A sound field recording method and system

Abstract

The application discloses a kind of sound field recording method and system, the method includes: the sound field in space is represented as the superposition of different direction plane wave, and introduce the weight function representing the importance of different direction plane wave, construct the weighted optimization model about modal decomposition base function in sound field recording;The weighted optimization model about modal decomposition base function in sound field recording is solved, and the optimal base function is obtained;Based on optimal base function, and considering plane wave distribution, the best encoding matrix of microphone is solved;The sound pressure signal at each microphone is measured, and the optimal modal coefficient estimation is carried out in combination with the optimal encoding matrix, and the sound field to be recorded is described using optimal modal coefficient estimation value and the optimal base function.The application obtains the optimal base function and the optimal encoding matrix that make the sound field recording error minimum by using the prior knowledge of sound wave distribution and direction importance, so as to minimize the error of direction-dependent sound field recording.

Description

Technical Field

[0001] This invention belongs to the field of sound field recording technology, and relates to a sound field recording method and system. Background Technology

[0002] The purpose of sound field recording is to capture and preserve sound field information of a specific region. Typically, the recorded sound field is decomposed into a superposition of modes using modal decomposition methods. One advantage of modal decomposition is that it makes the recorded sound field independent of the microphone setup. In three-dimensional space, spherical harmonic (SH) functions are a common choice for modal decomposition, and spherical microphone arrays are often used to obtain the coefficients of spherical harmonic functions. Modal decomposition based on SH functions is also known as higher-order ambisonics (HOA).

[0003] A key characteristic of mode decomposition based on the SH function is direction independence, meaning that SH basis mode decomposition treats sounds from different directions equally. However, in many practical applications, sound field recording problems are direction-dependent. For example, the directional distribution of sound waves emitted by a sound source may not be uniform in reality, and human voice localization resolution is higher when the sound source is close to the horizontal plane.

[0004] To adapt to direction-dependent sound field recording, researchers have proposed several improved direction-dependent mode decomposition (HOA) methods. However, these methods either have limited application scenarios or are not the least error-prone. For example, mixed-order Ambisonics improves horizontal performance by selecting an appropriate subset of SH functions and achieves non-uniform spatial resolution encoding of HOA based on spatial distortion; however, both of these approaches require empirical selection of certain parameters. Using spherical sector harmonics or spherical Slepian functions as basis functions requires the sound direction to be within a finite range. Spherical segment harmonics and spherical fraction harmonics require specific boundary conditions in the recording environment; they are only least error-prone when the actual recording environment meets these specific boundary conditions. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a sound field recording method and system. By utilizing prior knowledge of the importance of sound wave distribution and direction, the optimal basis function and optimal encoding matrix that minimize the sound field recording error are obtained, thereby minimizing the error in direction-dependent sound field recording.

[0006] The present invention adopts the following technical solution.

[0007] A sound field recording method, the method comprising the following steps: Step 1: Represent the sound field in space as the superposition of plane waves in different directions, and introduce weight functions representing the importance of plane waves in different directions to construct a weighted optimization model of the modal decomposition basis functions in the sound field record; Step 2: Solve the weighted optimization model of the modal decomposition basis functions in the sound field record to obtain the optimal basis functions; Step 3: Based on the optimal basis function obtained in Step 2, and considering the plane wave distribution, find the optimal coding matrix for the microphone; Step 4: Measure the sound pressure signal at each microphone, and estimate the optimal mode coefficients using the optimal coding matrix. Use the estimated optimal mode coefficients and the optimal basis function to describe the sound field to be recorded.

[0008] Preferably, in step 1, the weighted optimization model of the modal decomposition basis functions in the constructed sound field record is as follows:

[0009]

[0010] in, Let be the expected function. constraint; For basis function vectors Using optimal mode coefficients Weighted error for sound field recording; The complex amplitude of a plane wave During mode decomposition M Composed of basis functions The basis function vector, which in The direction value is ; A weight function greater than 0 represents The importance of directional plane waves; Zenith angle, It is the azimuth angle; H is the identity matrix; H is the conjugate transpose of the matrix. For a unit sphere Integrate the area on top.

[0011] Preferably, the weighted error is:

[0012] in, The complex amplitude of a plane wave in a specific direction; for . conjugate.

[0013] Preferably, the optimal modal coefficients are:

[0014] Preferably, in step 2, the optimal basis function obtained is:

[0015] in, for The optimal basis functions for the complex amplitude mode decomposition of a directional plane wave; ; for Discretization The vector formed by the SH functions, The number of SH functions; for ;

[0016] It is an orthogonal array. It is an orthogonal array; It is the set of complex numbers.

[0017] Preferably, in step 3, the microphone optimal coding matrix The solution function is:

[0018] in, The trace of the matrix; It is the transfer function matrix from the modality to the microphone sound pressure; for The coefficients corresponding to the discretization satisfy ; for Discretization A vector formed by the SH functions; for ; H is the identity matrix; H is the conjugate transpose of the matrix. As an intermediate variable; The standard deviation of the noise; for The covariance matrix, Let be the expected function. for The coefficients corresponding to discretization; Complex amplitude of a plane wave in the direction of motion. Zenith angle, This is the azimuth angle.

[0019] Preferably, in step 3, the obtained microphone optimal coding matrix is... for:

[0020] in, ; As an intermediate variable; The standard deviation of the noise; for The covariance matrix, Let be the expected function. for The coefficients corresponding to discretization, Complex amplitude of a plane wave in the direction of motion. Zenith angle, It is the azimuth angle; H is the identity matrix; H is the conjugate transpose of the matrix. It is the transfer function matrix from the modality to the microphone sound pressure.

[0021] Preferably, in step 4, the sound pressure signal at each microphone is... With the optimal encoding matrix Multiplication yields the optimal modal coefficient estimate. :

[0022] in, ; As an intermediate variable; The standard deviation of the noise; for The covariance matrix, Let be the expected function. for The coefficients corresponding to discretization, Complex amplitude of a plane wave in the direction of motion. Zenith angle, It is the azimuth angle; H is the identity matrix; H is the conjugate transpose of the matrix. It is the transfer function matrix from the modality to the microphone sound pressure.

[0023] Preferably, in step 4, the optimal modal coefficient estimate is... and the optimal basis function Multiply to describe the sound field that needs to be recorded:

[0024] in, For from The complex amplitude of a plane wave in a given direction represents the amplitude of a plane wave in space. Directional sound field; Zenith angle, It is the azimuth angle; ; As an intermediate variable; The standard deviation of the noise; for The covariance matrix, Let be the expected function. for The coefficients corresponding to discretization, Complex amplitude of a plane wave in the direction of motion. Zenith angle, It is the azimuth angle; H is the identity matrix; H is the conjugate transpose of the matrix. It is the transfer function matrix from the modality to the microphone sound pressure.

[0025] Preferably, intermediate variables for:

[0026] in, A weight function greater than 0 represents The importance of directional plane waves; For a unit sphere Integrate the area on top; for Discretization A vector formed by the SH functions; for ; H is the conjugate transpose of the matrix.

[0027] A sound field recording system, comprising: The model building module is used to represent the sound field in space as the superposition of plane waves in different directions, and introduces weight functions representing the importance of plane waves in different directions to build a weighted optimization model of the modal decomposition basis functions in the sound field record; The module solver is used to solve the weighted optimization model of modal decomposition basis functions in the sound field record to obtain the optimal basis functions; The matrix solving module is used to find the optimal coding matrix of the microphone based on the optimal basis function and taking into account the plane wave distribution. The sound field recording module is used to measure the sound pressure signal at each microphone, combine it with the optimal encoding matrix to estimate the optimal mode coefficients, and use the estimated optimal mode coefficients and the optimal basis function to describe the sound field to be recorded.

[0028] A terminal includes a processor and a storage medium; the storage medium is used to store instructions. The processor is configured to operate according to the instructions to execute the steps of the method.

[0029] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the method.

[0030] The beneficial effects of this invention are compared with those of the prior art: This invention utilizes prior knowledge of the importance of sound wave distribution and direction to obtain the basis functions and encoding matrix that minimize the error in sound field recording, thereby minimizing the error in direction-dependent sound field recording. Specifically: This invention represents the sound field as a superposition of plane waves. Considering the importance of sound wave distribution and direction, the modal decomposition problem of direction-dependent sound field recording is written as a weighted least squares problem of plane wave amplitude error. The optimal basis function and optimal encoding matrix are solved step by step to describe the sound field to be recorded. It utilizes prior knowledge of the importance of sound wave distribution and direction, avoiding the selection of parameters based on experience, and the error of sound field recording is lower. Furthermore, this problem does not restrict the sound direction or the boundary conditions of the actual recording environment. Therefore, the sound direction does not need to be within a limited range, nor does the actual recording environment need to meet certain specific boundary conditions. Attached Figure Description

[0031] Figure 1 This is a flowchart of a sound field recording method according to the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0033] Embodiment 1 of the present invention provides a sound field recording method. In a preferred but non-limiting embodiment of the present invention, such as... Figure 1 As shown, the method includes the following steps: Step 1: Represent the sound field in space as the superposition of plane waves in different directions, and introduce weight functions representing the importance of plane waves in different directions to construct a weighted optimization model of the modal decomposition basis functions in the sound field record; More preferably, the sound field in space can be represented as the superposition of plane waves in different directions, so the sound field in space can be represented by the complex amplitude of plane waves in different directions.

[0034] definition For from Complex amplitude of a plane wave in the direction of motion. Zenith angle, This refers to the azimuth angle. Generally... It is approximately decomposed into a superposition of a set of modes:

[0035] in for A column vector composed of basis functions. Let H be the number of basis functions, and H be the conjugate transpose of the matrix. It is a column vector consisting of modal coefficients.

[0036] Define a weight function greater than 0 Representing the importance of plane waves in different directions, the cost function, which is the error in sound field recording, can be defined as... and The weighted integral of the error between them, i.e.

[0037] in Represents a unit sphere. To perform area integrals on a unit sphere.

[0038] According to equation (2), the modal coefficients in the sound field record The weighted optimization problem can be written as

[0039] For the optimization problem described in equation (3), it can be solved by letting right Solve for the partial derivatives that are equal to 0.

[0040] make right When the partial derivative is equal to 0, the optimal value can be obtained. ,Right now The following equation is satisfied:

[0041] Furthermore, constraints For weighted orthogonal function vectors, i.e.

[0042] in Let be an identity matrix. Using this constraint, equation (4) can be simplified to:

[0043] The theoretically optimal modal coefficients are obtained from equation (6); Substituting (6) into (2), the error (cost function) of mode decomposition can be written as:

[0044] in, express The conjugate; For basis function vectors Using optimal mode coefficients Weighted error for sound field recording; The complex amplitude of a plane wave During mode decomposition M Composed of basis functions The basis function vector, which in The direction value is , The number of basis functions; For optimal modal coefficients, Let be the complex amplitude of the plane wave.

[0045] In order to find the answer for all possible... Basis functions with small errors According to equations (5) and (7), the acoustic field record contains information about the basis functions. The weighted optimization problem can be written in the form of taking the expectation of the cost function, i.e.:

[0046]

[0047] in This indicates the expectation of a statistic. This indicates that the following equation represents the constraints of this optimization problem.

[0048] Step 2: Solve the weighted optimization model of the modal decomposition basis functions in the sound field record to obtain the optimal basis functions; More preferably, the SH functions form an orthogonal complete basis on the unit sphere, therefore for any function defined on the unit sphere... , can be represented as

[0049] in yes The vector formed by the SH functions, It is the number of SH functions. yes The corresponding coefficients form a column vector. Equation (9) shows that a continuous function can be approximated by a set of discrete coefficients.

[0050] Due to basis functions Each element in the equation is a continuous function, making equation (8) difficult to solve directly. To solve the optimization problem in equation (8), it is first discretized.

[0051] Similar to (9), and It can be approximated as

[0052]

[0053] in and That is the corresponding coefficient.

[0054] Substituting equations (10) and (11) into equation (6), the optimal... It can be represented as

[0055] in

[0056] Substituting equations (7), (10), and (12) into equation (8) yields the weighted optimization problem for the coefficient T.

[0057]

[0058] Assuming the covariance of the plane wave amplitude is known prior, the sound wave distribution is described by the covariance of the plane wave amplitude. According to equation (11), the covariance of the plane wave amplitude can be written as:

[0059] definition By utilizing the orthogonality of the SH function, we can obtain

[0060] Utilizing the cyclic property of the trace of a matrix, i.e., tr(AB) = tr(BA), equation (14) can be further written as

[0061]

[0062] in Let A be the trace of the matrix. Since it is assumed that the covariance of the plane wave amplitude is known a priori, A can be calculated using equation (16). To solve the optimization problem of equation (17), the formula for eigenvalue decomposition of a matrix can be used to obtain A. Diagonalization

[0063] in satisfy ,

[0064] for middle Part of, namely It is a diagonal matrix with diagonal elements greater than 0. yes The rank. According to The diagonalized representation of , then It can be diagonalized as:

[0065] satisfy , It is a diagonal matrix with diagonal elements greater than or equal to 0. Therefore, the optimization problem in equation (17) becomes the standard form of the optimization problem corresponding to principal component analysis.

[0066]

[0067] in

[0068] Therefore, we can solve it.

[0069] According to equations (22) and (23), then The minimum norm solution is

[0070] Therefore, according to equation (10), the optimal basis function is... for

[0071] in, for The optimal basis functions for the complex amplitude mode decomposition of a directional plane wave; As an intermediate variable; Diagonalization yields an orthogonal matrix V and a diagonal matrix with diagonal elements greater than or equal to zero. . It is an orthogonal matrix that satisfies ; for middle The part. It is a diagonal matrix with diagonal elements greater than 0. It is an intermediate variable Rank. for Discretization The vector formed by the SH functions, The number of SH functions; for ;Will Diagonalization yields an orthogonal matrix. . for The covariance matrix, Let be the expected function. for The coefficients corresponding to discretization; It is an orthogonal matrix that satisfies ; H is the conjugate transpose of the matrix; It is the set of complex numbers.

[0072] but It can be approximated as

[0073] Step 3: Based on the optimal basis function obtained in Step 2, and considering the plane wave distribution, find the optimal coding matrix for the microphone; More preferably, for a sphere microphone array, assuming the array contains KIf there are 1 microphone, then the sound pressure signal received by each microphone is:

[0074] in A vector composed of sound pressure signals received by the microphone. The vector formed by combining the noise received by the microphone. It is the transfer function matrix from the modality to the microphone sound pressure.

[0075] It is generally assumed that noise and signal are uncorrelated, and that the covariance matrix of noise is... When estimating modal coefficients using a spherical microphone array, the modal coefficients can be obtained from the sound pressure levels measured by the microphones, i.e.

[0076] Let be the encoding matrix. The optimal encoding matrix can be obtained by solving the following optimization problem.

[0077]

[0078] Substituting equations (11), (25), (27), and (28) into equation (29) yields...

[0079] in, The trace of the matrix; It is the transfer function matrix from the modality to the microphone sound pressure; for The coefficients corresponding to the discretization satisfy ; for Discretization A vector formed by the SH functions; for ,for Complex amplitude mode decomposition of directional plane waves A column vector composed of basis functions; H is the identity matrix; H is the conjugate transpose of the matrix. As an intermediate variable; The standard deviation of the noise; for The covariance matrix, Let be the expected function. for The coefficients corresponding to discretization; Complex amplitude of a plane wave in the direction of motion. Zenith angle, This is the azimuth angle.

[0080] By setting the partial derivative of the cost function in equation (30) with respect to E to 0, the optimal coding matrix can be obtained as follows:

[0081] Step 4: Measure the sound pressure signal at each microphone, and estimate the optimal mode coefficients using the optimal coding matrix. Use the estimated optimal mode coefficients and the optimal basis function to describe the sound field to be recorded.

[0082] More preferably, based on equation (28), the sound pressure signal at each microphone is measured using a spherical microphone array. Then the corresponding optimal modal coefficient estimate is:

[0083] Based on equation (26), this modal coefficient can describe the sound field that needs to be recorded, i.e.:

[0084] The beneficial effects of this invention are compared with those of the prior art: This invention utilizes prior knowledge of the importance of sound wave distribution and direction to obtain the basis functions and encoding matrix that minimize the error in sound field recording, thereby minimizing the error in direction-dependent sound field recording. Specifically: This invention represents the sound field as a superposition of plane waves. Considering the importance of sound wave distribution and direction, the modal decomposition problem of direction-dependent sound field recording is written as a weighted least squares optimization problem of plane wave amplitude error. The theoretically optimal modal coefficients, optimal basis functions, and optimal encoding matrix are solved step by step to describe the sound field to be recorded. It utilizes prior knowledge of the importance of sound wave distribution and direction, avoiding the selection of parameters based on experience, and the error of sound field recording is lower. Furthermore, this optimization problem does not restrict the sound direction or the boundary conditions of the actual recording environment. Therefore, the sound direction does not need to be within a limited range, nor does the actual recording environment need to meet certain specific boundary conditions.

[0085] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0086] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0087] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0088] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A sound field recording method, characterized in that: The method includes the following steps: Step 1: Represent the sound field in space as the superposition of plane waves in different directions, and introduce weight functions representing the importance of plane waves in different directions to construct a weighted optimization model of the modal decomposition basis functions in the sound field record; The weighted optimization model for the modal decomposition basis functions in the constructed sound field record is as follows: in, Let be the expected function. Indicates constraints; For basis function vectors Using optimal mode coefficients Weighted error for sound field recording; The complex amplitude of a plane wave During mode decomposition M Composed of basis functions The basis function vector, which in The direction value is ; A weight function greater than 0 represents The importance of directional plane waves; Zenith angle, It is the azimuth angle; H is the identity matrix; H is the conjugate transpose of the matrix. For a unit sphere Integrate the area on top; Step 2: Solve the weighted optimization model of the modal decomposition basis functions in the sound field record to obtain the optimal basis functions; Step 3: Based on the optimal basis function obtained in Step 2, and considering the plane wave distribution, find the optimal coding matrix for the microphone; Step 4: Measure the sound pressure signal at each microphone, combine it with the optimal coding matrix to estimate the optimal mode coefficients, and use the optimal mode coefficient estimates and the optimal basis functions to describe the sound field to be recorded.

2. The sound field recording method according to claim 1, characterized in that: The weighted error is: in, For from The complex amplitude of a plane wave in a specific direction; for . conjugate.

3. The sound field recording method according to claim 2, characterized in that: The optimal modal coefficients are: 。 4. The sound field recording method according to claim 1, characterized in that: In step 2, the optimal basis function obtained is: in, for The optimal basis functions for the complex amplitude mode decomposition of a directional plane wave; It is a diagonal matrix with diagonal elements greater than 0. It is an intermediate variable rank; for Discretization The vector formed by the SH functions, The number of SH functions; basis function vector exist The value of the direction; Zenith angle, It is the azimuth angle; It is an orthogonal array. It is an orthogonal array; It is the set of complex numbers.

5. The sound field recording method according to claim 1, characterized in that: In step 3, the plane wave distribution is described by the covariance of the plane wave amplitude, and the optimal encoding matrix of the microphone is determined. The solution function is: in, The trace of the matrix; It is the transfer function matrix from the modality to the microphone sound pressure; for The coefficients corresponding to the discretization satisfy ; Let be the covariance decomposition parameter of the plane wave amplitude, representing Discretization A vector formed by the SH functions; basis function vector exist The value of the direction; H is the identity matrix; H is the conjugate transpose of the matrix. As an intermediate variable; The standard deviation of the noise; Let be the covariance decomposition parameter of the plane wave amplitude, representing The covariance matrix, Let be the expected function. for The coefficients corresponding to discretization; For from Complex amplitude of a plane wave in the direction of motion. Zenith angle, This is the azimuth angle.

6. The sound field recording method according to claim 1, characterized in that: In step 3, the optimal microphone encoding matrix is ​​obtained. for: in, Optimal basis function The coefficients corresponding to discretization; As an intermediate variable; The standard deviation of the noise; for The covariance matrix, Let be the expected function. for The coefficients corresponding to discretization, For from Complex amplitude of a plane wave in the direction of motion. Zenith angle, It is the azimuth angle; H is the identity matrix; H is the conjugate transpose of the matrix. It is the transfer function matrix from the modality to the microphone sound pressure.

7. The sound field recording method according to claim 1, characterized in that: In step 4, the sound pressure signals at each microphone are... With the best encoding matrix Multiplication yields the optimal modal coefficient estimate. : in, Optimal basis function The coefficients corresponding to discretization; As an intermediate variable; The standard deviation of the noise; for The covariance matrix, Let be the expected function. for The coefficients corresponding to discretization, For from Complex amplitude of a plane wave in the direction of motion. Zenith angle, It is the azimuth angle; H is the identity matrix; H is the conjugate transpose of the matrix. It is the transfer function matrix from the modality to the microphone sound pressure.

8. The sound field recording method according to claim 1, characterized in that: In step 4, the optimal modal coefficient estimates are... and the optimal basis function Multiply to describe the sound field that needs to be recorded: in, For from The complex amplitude of a plane wave in a given direction represents the amplitude of a plane wave in space. Directional sound field; Zenith angle, It is the azimuth angle; Optimal basis function The coefficients corresponding to discretization; As an intermediate variable; The standard deviation of the noise; for The covariance matrix, Let be the expected function. for The coefficients corresponding to discretization, For from Complex amplitude of a plane wave in the direction of motion. Zenith angle, It is the azimuth angle; H is the identity matrix; H is the conjugate transpose of the matrix. It is the transfer function matrix from the modality to the microphone sound pressure.

9. A sound field recording method according to any one of claims 4-8, characterized in that: intermediate variables for: in, A weight function greater than 0 represents The importance of directional plane waves; For a unit sphere Integrate the area on top; for Discretization A vector formed by the SH functions; basis function vector exist The value of the direction; H is the conjugate transpose of the matrix.

10. A sound field recording system, utilizing the method according to any one of claims 1-9, characterized in that: The system includes: The model building module is used to represent the sound field in space as the superposition of plane waves in different directions, and introduces weight functions representing the importance of plane waves in different directions to build a weighted optimization model of the modal decomposition basis functions in the sound field record; The module solver is used to solve the weighted optimization model of modal decomposition basis functions in the sound field record to obtain the optimal basis functions; The matrix solving module is used to find the optimal coding matrix of the microphone based on the optimal basis function and taking into account the plane wave distribution. The sound field recording module is used to measure the sound pressure signal at each microphone, combine it with the optimal encoding matrix to perform optimal mode coefficient estimation, and use the optimal mode coefficient estimate and the optimal basis function to describe the sound field to be recorded.

11. A terminal, comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1-9.

12. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1-9.

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