Wave number domain-based beam forming method

Abstract

The invention provides a wave number domain-based beam forming method. The method comprises the following steps of: 1) establishing a signal model and a performance index; 2) providing a hybrid beam former; 3) enabling the sound field to be approximate to limited superposition of plane waves, and converting calculation from a spatial domain to a wavenumber domain; 4) deriving the superposed sound field, and calculating a spatial derivative in a wavenumber domain; and 5) calculating the weight through the spatial derivative, and synthesizing an ideal wave beam. An equipment end and upper computer software. According to the method, derivative calculation of a space domain is converted into multiplication in a wavenumber domain, a beam former irrelevant to frequency is generated, calculation complexity is reduced, meanwhile, robustness of the beam former is improved, noise and interference in the non-target direction are effectively restrained, and a target sound source can be accurately recognized in a complex sound field environment.

Description

Technical Field

[0001] The present invention relates to the field of beamforming, and in particular to a beamforming method based on wave number domain. Background Art

[0002] With the continuous advancement of science and technology, microphone array technology has been widely used in voice communication, smart speakers, video conferencing and other fields. In these applications, accurate and efficient recognition and processing of sound signals are crucial. Beamforming technology, as a technology for directionally receiving or transmitting sound signals in space, provides important support for improving the performance of microphone arrays. However, traditional beamforming technology faces many challenges in practical applications, especially in complex sound field environments and multi-sound source scenarios.

[0003] Traditional beamforming technology mainly relies on the adjustment of phase and amplitude. By adjusting the phase and amplitude of each element in the microphone array, the signal directionality control is achieved. Currently, the common microphone array beamforming technologies mainly include delay summation, filter summation, adaptive beamforming, etc. Delay summation and filter summation cannot identify the sound source well in complex environments or environments with reverberation, and adaptive beamforming is prone to fall into local optimal solutions. Differential beamforming has attracted attention due to its high positioning accuracy and resolution, but the beam directivity and robustness will decrease with the increase of signal frequency, thereby reducing the accuracy of signal recognition. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and propose a beamforming method based on the wavenumber domain, which converts the derivative calculation in the spatial domain into a multiplication operation in the wavenumber domain, generates a frequency-independent beamformer, reduces the computational complexity, effectively suppresses noise and interference in non-target directions, and accurately identifies the target sound source in a complex sound field environment.

[0005] In order to achieve the above object, the technical solution adopted by the present invention comprises the following steps:

[0006] (1) Establish signal model and performance indicators:

[0007] Design a microphone array and establish a spatial coordinate system. The microphone array consists of M microphones arranged linearly. The distance between adjacent microphones is d. It is used to collect sound signals. The spatial coordinate system takes the left end of the microphone array as the coordinate center, and extends to the right end as the positive direction of the z axis. The angle between the target sound source direction and the z axis is θ s , the signal received by M microphones is The signal containing the target sound source and noise signal By introducing the weight vector To improve the signal-to-noise ratio, the output Z(ω,s) of the beamforming algorithm is obtained. The exponential factor DI is used to evaluate the directivity of the beamforming algorithm, and the white noise gain WNG is used to evaluate the robustness of the beamforming algorithm.

[0008] (2) Propose a hybrid beamformer:

[0009] Hybrid beamformer B(θ s ) by the frequency-dependent beamformer B1(θ s ) and the delay-sum beamformer B2(θ s ) mixed to obtain;

[0010] (3) Approximate the sound field to a finite superposition of plane waves and transform the calculation from the spatial domain to the wavenumber domain:

[0011] Since the distance from the target sound source to the microphone array is much greater than the distance between each microphone, the sound wave emitted by the target sound source is equivalent to a plane wave. The sound field at the location of any microphone in the microphone array can be equivalent to the superposition of plane waves in all directions. In the Cartesian coordinate system, the sound field of any point r (x, y, z) is p (r). Since x and y are both 0, the sound field can be further expressed as the sound field p (z) of the superposition of finite plane waves. The sound field p (z) is discretized, and the sound field of M microphones is represented by the vector product Ax. Through a series of transformations, the solution x is obtained in the wave number domain.

[0012] (4) Derivative the superimposed sound field and calculate the spatial derivative in the wavenumber domain:

[0013] Taking the nth-order differential of the sound field after finite superposition, we get the nth-order derivative with respect to the z axis. Compute spatial derivatives in the wavenumber domain:

[0014] (5) Calculate the weights through spatial derivatives and synthesize the beam in the direction of the target sound source:

[0015] Through the spatial derivative Calculate the weight vector w H , and the weight vector w H Substituting into the output Z(ω,s) of the beamforming algorithm, we get the target sound source direction θ s Enhanced sound signal.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] The derivative calculation in the spatial domain is converted into a multiplication operation in the wavenumber domain to obtain the weight vector, which generates a frequency-independent beamformer, making it have better directivity in high-frequency conditions. At the same time, the optimal truncation parameters determined by the experiment improve the robustness of the beamformer, effectively suppress noise and interference in non-target directions, and accurately identify the target sound source in a complex sound field environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is an implementation flow chart of the present invention. DETAILED DESCRIPTION

[0019] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0020] Reference Figure 1 , the present invention comprises the following steps:

[0021] Step 1) Establish signal model and performance indicators:

[0022] (1a) Design a microphone array and establish a spatial coordinate system. The microphone array consists of M microphones arranged linearly, with the distance between adjacent microphones being d. It is used to collect sound signals. The spatial coordinate system takes the left end of the microphone array as the coordinate center, and extends to the right end as the positive direction of the z axis. The angle between the target sound source direction and the z axis is θ s , the sound signal received by a microphone can be expressed as:

[0023]

[0024] Where k = 2πf / c is the wave number, f is the frequency, and c is the speed of sound.

[0025] The signal received by M microphones is The signal containing the target sound source and noise signal

[0026] y=[Y1(ω)Y2(ω)…Y M (ω)] T =p s +v(2)

[0027] in, T stands for transpose, z1,…,z M represents the position of the microphone, z m =z1+(m-1)d,m=1,...,M;

[0028] By introducing the weight vector To improve the signal-to-noise ratio, we can get the output Z(ω,s) of the beamforming algorithm:

[0029]

[0030] where w = [H1(ω)H2(ω)…H M (ω)] T , H represents the complex conjugate transpose, and the beamformer can be defined as B(θ S )=w H p s

[0031] (1b) The exponential factor DI is used to evaluate the directivity of the beamforming algorithm:

[0032] DI=10log 10 (Q)(4)n

[0033]

[0034] in is the steering vector, is the noise pseudo-coherence matrix, v1 is the noise signal collected by the first microphone at position z1;

[0035] The robustness of the beamforming algorithm is evaluated using the white noise gain WNG:

[0036]

[0037] Step 2) Propose a hybrid beamformer:

[0038] Hybrid beamformer B(θ s ) by the frequency-dependent beamformer B1(θ s ) and the delay-sum beamformer B2(θ s ) is mixed, where the frequency-independent beamformer B1(θ s ) is expressed as:

[0039]

[0040] The delay-sum beamformer B2(θ s ) is expressed as:

[0041]

[0042] The hybrid beamformer B(θ s ) is expressed as:

[0043]

[0044] in represents the Hadamard product, is a column vector. When only the [(M+1) / 2]th element in vector b is 1 and the rest are 0, |B(θ s )|=|B1(θ s )|, [·] represents the integer part. When all elements in vector b are 1, |B(θ s )|=|B2(θ s )|, according to Euler's formula and binomial theorem, cos(nθ s ) can be expressed as:

[0045]

[0046] Substituting (11) into (10), the hybrid beamformer B(θ s ) is further expressed as:

[0047]

[0048] Hybrid beamformer B(θ s ) can finally be expressed as:

[0049]

[0050] in For m = 1, 2, ..., M,

[0051] Step 3) Approximate the acoustic field as a finite superposition of plane waves and transform the calculation from the spatial domain to the wavenumber domain:

[0052] (3a) Since the distance from the target sound source to the microphone array is much greater than the distance between each microphone, the sound wave emitted by the target sound source is equivalent to a plane wave. The sound field at the location of any microphone in the microphone array can be equivalent to the superposition of plane waves in all directions. In the Cartesian coordinate system, the sound field at any point r (x, y, z) is p (r), which can be expressed as:

[0053]

[0054] Since both x and y are 0, the sound field can be further expressed as:

[0055]

[0056] Among them, the angle θ g The corresponding plane wave amplitude is Traversing from 0 to 180 degrees, when θ g =θ s hour, There is a maximum value, that is, the plane wave amplitude in the direction of the target sound source is the largest, θ s is the direction of the target sound source;

[0057] Discretizing (15), we can obtain the sound field p(z) of finite plane wave superposition:

[0058]

[0059] in L is the number of angular discrete points, l = 1, ..., L, for M microphones on the z-axis;

[0060] (3b) Next, the calculation is converted from the spatial domain to the wavenumber domain:

[0061] According to (16), the sound field of M microphones can be expressed by a vector:

[0062] p≈Ax(16)

[0063] in and A is a full rank matrix, so (17) can be equivalent to:

[0064] x≈A H (AA H ) -1 p(17)

[0065] The matrix A can be decomposed into:

[0066] A=UDV H (18)

[0067] in and is the identity matrix, It can be expressed as:

[0068] D=[∑ O] (19)

[0069] in σ m are singular values, is a matrix with all elements equal to zero. By using formulas (19) and (20), we can obtain:

[0070] AA H =U∑∑ H U H (20)

[0071] By using formulas (19) and (21), we can obtain:

[0072]

[0073] In order to increase the robustness of x, the filter factor s is introduced into the matrix ∑ m ,get:

[0074]

[0075] in m t is the cutoff parameter, which can be obtained through experiments. Substituting formula (23) into (22), we can get:

[0076]

[0077] in

[0078] Step 4) Derivative the superimposed sound field and calculate the spatial derivative in the wavenumber domain:

[0079] Taking the nth-order differential of the sound field after finite superposition, we can obtain the nth-order derivative of the sound field at any microphone:

[0080]

[0081] By discretizing it, we can get:

[0082]

[0083] in

[0084] and For m = 1, 2, ..., M, Substituting formula (24) into (26), we can obtain:

[0085]

[0086] In formula (26), the left side is the real high-order derivative of the sound field, and the right side is the high-order derivative of the reconstructed sound field. For the angle θ of the target sound source, s , whose derivative is:

[0087]

[0088] Step 5) Calculate the weights through spatial derivatives to synthesize the ideal beam:

[0089] Substituting (27) into the hybrid beamformer B(θ s ), we can get the weight vector w H :

[0090] Finally, the weight vector w H Substituting into Z(ω,s), we get θ sDirectional enhancement signal.

Claims

1. A beamforming method based on wavenumber domain, characterized in that: The steps include: (1) Establish signal model and performance indicators: Design a microphone array and establish a spatial coordinate system. The microphone array consists of M microphones arranged linearly. The distance between adjacent microphones is d. It is used to collect sound signals. The spatial coordinate system takes the left end of the microphone array as the coordinate center, and extends to the right end as the positive direction of the z axis. The angle between the target sound source direction and the z axis is θ s , the signal received by M microphones is The signal containing the target sound source and noise signal By introducing the weight vector To improve the signal-to-noise ratio, the output Z(ω,s) of the beamforming algorithm is obtained. The exponential factor DI is used to evaluate the directivity of the beamforming algorithm, and the white noise gain WNG is used to evaluate the robustness of the beamforming algorithm. (2) Propose a hybrid beamformer: Hybrid beamformer B(θ s ) is generated by the frequency-dependent beamformer B1(θ s ) and the delay-sum beamformer B2(θ s ) mixed to obtain; (3) Approximate the sound field to a finite superposition of plane waves and transform the calculation from the spatial domain to the wavenumber domain: Since the distance from the target sound source to the microphone array is much greater than the distance between each microphone, the sound wave emitted by the target sound source is equivalent to a plane wave. The sound field at the location of any microphone in the microphone array can be equivalent to the superposition of plane waves in all directions. In the Cartesian coordinate system, the sound field of any point r (x, y, z) is p (r). Since x and y are both 0, the sound field can be further expressed as the sound field p (z) of the superposition of finite plane waves. The sound field p (z) is discretized, and the sound field of M microphones is represented by the vector product Ax. Through a series of transformations, the solution x is obtained in the wave number domain. (4) Derivative the superimposed sound field and calculate the spatial derivative in the wavenumber domain: Taking the nth-order differential of the sound field after finite superposition, we get the nth-order derivative with respect to the z axis. Realize the transformation of the calculation of spatial derivatives into multiplication operations in the wavenumber domain: (5) Calculate the weights through spatial derivatives to synthesize the ideal beam: Through the spatial derivative Calculate the weight vector w H , and the weight vector w H Substituting into the output Z(ω,s) of the beamforming algorithm, we get the target sound source direction θ s Enhanced sound signal.

2. The method according to claim 1, characterized in that The signal y in step (1) can be expressed as: y=[Y1(ω) Y2(ω)…Y M (ω)] T =p s +v in, T stands for transpose, z1,…,z M represents the position of the microphone, z m =z1+(m-1)d,m=1,...,M; The output Z(ω,s) of the beamforming algorithm can be expressed as: where w = [H1(ω)H2(ω)…H M (ω)] T , H represents the complex conjugate transpose, and the beamformer can be defined as B(θ S )=w H p s ; The exponential factor DI can be expressed as: DI=10log 10 (Q) in is the steering vector, is the noise pseudo-coherence matrix, v1 is the noise signal collected by the first microphone at position z1; The white noise gain WNG can be expressed as:

3. The method according to claim 1, characterized in that The frequency-dependent beamformer B1(θ s ) is expressed as: The delay-sum beamformer B2(θ s ) is expressed as: The hybrid beamformer B(θ s ) is expressed as: where ο represents the Hadamard product, is a column vector. When only the [(M+1) / 2]th element in vector b is 1 and the rest are 0, |B(θ S )|=|B1(θ S )|, [·] represents the integer part. When all elements in vector b are 1, |B(θ S )|=|B2(θ S )|, according to Euler's formula and binomial theorem, the hybrid beamformer B(θ s ) can finally be expressed as: in For m = 1, 2, ..., M, 4. The method according to claim 1, characterized in that: The sound field p(r) in step (3) is expressed as: The sound field p(z) of the finite plane wave superposition is expressed as: in L is the number of angular discrete points, For the M microphones on the z-axis, the sound field can be expressed by a vector: p≈Ax in and A is a full rank matrix, so the above formula can be expressed as: x≈A H (CHALLENGE ACCEPTED H ) -1 pp After a series of transformations, we can finally get: in and is the identity matrix, in σ m are singular values, m t is the cutoff parameter, which can be obtained experimentally. is a matrix with all elements zero and T is the transpose.

5. The method according to claim 1, characterized in that In step (4), the n-th order differentiation of the sound field after finite superposition can be obtained: Therefore, the derivative It can be expressed as: in and For m = 1, 2, ..., M, Substitute x into the above formula, and for the angle θ of the target sound source s , we can get: Substituting it into the hybrid beamformer, we can get the weight vector w H : The weight vector w H Substituting into the output Z(ω,s) of the beamforming algorithm, we get the target sound source direction θ s Enhanced sound signal.

Images