Method for reconstructing reverberation sound field by rigid spherical microphone array

Abstract

The application discloses a rigid spherical microphone array reverberation sound field reconstruction method, comprising the following steps: 1, mixed wave model construction; 2, mixed wave model solving; 3, reconstruction of reverberation sound field. The technical effect of the application is that the spherical microphone array is used to realize the reconstruction of the reverberation sound field with a large range and high precision.

Description

Technical Field

[0001] This invention relates to the field of sound field reconstruction technology, specifically a method for reverberating sound field reconstruction using a rigid spherical microphone array. Background Technology

[0002] Sound field reconstruction technology recovers sound field information from unmeasured locations by collecting signals from microphones, and has significant application value in fields such as virtual reality, intelligent sound field modulation, and noise control. Among them, spherical microphone arrays have attracted much attention due to their compact structure, flexible deployment, and ability to comprehensively record three-dimensional spatial sound field information.

[0003] Currently, most sound field reconstruction methods based on spherical microphone arrays are based on the free field assumption, which assumes that sound waves propagate in a space without reflection or reverberation.

[0004] However, in practical applications, sound fields are often located within closed or semi-closed bounded regions, exhibiting complex reflection and reverberation effects, thus forming reverberant sound fields. Under these conditions, the propagation path of sound waves significantly contradicts the free-field assumption upon which existing methods rely, leading to decreased accuracy and insufficient stability in estimating reverberant sound fields using traditional reconstruction methods. This limits the effective application of this technology in real-world environments. Therefore, developing high-precision and robust reconstruction methods for bounded reverberant sound fields has become a critical technical challenge that urgently needs to be addressed. Summary of the Invention

[0005] The purpose of this invention is to provide a method for reconstructing the reverberant sound field of a rigid spherical microphone array, comprising the following steps:

[0006] Step 1) Establish a mixed wave model of the sound pressure signal acquired by the rigid spherical microphone array;

[0007] Step 2) Solve the hybrid wave model to obtain the intensities of the spherical wave equivalent source and the plane wave equivalent source;

[0008] Step 3) Reconstruct the reverberant sound field based on the intensity of the spherical wave equivalent source and the plane wave equivalent source.

[0009] Furthermore, in step 1), a near-field spherical wave equivalent source model and a far-field plane wave equivalent source model are used to simulate the direct sound and reflected sound components in the sound field, and a mixed wave model of the sound pressure signal collected by the rigid spherical microphone array is constructed.

[0010] Furthermore, the equivalent source models for near-field spherical waves and far-field plane waves are shown below:

[0011] (1)

[0012] (2)

[0013] In the formula, and Positions The direct sound component and the reflected sound component of the sound field. It is the angular frequency. and For the first The location of the first spherical wave equivalent source and the first The direction of the equivalent source of a plane wave L and L represent the number of equivalent sources for spherical waves and plane waves, respectively. and The first The spherical wave equivalent source and the first Equivalent source intensity of a plane wave.

[0014] Furthermore, the first Equivalent source and location of spherical waves Transfer function between , No. Equivalent source and location of a plane wave Transfer function between As shown below:

[0015] (3)

[0016] (4)

[0017] In the formula, The imaginary unit, For direction nth order m-th spherical harmonic function on Let be the nth order spherical Bessel function. For the nth order sphere of the second kind, the Hankel function is... and They are respectively and The first derivative, Let be the wave number, and the superscript "*" indicates complex conjugate. 'a' is the radius of the rigid sphere.

[0018] Furthermore, the mixed wave model of the sound pressure signal acquired by the rigid spherical microphone array is shown below:

[0019] (5)

[0020] In the formula, This represents the received sound pressure level of a rigid spherical microphone array. For the first The microphone position, Q is the number of microphones, and the superscript "" indicates the microphone position. T "Represents transposition, and These are the equivalent source intensity vectors for spherical waves and plane waves. and For the transfer function matrix, , .

[0021] Furthermore, in step 2), the steps for solving the hybrid wave model include:

[0022] Step 2.1) Transform the acoustic pressure signal mixed wave model to obtain the following optimized model:

[0023] (6)

[0024] In the formula, express Norm, and For regularization parameters;

[0025] Step 2.2) Introduce additional variables into the optimization model and This yields an optimization model with additional variables, namely:

[0026] (7)

[0027] Step 2.3) Transform the optimization model with additional variables into an unconstrained optimization problem, that is:

[0028] (8)

[0029] In the formula, and Let Lagrange multiplier vector be the vector. Indicates taking the real part, superscript " H " indicates complex conjugate transpose. , For penalty parameters;

[0030] Step 2.4) Let and The unconstrained optimization problem is transformed to obtain the transformed unconstrained optimization problem, namely:

[0031] (9)

[0032] Step 2.5) Solve the transformed unconstrained optimization problem to obtain the intensities of the spherical wave equivalent source and the plane wave equivalent source.

[0033] Furthermore, in step 2.5), the transformed unconstrained optimization problem is solved iteratively using the alternating direction multiplier algorithm until the iteration termination condition is met or the maximum number of iterations is reached.

[0034] Furthermore, the iteration termination condition is and .

[0035] Furthermore, in step 2.5), in the first... The results of the iterative solution in this iteration are shown below:

[0036] (10)

[0037] in, This is a soft threshold operator.

[0038] Furthermore, in step 3), the reconstructed reverberant sound field is shown below:

[0039] (11)

[0040] In the formula, V reconstruction locations The sound pressure vector at that location; ; and The dimensions are respectively and Matrix; , , , ; and The intensities of the spherical wave equivalent source and the plane wave equivalent source are given.

[0041] The technical effectiveness of this invention is undeniable. The method provided by this invention utilizes spherical wave equivalent source models and plane wave equivalent source models to simulate the direct and reflected sound components in a sound field, thereby establishing a mixed wave model. This model is then solved using the alternating direction multiplier algorithm to obtain the equivalent source intensity, thus achieving reverberant sound field reconstruction. Because the reflected sound component is modeled separately during the sound field modeling process, the method provided by this invention can achieve accurate sound field reconstruction in reverberant environments. Attached Figure Description

[0042] Figure 1 is a schematic diagram of the equivalent source model of the present invention;

[0043] Figure 2 The diagram shows the theoretical and reconstructed real part of the sound pressure in a plane within a semi-enclosed space at 1000 Hz in Example 11, as well as the reconstruction error diagram. Detailed Implementation

[0044] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0045] Example 1:

[0046] A method for reverberating sound field reconstruction using a rigid spherical microphone array includes the following steps:

[0047] Step 1) Establish a mixed wave model of the sound pressure signal acquired by the rigid spherical microphone array;

[0048] Step 2) Solve the hybrid wave model to obtain the intensities of the spherical wave equivalent source and the plane wave equivalent source;

[0049] Step 3) Reconstruct the reverberant sound field based on the intensity of the spherical wave equivalent source and the plane wave equivalent source.

[0050] Example 2:

[0051] The method for reverberating sound field reconstruction of rigid spherical microphone array is the same as that in Example 1. Further, in step 1), a near-field spherical wave equivalent source model and a far-field plane wave equivalent source model are used to simulate the direct sound and reflected sound components in the sound field, and a mixed wave model of the sound pressure signal collected by the rigid spherical microphone array is constructed.

[0052] Example 3:

[0053] The method for reverberating sound field reconstruction of a rigid spherical microphone array is the same as any one of Examples 1-2. Further, the near-field spherical wave equivalent source model and the far-field plane wave equivalent source model are shown below:

[0054] (1)

[0055] (2)

[0056] In the formula, and Positions The direct sound component and the reflected sound component of the sound field. It is the angular frequency. and For the first The location of the first spherical wave equivalent source and the first The direction of the equivalent source of a plane wave L and L represent the number of equivalent sources for spherical waves and plane waves, respectively. and The first The spherical wave equivalent source and the first Equivalent source intensity of a plane wave.

[0057] Example 4:

[0058] The method for reverberating sound field reconstruction of rigid spherical microphone arrays is the same as any one of embodiments 1-3, and further, the... Equivalent source and location of spherical waves Transfer function between , No. Equivalent source and location of a plane wave Transfer function between As shown below:

[0059] (3)

[0060] (4)

[0061] In the formula, The imaginary unit, For direction nth order m-th spherical harmonic function on Let be the nth order spherical Bessel function. For the nth order sphere of the second kind, the Hankel function is... and They are respectively and The first derivative, Let be the wave number, and the superscript "*" indicates complex conjugate. 'a' is the radius of the rigid sphere.

[0062] Example 5:

[0063] The method for reverberating sound field reconstruction using a rigid spherical microphone array is the same as any one of Examples 1-4. Further, the mixed wave model of the sound pressure signal acquired by the rigid spherical microphone array is shown below:

[0064] (5)

[0065] In the formula, This represents the received sound pressure level of a rigid spherical microphone array. For the first The microphone position, Q is the number of microphones, and the superscript "" indicates the microphone position. T "Represents transposition, and These are the equivalent source intensity vectors for spherical waves and plane waves. and For the transfer function matrix, , .

[0066] Example 6:

[0067] The method for reverberating sound field reconstruction of a rigid spherical microphone array is the same as any one of embodiments 1-5. Further, in step 2), the steps for solving the mixed wave model include:

[0068] Step 2.1) Transform the acoustic pressure signal hybrid wave model to obtain the optimized model, i.e.:

[0069] (6)

[0070] In the formula, express Norm, and For regularization parameters;

[0071] Step 2.2) Introduce additional variables into the optimization model and This yields an optimization model with additional variables, namely:

[0072] (7)

[0073] Step 2.3) Transform the optimization model with additional variables into an unconstrained optimization problem, that is:

[0074] (8)

[0075] In the formula, and Let Lagrange multiplier vector be the vector. Indicates taking the real part, superscript " H " indicates complex conjugate transpose. , For penalty parameters;

[0076] Step 2.4) Let and The unconstrained optimization problem is transformed to obtain the transformed unconstrained optimization problem, namely:

[0077] (9)

[0078] Step 2.5) Solve the transformed unconstrained optimization problem to obtain the intensities of the spherical wave equivalent source and the plane wave equivalent source.

[0079] Example 7:

[0080] The method for reverberating sound field reconstruction of rigid spherical microphone array is the same as any one of embodiments 1-6. Further, in step 2.5), the transformed unconstrained optimization problem is solved iteratively by alternating direction multiplier algorithm until the iteration termination condition is met or the maximum number of iterations is reached.

[0081] Example 8:

[0082] The method for reverberating sound field reconstruction of a rigid spherical microphone array is the same as any one of Examples 1-7, except that the iteration termination condition is... and .

[0083] Example 9:

[0084] The method for reverberating sound field reconstruction of a rigid spherical microphone array is the same as any one of embodiments 1-8, further, in step 2.5), in the... The results of the iterative solution in this iteration are shown below:

[0085] (10)

[0086] in, This is a soft threshold operator.

[0087] Example 10:

[0088] The method for reconstructing the reverberant sound field of a rigid spherical microphone array is the same as any one of embodiments 1-9. Further, in step 3), the reconstructed reverberant sound field is as follows:

[0089] (11)

[0090] In the formula, V reconstruction locations The sound pressure vector at that location; ; and The dimensions are respectively and Matrix; , , , ; and The intensities of the spherical wave equivalent source and the plane wave equivalent source are given.

[0091] Example 11:

[0092] The method for reverberating sound field reconstruction of rigid spherical microphone array includes the following steps:

[0093] Step 1: Establish a hybrid wave model

[0094] Step 101: Model the direct sound component of the sound field using the spherical wave equivalent source model. (1)

[0095] in, For position The direct sound component of the sound field. It is the angular frequency. For the first The location of the equivalent source of a spherical wave The number of equivalent sources for spherical waves. For the equivalent source intensity of spherical waves, For the first Equivalent source and location of spherical waves The transfer function between them

[0096] (2)

[0097] The imaginary unit, For direction nth order m-th spherical harmonic function on Let be the nth order spherical Bessel function. For the nth order sphere of the second kind, the Hankel function is... and They are their first derivatives, The wave number is indicated by the superscript "*", which indicates complex conjugate.

[0098] Step 102: Model the sound field reflection components using a plane wave equivalent source model.

[0099] (3)

[0100] in, For position The reflected sound components of the sound field. For the first The directions of the equivalent plane wave sources, where L is the number of equivalent plane wave sources. The equivalent source intensity of the plane wave, For the first Equivalent source and location of a plane wave The transfer function between them

[0101] (4)

[0102] Step 103: Construct a hybrid wave model

[0103] Based on formulas (1) and (3), a hybrid wave model of the sound pressure signal acquired by the rigid spherical microphone array is constructed.

[0104] (5)

[0105] in, This represents the received sound pressure level of a rigid sphere microphone array. For the first The microphone position, Q is the number of microphones, and the superscript "" indicates the microphone position. T "Represents transposition, and These are the equivalent source intensity vectors for spherical waves and plane waves. and For the transfer function matrix, , .

[0106] Step 2: Solve the hybrid wave model to obtain the equivalent source intensity.

[0107] Step 201: Based on the sparsity assumption, construct the optimization problem.

[0108] Assuming the number of sound sources is much smaller than the number of equivalent sources, i.e., the distribution of equivalent sources is sparse, and Most elements approach zero. For estimation... and Equation (5) can be transformed into:

[0109] (6)

[0110] In the formula, express Norm, and This is the regularization parameter.

[0111] Step 202: Solve the mixed wave model using the alternating direction multiplier algorithm to obtain the equivalent source intensity.

[0112] Introducing additional variables and Equation (6) is transformed into:

[0113] (7)

[0114] Transform equation (7) into an unconstrained optimization problem:

[0115] (8)

[0116] In the formula, and Let Lagrange multiplier vector be the vector. Indicates taking the real part, superscript " H " indicates complex conjugate transpose. , This is the penalty parameter. Let... and Then equation (8) is transformed into:

[0117] (9)

[0118] Equation (9) is solved iteratively, and at the th... In each iteration, taking the partial derivative with respect to each component and setting it to 0, we obtain:

[0119] (10)

[0120] in, This is a soft threshold operator. The initial value for each component is set to the zero vector of its corresponding dimension, and the maximum number of iterations is set to 1000. When two consecutive iterations... and The relative change between and The iteration terminates when the maximum number of iterations is reached.

[0121] Step 3: Reconstruct the reverberant sound field

[0122] Obtained by iterative solution and Perform sound field reconstruction:

[0123] (11)

[0124] In the formula, V reconstruction locations ( The sound pressure vector at point () and The dimensions are respectively and The matrix, and the matrix in equation (5) and If there are similar forms, simply... Replace with You can get it immediately.

[0125] Simulation test

[0126] To verify the accuracy of this invention, a sound field reconstruction simulation was performed. The specific process is as follows:

[0127] 1. Construct a semi-enclosed space, determine the boundary conditions, determine the array position, assume a virtual sound source, and use the mirror source method to calculate the theoretical sound pressure generated by the sound source in the area to be reconstructed, in order to evaluate the accuracy of the present invention; then, determine the equivalent source model.

[0128] 2. Construct a hybrid wave model based on step 1;

[0129] 3. Obtain the equivalent source strength according to step 2;

[0130] 4. Reconstruct the sound field according to step 3;

[0131] The simulation settings are as follows: To simulate a semi-enclosed rectangular space, an infinitely long rectangular pipe space is set up: Set free boundary conditions in the direction, that is, in space... The positive and negative directions are infinitely long. and In direction, , , , A hard boundary condition is set at the location, with a sound absorption coefficient of . The sound source is located at At that location, the sound source intensity is 94 dB (reference). Equivalent source model such as Figure 1 As shown, the array center is located at the origin of the coordinate system, and the array radius is 0.0975 m. The equivalent source surface of the plane wave is set as a sphere 1 m away from the array center, and spaced at intervals... , Discretize this equivalent source surface; the spherical wave equivalent source surface is located at a distance from the array center. The position and size are , , and The plane, with grid spacing set to Reconstruction area It is located in A square passive region centered on the spherical array in the plane, with dimensions of [missing information]. .

[0132] Simulation results:

[0133] Figure 2 The reconstructed region at 1000 Hz was shown. The real part plots of the theoretical sound pressure and the reconstructed sound pressure, as well as the reconstruction error plot, are shown. The real part results of the reconstructed sound pressure are in excellent agreement with the theoretical results. Correspondingly, in the reconstruction error plot, the area with an error of less than 10%, i.e., the bright area, accounts for as much as 80%, indicating that the present invention has a large reconstruction range and high reconstruction accuracy when reconstructing the reverberant sound field.

Claims

1. A method for reconstructing the reverberant sound field of a rigid spherical microphone array, characterized in that, Includes the following steps: Step 1) Establish a mixed wave model of the sound pressure signal acquired by the rigid spherical microphone array; Step 2) Solve the hybrid wave model to obtain the intensities of the spherical wave equivalent source and the plane wave equivalent source; Step 3) Reconstruct the reverberant sound field based on the intensity of the spherical wave equivalent source and the plane wave equivalent source.

2. The method for reconstructing the reverberant sound field of a rigid spherical microphone array according to claim 1, characterized in that, A hybrid wave model of the sound pressure signal collected by a rigid spherical microphone array is constructed by simulating the direct and reflected sound components in the sound field using a near-field spherical wave equivalent source model and a far-field plane wave equivalent source model.

3. The method for reconstructing the reverberant sound field of a rigid spherical microphone array according to claim 2, characterized in that, The equivalent source models for near-field spherical waves and far-field plane waves are shown below: (1) (2) In the formula, and Positions The direct sound component and the reflected sound component of the sound field. It is the angular frequency. and For the first The location of the first spherical wave equivalent source and the first The direction of the equivalent source of a plane wave L and L represent the number of equivalent sources for spherical waves and plane waves, respectively. and The first The spherical wave equivalent source and the first Equivalent source intensity of a plane wave.

4. The method for reconstructing the reverberant sound field of a rigid spherical microphone array according to claim 3, characterized in that, No. Equivalent source and location of spherical waves Transfer function between , No. Equivalent source and location of a plane wave Transfer function between As shown below: (3) (4) In the formula, The imaginary unit, For direction nth order m-th spherical harmonic function on Let be the nth order spherical Bessel function. For the nth order sphere of the second kind, the Hankel function is... and They are respectively and The first derivative, denoted by wave number, with the superscript "*" indicating complex conjugate; a is the radius of the rigid sphere.

5. The method for reconstructing the reverberant sound field of a rigid spherical microphone array according to claim 2, characterized in that, The mixed wave model of the sound pressure signal acquired by the rigid spherical microphone array is shown below: (5) In the formula, This represents the received sound pressure level of a rigid spherical microphone array. For the first The microphone position, Q is the number of microphones, and the superscript "" indicates the microphone position. T "Represents transposition, and Let these be the equivalent source intensity vectors for spherical waves and plane waves. and For the transfer function matrix, , .

6. The method for reconstructing the reverberant sound field of a rigid spherical microphone array according to claim 1, characterized in that, Step 2) involves solving the mixed-wave model, including the following steps: Step 2.1) Transform the acoustic pressure signal mixed wave model to obtain the optimized model: (6) In the formula, express Norm, and For regularization parameters; Step 2.2) Introduce additional variables into the optimization model and This yields an optimization model with additional variables, namely: (7) Step 2.3) Transform the optimization model with additional variables into an unconstrained optimization problem, that is: (8) In the formula, and Let Lagrange multiplier vector be the vector. Indicates taking the real part, superscript " H " indicates complex conjugate transpose. , For penalty parameters; Step 2.4) Let and The unconstrained optimization problem is transformed to obtain the transformed unconstrained optimization problem, namely: (9) Step 2.5) Solve the transformed unconstrained optimization problem to obtain the intensities of the spherical wave equivalent source and the plane wave equivalent source.

7. The method for reconstructing the reverberant sound field of a rigid spherical microphone array according to claim 6, characterized in that, In step 2.5), the transformed unconstrained optimization problem is solved iteratively using the alternating direction multiplier algorithm until the iteration termination condition is met or the maximum number of iterations is reached.

8. The method for reconstructing the reverberant sound field of a rigid spherical microphone array according to claim 7, characterized in that, The iteration termination condition is and .

9. The method for reconstructing the reverberant sound field of a rigid spherical microphone array according to claim 7, characterized in that, In step 2.5), in the first The results of the iterative solution in this iteration are shown below: (10) in, This is a soft threshold operator.

10. The method for reconstructing the reverberant sound field of a rigid spherical microphone array according to claim 1, characterized in that, In step 3), the reconstructed reverberant sound field is shown below: (11) In the formula, V reconstruction locations The sound pressure vector at that location; ; and The dimensions are respectively and Matrix; , , , ; and The intensities of the spherical wave equivalent source and the plane wave equivalent source are given.

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