CN108398664B - Analytic spatial de-aliasing method for microphone array - Google Patents

Analytic spatial de-aliasing method for microphone array Download PDF

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CN108398664B
CN108398664B CN201710068121.3A CN201710068121A CN108398664B CN 108398664 B CN108398664 B CN 108398664B CN 201710068121 A CN201710068121 A CN 201710068121A CN 108398664 B CN108398664 B CN 108398664B
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应冬文
战鸽
黄兆琼
潘接林
颜永红
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Abstract

The invention relates to an analytic spatial de-aliasing method for a microphone array, which comprises the following steps: a microphone array receives a sound source signal, and the sound source signal is converted into a digital sound signal; extracting the frequency spectrum of the digital sound signal to obtain the frequency spectrum of the digital sound signal of each microphone in the microphone array; estimating a spatial correlation matrix on each frequency point according to the frequency spectrum of the digital sound signal of each microphone; decomposing the spatial correlation matrix on each frequency point to obtain a main eigenvector, wherein each component of the main eigenvector corresponds to a collected signal of one microphone; according to the main characteristic vector on each frequency point, the time phase difference between any two microphones is obtained; and according to the time phase difference between the microphones, calculating a periodicity combination through an aliasing-removing formula, and further finding out an optimal periodicity value.

Description

Analytic spatial de-aliasing method for microphone array
Technical Field
The invention relates to the field of sound source positioning and voice enhancement, in particular to an analytic spatial de-aliasing method for a microphone array.
Background
The microphone array based method occupies an important position in speech signal processing, can be used for teleconferencing, positions the position of a speaker, indicates the direction of beam focusing for a microphone array, provides pointing information for a conference camera, and can separate and enhance target source signals.
In array processing, it is often necessary to calculate the time delay between the arrival of a sound source at two microphones from the phase spectrum of the signal. Whereas phase is a periodic variable, the real time delay is the sum of several time periods and the phase time difference. In the case of a sufficiently large microphone pitch, the number of periods may be several, and there is a one-to-many relationship between the phase difference and the practical delay, i.e., the periods are aliased. De-aliasing is the selection of the correct number of cycles out of a plurality of candidate time delays.
In the existing literature, the spacing of the microphones is limited to make only a single value of the number of cycles possible, however, the small size of the microphone array limits the performance of the array. There is also a method of checking the validity of each period value, however, for an array of several pairs of microphones, the combination of the period values may be a huge number, which easily results in a huge amount of calculation.
Disclosure of Invention
The invention aims to overcome the trouble of the time-frequency analysis technology brought by the cycle aliasing, thereby providing a space de-aliasing method.
In order to achieve the above object, the present invention provides an analytic spatial de-aliasing method for a microphone array, comprising:
step 1), a microphone array receives a sound source signal, and the sound source signal is converted into a digital sound signal;
step 2), extracting the frequency spectrum of the digital sound signal to obtain the frequency spectrum of the digital sound signal of each microphone in the microphone array;
step 3), estimating a spatial correlation matrix on each frequency point according to the frequency spectrum of the digital sound signal of each microphone obtained in the step 2);
step 4), decomposing the spatial correlation matrix on each frequency point obtained in the step 3) to obtain a main eigenvector, wherein each component of the main eigenvector corresponds to a collected signal of one microphone;
step 5), solving the time phase difference between any two microphones according to the main characteristic vector on each frequency point;
and 6) according to the time phase difference between the microphones, solving the periodicity combination through an anti-aliasing formula, and further finding out the optimal periodicity value.
In the above technical solution, the step 2) includes:
step 2-1), caching the digital sound signal;
step 2-2), each frame in the digital sound signal is zero-filled to N points, wherein N is 2jJ is an integer, and j is not less than 8;
and 2-3) performing fast Fourier transform of N points on each frame from zero filling to N points in the digital sound signal to obtain the discrete frequency spectrum of the digital sound signal of one frame.
In the above technical solution, a step of preprocessing the digital sound signal of each frame is further included between step 2-2) and step 2-3), and the preprocessing includes: windowing and/or pre-emphasis processing.
In the above technical solution, the step 3) includes:
step 3-1), forming a complex vector according to Fourier coefficients of the digitized sounds of all the microphones on each frequency point, wherein the dimensionality of the complex vector is the number of the microphones;
and 3-2) calculating the mean value estimation of the complex autocorrelation matrix of the complex vector on each frequency point.
In the above technical solution, in the step 4), if the spatial correlation matrix is a singular matrix, a singular value decomposition method is adopted when the spatial correlation matrix is decomposed; otherwise, adopting a characteristic value decomposition method.
In the above technical solution, the step 5) includes:
step 5-1), calculating the time delay between each pair of microphones; the calculation formula is as follows:
Figure BDA0001221423410000021
wherein ∠ denotes the operation of obtaining the complex phase,/m,t,fRepresenting a possible occurrence of phase aliasing,
Figure BDA0001221423410000022
the angular frequency is represented by the angular frequency,
Figure BDA0001221423410000023
indicating the time period at this frequency and,
Figure BDA0001221423410000024
which is indicative of the corresponding time phase,
Figure BDA0001221423410000025
step 5-2), at the frequency points (t, f), according to the distance r of each pair of microphonesmThe constraint, in combination with the time delay between each pair of microphones obtained in step 105-1), determines a set of possible arrival times:
Figure BDA0001221423410000031
wherein c represents the speed of sound;
step 5-3), repeating the step 5-2) until the time phase difference of M ═ K (K-1)/2 pairs of microphones on each frequency point is calculated, and forming a time phase difference array; wherein each pair of microphones corresponds to a set B on each frequency pointm,t,fAnd K is the number of the microphones.
In the above technical solution, the step 6) includes:
step 6-1), obtaining a cost function of an aliasing combination based on the time difference phase arrays of the plurality of pairs of microphones obtained in step 5), wherein the expression is as follows:
Figure BDA0001221423410000032
wherein: g'mRepresenting a two-dimensional vector formed by a first dimension and a second dimension in the spatial direction three-dimensional coordinates of the m-th pair of microphone connecting lines, and assuming that all the microphones are positioned in one plane and the third dimensions are the same, the third dimension of the direction vector is zero; z is a matrix related to the array topology defined as:
Figure BDA0001221423410000033
step 6-2), calculating a derivative of the cost function obtained in the step 6-1), and enabling the derivative to be zero to obtain an optimal solution of the periodicity combination:
Figure BDA0001221423410000034
wherein
Figure BDA0001221423410000035
Figure BDA0001221423410000036
Figure BDA0001221423410000037
Figure BDA0001221423410000038
Figure BDA0001221423410000039
Figure BDA00012214234100000310
Figure BDA00012214234100000311
Step 6-3), from set Bm,t,fSelecting an integer close to the optimal solution as the integer solution of the cycle number:
Figure BDA0001221423410000041
the invention has the advantages that:
the analytic spatial de-aliasing method for the microphone array provides an optimal estimation formula of the periodicity, overcomes the trouble brought to a time-frequency analysis technology by periodic aliasing, and clears a technical obstacle for sound source positioning and signal separation. Its computational efficiency is significantly better than that of the traditional hypothesis testing method.
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FIG. 1 is a flow chart of an analytical spatial de-aliasing method for a microphone array of the present invention.
Detailed Description
The invention will now be further described with reference to the accompanying drawings.
The invention provides an analytic spatial de-aliasing method for a microphone array, which comprises the following steps: the system comprises a microphone array, a processing unit and a control unit, wherein the microphone array is used for converting a sound source signal received by the microphone array into a digital sound signal, and a plurality of microphones are included in the microphone array; spectrum extraction, which is used for performing spectrum extraction on the digital sound signal to obtain the spectrum of the digital sound signal of each microphone; aiming at each frequency point, calculating a spatial correlation matrix of the frequency point and spatial correlation matrices of adjacent frequency points in the time direction, and solving the mean value of the matrices as the estimation of the spatial correlation matrix on the frequency point; obtaining a plurality of principal components by adopting a method of eigenvalue decomposition or singular value decomposition; extracting the principal component with the largest characteristic value as an analysis object, and calculating the phase difference between the principal component dimensions as the pairing time delay; given a formula for knowing the period aliasing, the number of aliasing periods can be directly determined from the formula.
With reference to fig. 1, the method of the invention comprises in particular the following steps:
step 101), a microphone array comprising K microphones receives a sound source signal and converts the received sound source signal into a digital sound signal.
Step 102), extracting the frequency spectrum of the digital sound signal obtained in step 101), and obtaining the frequency spectrum of the digital sound signal for each microphone in the microphone array.
Step 103), estimating a spatial correlation matrix on each frequency point according to the frequency spectrum of the digital sound signal of each microphone obtained in the step 102).
Step 104), carrying out eigenvalue or singular value decomposition on the spatial correlation matrix on each frequency point obtained in the step 103) to obtain a main eigenvector [ u ]1,t,f,u2,t,f,......,uK,t,f]Each component of the principal eigenvector corresponds to the acquired signal of one microphone.
If the spatial correlation matrix is a singular matrix, a singular value decomposition method can be adopted when the spatial correlation matrix is decomposed; otherwise, a method of eigenvalue decomposition may be employed. In the lower subscript of each component of the principal eigenvector involved in this step, t represents time, f represents frequency point, and K represents the number of microphones.
And 105) calculating the time phase difference of the microphones for the main characteristic vectors on each frequency point pairwise.
Step 106), according to the time phase difference between the microphones, calculating the period combination through an anti-aliasing formula, and further finding out the optimal period value.
The steps of the method of the present invention are further described below.
The step 102) further comprises:
step 102-1), buffering the received digital sound signal;
step 102-2), each frame of the digital sound signal is zero-filled to N points, N is larger than or equal to F, and N is 2jJ is an integer, and j is not less than 8;
step 102-3), performing fast Fourier transform of N points on the result obtained in the step 102-2) to obtain the discrete frequency spectrum of the digital sound signal of one frame
Figure BDA0001221423410000051
Wherein,
Figure BDA0001221423410000052
indicating the first in the cache
Figure BDA0001221423410000055
Each microphone collects the nth sample point of the signal,
Figure BDA0001221423410000054
indicating the first in the cache
Figure BDA0001221423410000053
Each microphone acquires fourier transform coefficients (k 0, 1.., N-1) of the signal.
Preferably, before the spectrum extraction (i.e. after step 102-2), the digital audio signal of each frame is preprocessed, and the length of each frame can be set to be F point, the preprocessing includes windowing and/or pre-emphasis, and the windowing function can be hamming window (hamming) or hanning window (hanning).
The step 103) further comprises:
step 103-1), forming a complex vector according to Fourier coefficients of the digitized sounds of all the microphones on each frequency point, wherein the dimensionality of the complex vector is the number of the microphones;
step 103-2), calculating the mean value estimation of the complex autocorrelation matrix of the complex vector on each frequency point.
For example, at the f-th frequency point at time t, the complex vector x is obtainedt,f(ii) a The complex autocorrelation matrix of the obtained complex phasor is represented as the mean of the autocorrelation matrices at adjacent frequency points,
Figure BDA0001221423410000061
wherein A represents the number of frames adjacent in the time direction, ()HRepresenting a conjugate transpose.
Said step 105) further comprises:
step 105-1), calculating the time delay between each pair of microphones; the calculation formula is as follows:
Figure BDA0001221423410000062
wherein ∠ denotes the operation of obtaining the complex phase,/m,t,fRepresenting a possible occurrence of phase aliasing,
Figure BDA0001221423410000063
to representThe angular frequency of the wave is such that,
Figure BDA0001221423410000064
indicating the time period at this frequency and,
Figure BDA0001221423410000065
which is indicative of the corresponding time phase,
Figure BDA0001221423410000066
105-2) at the frequency points (t, f), according to the distance r of each pair of microphonesmThe constraint, in combination with the time delay between each pair of microphones obtained in step 105-1), determines a set of possible arrival times:
Figure BDA0001221423410000067
where c represents the speed of sound.
Step 105-3), repeating step 105-2) until the time phase difference of M ═ K (K-1)/2 pairs of microphones on each frequency point is calculated, and forming a time phase difference array; wherein each pair of microphones corresponds to a set B on each frequency pointm,t,f。
The step 106) further comprises:
step 106-1), the time phase difference array of the microphones obtained in step 105) is an aliasing combination, and a cost function of the aliasing combination is obtained based on the time phase difference array of the microphones obtained in step 105), and the expression is:
Figure BDA0001221423410000068
wherein: g'mRepresenting a two-dimensional vector formed by the first and second dimensions in the spatial directional three-dimensional coordinates of the m-th pair of microphone lines, the third dimension of the directional vector is zero, assuming that all the microphones lie within one plane and their third dimensions are the same. Z is a matrix related to the array topology defined as:
Figure BDA0001221423410000069
step 106-2), calculating a derivative of the cost function obtained in the step 106-1), and enabling the derivative to be zero to obtain an optimal solution of the cycle number combination:
Figure BDA0001221423410000071
wherein
Figure BDA0001221423410000072
Figure BDA0001221423410000073
Figure BDA0001221423410000074
Figure BDA0001221423410000075
Figure BDA0001221423410000076
Figure BDA0001221423410000077
Figure BDA0001221423410000078
Step 106-3), from set B, since the number of cycles is an integerm,t,fSelecting an integer close to the optimal solution as the integer solution of the cycle number:
Figure BDA0001221423410000079
finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (5)

1. An analytical spatial de-aliasing method for a microphone array, comprising:
step 1), a microphone array receives a sound source signal, and the sound source signal is converted into a digital sound signal;
step 2), extracting the frequency spectrum of the digital sound signal to obtain the frequency spectrum of the digital sound signal of each microphone in the microphone array;
step 3), estimating a spatial correlation matrix on each frequency point according to the frequency spectrum of the digital sound signal of each microphone obtained in the step 2);
step 4), decomposing the spatial correlation matrix on each frequency point obtained in the step 3) to obtain a main eigenvector, wherein each component of the main eigenvector corresponds to a collected signal of one microphone;
step 5), solving the time phase difference between any two microphones according to the main characteristic vector on each frequency point;
step 6), according to the time phase difference between the microphones, calculating a periodicity combination through an anti-aliasing formula, and further finding out an optimal periodicity value from the periodicity combination;
the step 5) comprises the following steps:
step 5-1), calculating the time delay between each pair of microphones; the calculation formula is as follows:
Figure FDA0002499924890000011
wherein ∠ denotes the operation of obtaining the complex phase,/m,t,fRepresenting a possible occurrence of phase aliasing,
Figure FDA0002499924890000012
the angular frequency is represented by the angular frequency,
Figure FDA0002499924890000013
indicating the time period at this frequency and,
Figure FDA0002499924890000014
which is indicative of the corresponding time phase,
Figure FDA0002499924890000015
up,t,fand uq,t,fRespectively collecting signals of a p microphone and a q microphone;
step 5-2), at the frequency points (t, f), according to the distance r of each pair of microphonesmAnd (3) determining a set of possible arrival times by combining the time delays between each pair of microphones obtained in the step 5-1):
Figure FDA0002499924890000016
wherein c represents the speed of sound;
step 5-3), repeating the step 5-2) until the time phase difference of M ═ K (K-1)/2 pairs of microphones on each frequency point is calculated, and forming a time phase difference array; wherein each pair of microphones corresponds to a set B on each frequency pointm,t,fK is the number of the microphones;
the step 6) comprises the following steps:
step 6-1), obtaining a cost function of an aliasing combination based on the time difference phase arrays of the plurality of pairs of microphones obtained in step 5), wherein the expression is as follows:
Figure FDA0002499924890000021
wherein: g'mA two-dimensional vector consisting of the first and second dimensions in the three-dimensional coordinates of the m-th pair of microphones in the spatial direction, assuming that all microphones lie within one planeAnd their third dimensions are the same, then the third dimension of the direction vector is zero; z is a matrix related to the array topology defined as:
Figure FDA0002499924890000022
step 6-2), calculating a derivative of the cost function obtained in the step 6-1), and enabling the derivative to be zero to obtain an optimal solution of the periodicity combination
Figure FDA0002499924890000023
Figure FDA0002499924890000024
Wherein
Figure FDA0002499924890000025
γt,f＝[Υ1,t,f,Υ2,t,f,…,ΥM,t,f]T；
Figure FDA0002499924890000026
Figure FDA0002499924890000027
Figure FDA0002499924890000028
Figure FDA0002499924890000029
Figure FDA00024999248900000210
Step 6-3), from set Bm,t,fSelecting an integer close to the optimal solution as the integer solution of the cycle number:
Figure FDA00024999248900000211
2. the analytical spatial de-aliasing method for microphone arrays according to claim 1, wherein the step 2) comprises:
step 2-1), caching the digital sound signal;
step 2-2), each frame in the digital sound signal is zero-filled to N points, wherein N is 2jJ is an integer, and j is not less than 8;
and 2-3) performing fast Fourier transform of N points on each frame from zero filling to N points in the digital sound signal to obtain the discrete frequency spectrum of the digital sound signal of one frame.
3. The analytical spatial de-aliasing method for microphone arrays according to claim 2, further comprising the step of pre-processing the digital sound signal of each frame between step 2-2) and step 2-3), said pre-processing comprising: windowing and/or pre-emphasis processing.
4. The analytical spatial de-aliasing method for microphone arrays according to claim 1, wherein the step 3) comprises:
step 3-1), forming a complex vector according to Fourier coefficients of the digitized sounds of all the microphones on each frequency point, wherein the dimensionality of the complex vector is the number of the microphones;
and 3-2) calculating the mean value estimation of the complex autocorrelation matrix of the complex vector on each frequency point.
5. The analytical spatial de-aliasing method for microphone arrays according to claim 1, wherein in the step 4), if the spatial correlation matrix is a singular matrix, a singular value decomposition method is adopted in the decomposition of the spatial correlation matrix; otherwise, adopting a characteristic value decomposition method.
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