology of the microphone array in the prior art, since only the gain between the microphones in the microphone array is calibrated, the frequency response of each microphone cannot be guaranteed to be consistent with each other, resulting in the amplitude-frequency response and phase-frequency response of each microphone after calibration. there are still some differences

Contents of the invention

According to the problems existing in the prior art, the present invention discloses a microphone array frequency response calibration method, comprising the following steps:

S1: The electric audio signal w(n) reaches the microphone array through the speaker and the acoustic propagation channel, and the input acoustic signal of the microphone array is x(n);

S2: The acoustic signal x(n) passes through k different microphones and preamplifiers to obtain different electrical signals x ₁ (n)~x _k (n);

S3: The electrical signals x ₁ (n) to x _k (n) are respectively used as input signals of each calibration filter to adjust the filter coefficients of each calibration filter; the adjustment method of the filter coefficients of the calibration filters is: By adjusting the filter coefficients of each filter, the output signals y ₁ (n)~y _k (n) are all approached to the target signal d(n), and the approximation principle is to make y ₁ (n)~y _k (n) and d The mean square errors between (n) are the smallest respectively;

S4: Calculate the filter coefficients of each calibration filter according to the above adjustment method, so as to complete the frequency response calibration of the microphone array.

Further, when the calibration filter output signals y ₁ (n)~y _k (n) of each channel approach the target signal d(n) to realize array frequency response calibration, the following method is adopted: set the length of one frame of digital signal to N, Then the input signal x _i (n) and the target signal d(n) of the i-th calibration filter are written in the following vector form

x _i =[x _i (0), x _i (1),..., x _i (N-1)] ^T (2)

d=[d(0),d(1),...,d(N-1)] ^T (3)

Among them, [] ^T represents the transpose of a vector or matrix, and the following cost functions are listed

Among them, Σ represents the series summation, so that the cost function J is minimized, and the target signal d(n) is obtained as

d=(x ₀ +x ₁ +...+x _k )/k (5)

That is, the vector form d of the target signal is equal to averaging the sum of the input vectors of the filters.

When the target signal d(n) is determined, the i-th filter coefficient h _i is calculated based on the minimum mean square error between the i-th filter output signal y _i (n) and the target signal d(n) (n) in the following manner:

y _i =[y _i (0),y _i (1),...,y _i (N-1)] ^T (6)

Then the error signal e _i (n) between y _i (n) and d(n) is written in the following vector form

e _i ＝[e _i (0),e _i (1),...,e _i (N-1)] ^T ＝y _i -d (7)

List another set of cost functions

F _i =e _i ^T e _i (8)

Wherein, i=1,2,...,k, k is the number of microphones to be calibrated, so that F _i is the smallest, and the filter coefficient h _i (n) of the i-th road calibration filter is calculated, and the calculation rule is:

h _i ＝[h _i (0),h _i (1),...,h _i (M _i -1)] ^T ＝(X _i ^T X _i ) ^-1 D ^T x _{i_m} (9)

Among them, x _{i_m} is a vector composed of the first NM _i + 1 elements of the i-th calibration filter input vector, namely

x _{i_m} = [x _i (0), x _i (1),..., x _i (NM _i )] ^T (10)

And _Xi and D in formula (9) are respectively

When i ranges from 1 to k, use the above method to calculate the filter coefficient of each calibration filter to complete the microphone array frequency response calibration.

When the multi-frame input data is calibrated separately, the obtained multiple sets of filter coefficients are fused to obtain the filter coefficients in the following way:

Assume that the i-th microphone is calibrated by Q frame data, and the Q-group filter coefficient vectors are obtained according to formula (9) as h _{i_1} , h _{i_2} , ... h _{i_Q} , where h _{i_Q} means that the i-th microphone is at the Qth The filter coefficient vector obtained from the frame input data; in addition, the average vector of Q filter coefficient vectors is defined as

H _i =(h _{i_1} +h _{i_2} +...+h _{i_Q} )/Q (13)

The variance vector of the i-th road q-th frame filter coefficient vector is defined as

δ _{i_q} = (h _{i_q} -H _i )·(h _{i_q} -H _i ) (14)

Among them, the symbol "·" represents the vector dot product, q=1,2,...,Q, the reciprocal variance vector θ _{i_q} of the filter coefficient vector of the i-th road and the q-th frame is defined as

θ _{i_q} =[1/δ _{i_q} (0),1/δ _{i_q} (1),...,1/δ _{i_q} (M _i -1)] ^T (15)

That is, each element in the vector _{θi_q} is the reciprocal of the corresponding element of the vector _{δi_q} , and for the i-th calibration filter, the vector sum of the reciprocal variance of the filter coefficient vector is defined as

θ _i =θ _{i_1} +θ _{i_2} +. . . +θ _{i_Q} (16)

According to θ _i and θ _{i_q} (q=1,2,...,Q), Q filter coefficient weight vectors C _{i_1} , C _{i_2} ,..., C _{i_q} ,..., C _{i_Q are obtained} , where,

C _{i_q} ＝[θ _{i_q} (0)/θ _i (0),θ _{i_q} (1)/θ _i (1),...,θ _{i_q} (M _i -1)/θ _i (M _i -1)] ^T (17)

According to h _{i_q} and C _{i_q} , the final filter coefficient of the i-th calibration filter is obtained

h _i ＝h _{i_1} ·C _{i_1} +h _{i_2} ·C _{i_2} +...+h _{i_Q} ·C _{i_Q} (18)

Wherein, i=1,2,...,k, k is the number of microphones.

Due to the adoption of the above technical solution, the present invention provides a microphone array frequency response calibration method, which makes the frequency responses of different microphones in the same array nearly consistent, thereby improving the signal processing capability of the microphone array. Therefore, some microphone array applications, such as sound source localization or speech enhancement, use the microphone array frequency response calibration method disclosed in the present invention to process signals.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments described in this application. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

Fig. 1 is the flowchart of the calibration method of microphone array frequency response of the present invention;

Fig. 2 is the schematic diagram of the distance between microphone and loudspeaker, microphone and microphone in the present invention;

Fig. 3 is a working principle diagram of the calibration filter in the present invention;

Fig. 4 is the schematic diagram of the effect of the microphone array frequency response calibration method in the present invention;

5 is a schematic diagram of the effect of the method for calibrating the frequency response of the microphone array in the present invention;

6 is a schematic diagram of the effect of the method for calibrating the frequency response of the microphone array in the present invention;

FIG. 7 is a schematic diagram of the effect of the method for calibrating the frequency response of the microphone array in the present invention.

Detailed ways

In order to make the technical solutions and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with the drawings in the embodiments of the present invention:

A method for calibrating the frequency response of a microphone array as shown in Figure 1 specifically includes the following steps:

S1: The electric audio signal w(n) reaches the microphone array through the speaker and the acoustic propagation channel, and the input acoustic signal of the microphone array is x(n);

S2: The acoustic signal x(n) passes through k different microphones and preamplifiers to obtain different electrical signals x ₁ (n)~x _k (n);

S3: The electrical signals x ₁ (n) to x _k (n) are respectively used as input signals of each calibration filter to adjust the filter coefficients of each calibration filter; the adjustment method of the filter coefficients of the calibration filters is: By adjusting the filter coefficients of each filter, the output signals y ₁ (n)~y _k (n) are all approached to the target signal d(n), and the approximation principle is to make y ₁ (n)~y _k (n) and d The mean square errors between (n) are the smallest respectively;

S4: Calculate the filter coefficients of each calibration filter according to the above adjustment method, so as to complete the frequency response calibration of the microphone array.

As shown in Figure 1: In this method, the input signals of different microphones are required to be x(n), that is, the same input signals need to be kept between different microphones. However, in an actual environment, since the positions of the microphones are different, there are differences among the signals received by each microphone. During calibration, in order to make the received signals of each microphone close to the same, the placement rules of the loudspeaker and the microphone array are shown in Figure 2, where: (1) the distance L between the loudspeaker and the microphone array is kept sufficiently large; (2) The distance l between the microphones should be small enough.

Further, the calibration filter is composed of k FIR filters, and its function is to make the frequency responses of the microphones to be calibrated approach each other. Define the input signal of the calibration filter corresponding to the i-th microphone as x _i (n), and the output is the filtering result y _i (n), namely

Among them, M _i is the order of the i-th calibration filter, h _i (m) is the m-th filter coefficient, y _i (n) is the filtering result at time n, and x _i (nm) is the input at time nm Signal, the value range of i is an integer between 1 and k. The block diagram of the filter is shown in Figure 3. In addition, the filter coefficient h _i (m) of the i-th calibration filter depends on its filter input signal _xi (n) and target signal d(n). After the input signal w(n) is determined, the i-th filter input signal _xi (n) only depends on the frequency response of the i-th microphone and the preamplifier, so the calculation of the target signal d(n) is particularly important.

Further, in order to make the output signals y ₁ (n)˜y _k (n) of each calibration filter approach the target signal d(n), so as to achieve the purpose of calibration. Assuming that the length of a frame of digital signal is N, the input signal x _i (n) and the target signal d(n) of the i-th calibration filter can be written in the following vector form

x _i =[x _i (0), x _i (1),..., x _i (N-1)] ^T (2)

d=[d(0),d(1),...,d(N-1)] ^T (3)

where [] ^T represents the transpose of a vector or matrix. In order to minimize the mean square error between the target signal and the input signal of each filter, the following cost function can be listed

where Σ represents the series summation. To minimize the cost function J, the target signal d(n) can be obtained as

d=(x ₀ +x ₁ +...+x _k )/k (5)

That is, the vector form d of the target signal is equal to averaging the sum of the input vectors of the filters.

The filter coefficients are calculated as follows:

After the target signal d(n) is determined, the present invention calculates the i-th filter coefficient based on the minimum mean square error between the i-th filter output signal y _i (i) and the target signal d(n) h _i (n). Define the vector form of the output signal y _i (n) of the i-th calibration filter as

y _i =[y _i (0),y _i (1),...,y _i (N-1)] ^T (6)

Then the error signal e _i (n) between y _i (i) and d(n) can be written in the following vector form

e _i ＝[e _i (0),e _i (1),...,e _i (N-1)] ^T ＝y _i -d (7)

At this point, another set of cost functions can be listed

F _i =e _i ^T e _i (8)

Wherein, i=1,2,...,k, k is the number of microphones to be calibrated. Make F _i the smallest, the filter coefficient h _i (n) of the i-th calibration filter can be calculated, and the calculation rule is:

h _i ＝[h _i (0),h _i (1),...,h _i (M _i -1)] ^T ＝(X _i ^T X _i ) ^-1 D ^T x _{i_m} (9)

Among them, x _{i_m} is a vector composed of the first NM _i + 1 elements of the i-th calibration filter input vector, namely

x _{i_m} = [x _i (0), x _i (1),..., x _i (NM _i )] ^T (10)

And _Xi and D in formula (9) are respectively

When i ranges from 1 to k, the above method can be used to calculate the filter coefficient of each calibration filter, thereby completing the microphone array frequency response calibration.

In order to further improve the calibration effect, the above method can be used to calibrate multiple frames of input data, and then fuse the obtained sets of filter coefficients to obtain more accurate filter coefficients. Assuming that the i-th microphone is calibrated by Q frame data, the Q group of filter coefficient vectors can be obtained according to formula (9), which are h _{i_1} , h _{i_2} , ... h _{i_Q} , where h _{i_Q} means that the i-th microphone is in The filter coefficient vector obtained from the input data of the Qth frame. Furthermore, the average vector of Q filter coefficient vectors can be defined as

H _i =(h _{i_1} +h _{i_2} +...+h _{i_Q} )/Q (13)

At this time, the variance vector of the filter coefficient vector of the i-th channel and the q-th frame can be defined as

δ _{i_q} = (h _{i_q} -H _i )·(h _{i_q} -H _i ) (14)

Wherein, the symbol '·' represents vector dot product, q=1,2,...,Q. The reciprocal variance vector θ _{i_q} of the filter coefficient vector of the i-th frame q-th frame is defined as

θ _{i_q} =[1/δ _{i_q} (0),1/δ _{i_q} (1),...,1/δ _{i_q} (M _i -1)] ^T (15)

That is, each element in the vector θ _{i_q} is the reciprocal of the corresponding element in the vector δ _{i_q} . Regarding the i-th calibration filter, the vector sum of the reciprocal variance of the filter coefficient vector is defined as

θ _i =θ _{i_1} +θ _{i_2} +. . . +θ _{i_Q} (16)

At this time, according to θ _i and θ _{i_q} (q=1,2,...,Q), Q filter coefficient weight vectors C _{i_1} , C _{i_2} ,..., C _{i_q} ,..., C _{i_Q} . in,

C _{i_q} ＝[θ _{i_q} (0)/θ _i (0),θ _{i_q} (1)/θ _i (1),...,θ _{i_q} (M _i -1)/θ _i (M _i -1)] ^T (17)

Finally, according to h _{i_q} and C _{i_q} , the final filter coefficient of the i-th calibration filter is obtained

h _i ＝h _{i_1} ·C _{i_1} +h _{i_2} ·C _{i_2} +...+h _{i_Q} ·C _{i_Q} (18)

Wherein, i=1,2,...,k, k is the number of microphones.

In order to verify the effect of the method of the present invention, two microphones with different frequency responses are used for calibration experiments, and their amplitude-frequency responses and phase-frequency responses are shown in Fig. 4 and Fig. 5 respectively. It can be seen from Figure 4 and Figure 5 that there are certain differences in the frequency responses of the two microphones in the passband, stopband, amplitude frequency, and phase frequency.

The above two microphones are calibrated by using the calibration method proposed by the present invention. The system parameters are selected as follows: the sampling frequency is 16KHz, the number of microphones k=2, the length of one frame of digital signal N=32768, the order of two calibration filters M ₁ =M ₂ =128, the number of input data frames Q=2, The input signal w(n) is uniform white noise. The calibration results are shown in Figure 6 and Figure 7. It can be seen that the frequency responses of the two microphones are close to each other in the passband, stopband, amplitude frequency, and phase frequency after calibration.

The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto, any person familiar with the technical field within the technical scope disclosed in the present invention, according to the technical solution of the present invention Any equivalent replacement or change of the inventive concepts thereof shall fall within the protection scope of the present invention.

Claims (3)

1. a microphone array frequency response calibration method, is characterized in that: comprise the following steps: S1: The electric audio signal w(n) reaches the microphone array through the speaker and the acoustic propagation channel, and the input acoustic signal of the microphone array is x(n); S2: The acoustic signal x(n) passes through k different microphones and preamplifiers to obtain different electrical signals x ₁ (n)~x _k (n); S3: The electrical signals x ₁ (n) to x _k (n) are respectively used as input signals of each calibration filter to adjust the filter coefficients of each calibration filter; the adjustment method of the filter coefficients of the calibration filters is: By adjusting the filter coefficients of each filter, the output signals y ₁ (n)~y _k (n) are all approached to the target signal d(n), and the approximation principle is to make y ₁ (n)~y _k (n) and d The mean square errors between (n) are the smallest respectively; S4: Calculate the filter coefficients of each calibration filter according to the above adjustment method to complete the frequency response calibration of the microphone array; When the output signals y ₁ (n)~y _k (n) of each calibration filter approach the target signal d(n) to realize array frequency response calibration, the following method is adopted: assuming that the length of a frame of digital signal is N, then the i-th The input signal x _i (n) and the target signal d(n) of the calibration filter are written in the following vector form x _i ＝[ _xi (0), _xi (1),..., _xi (N-1)] ^T formula 2 d=[d(0),d(1),...,d(N-1)] ^T Formula 3 Among them, [] ^T represents the transpose of a vector or matrix, and the following cost functions are listed Among them, Σ represents the series summation, so that the cost function J is minimized, and the target signal d(n) is obtained as d=(x ₀ +x ₁ +...+x _k )/k Formula 5 That is, the vector form d of the target signal is equal to averaging the sum of the input vectors of the filters. 2. a kind of microphone array frequency response calibration method according to claim 1 is characterized in that: after target signal d (n) is determined, output signal y _i (n) and target signal d with the i-th road filter The minimum mean square error between (n) is the criterion, and the i-th filter coefficient h _i (n) is calculated in the following way: y _i ＝[y _i (0),y _i (1),...,y _i (N-1)] ^T formula 6 Then the error signal e _i (n) between y _i (n) and d(n) is written in the following vector form e _i ＝[e _i (0),e _i (1),...,e _i (N-1)] ^T ＝y _i -d Equation 7 List another set of cost functions F _i ＝ e _i ^T e _i Formula 8 Wherein, i=1,2,...,k, k is the number of microphones to be calibrated, so that F _i is the smallest, and the filter coefficient h _i (n) of the i-th road calibration filter is calculated, and the calculation rule is: h _i ＝[h _i (0),h _i (1),...,h _i (M _i -1)] ^T ＝(X _i ^T X _i ) ^-1 D ^T x _{i_m} Formula 9 Among them, x _{i_m} is a vector composed of the first NM _i + 1 elements of the i-th calibration filter input vector, and Mi is the order of the i-th calibration filter, namely x _{i_m} ＝[ _xi (0), _xi (1),..., _xi (NM _i )] ^T formula 10 And _Xi and D in Formula 9 are respectively When i ranges from 1 to k, use the above method to calculate the filter coefficient of each calibration filter to complete the microphone array frequency response calibration. 3. a kind of microphone array frequency response calibration method according to claim 2, it is also characterized in that: when multi-frame input data is calibrated respectively, the multi-group filter coefficients that obtain are fused, obtain filter coefficient using As follows: Assuming that the i-th microphone is calibrated by Q frame data, the Q group filter coefficient vectors are obtained according to formula 9 as h _{i_1} , h _{i_2} , ... h _{i_Q} , where h _{i_Q} means that the i-th microphone is input in the Q frame The filter coefficient vector obtained from the data; in addition, the average vector of Q filter coefficient vectors is defined as H _i ＝(h _{i_1} +h _{i_2} +...+h _{i_Q} )/Q Formula 13 The variance vector of the i-th road q-th frame filter coefficient vector is defined as δ _{i_q} = (h _{i_q} -H _i )·(h _{i_q} -H _i ) Formula 14 Among them, the symbol "·" represents the vector dot product, q=1,2,...,Q, the reciprocal variance vector θ _{i_q} of the filter coefficient vector of the i-th road and the q-th frame is defined as θ _{i_q} = [1/δ _{i_q} (0), 1/δ _{i_q} (1),...,1/δ _{i_q} (M _i -1)] ^T formula 15 That is, each element in the vector _{θi_q} is the reciprocal of the corresponding element of the vector _{δi_q} , and for the i-th calibration filter, the vector sum of the reciprocal variance of the filter coefficient vector is defined as θ _i ＝θ _{i_1} +θ _{i_2} +...+θ _{i_Q} Formula 16 According to θ _i and θ _{i_q} (q=1,2,...,Q), Q filter coefficient weight vectors C _{i_1} , C _{i_2} ,..., C _{i_q} ,..., C _{i_Q are obtained} , where, C _{i_q} ＝[θ _{i_q} (0)/θ _i (0),θ _{i_q} (1)/θ _i (1),...,θ _{i_q} (M _i -1)/θ _i (M _i -1)] ^T type 17 According to h _{i_q} and C _{i_q} , the final filter coefficient of the i-th calibration filter is obtained h _i ＝h _{i_1} ·C _{i_1} +h _{i_2} ·C _{i_2} +...+h _{i_Q} ·C _{i_Q} Formula 18 Wherein, i=1,2,...,k, k is the number of microphones.