JP2014160953A - Acoustic field plane wave spreading method, device and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an acoustic field plane wave spreading technology capable of spreading a plane wave even if a microphone array is cylindrical.SOLUTION: A spread angle storage section 2 stores a discretization angle (θ,φ)(d=1, ..., D) with D as a predetermined positive integer and a plane wave spread section 3 uses a sound pressure signal P(k) generated on the basis of signals collected by a microphone to compute a plane wave spread signal P(k) corresponding to each discretization angle (θ,φ) read from the spread angle storage section while considering a change of a transfer route caused by baffling a rigid body.

Description

  The present invention relates to a technique for collecting a sound signal with a microphone installed in a certain sound field and expanding the sound signal into a plane wave.

  The plane wave expansion of a sound field is a technique that can be used for various applications such as sound field analysis, sound field coding, and sound field reproduction. In the sound field reproduction technology, if the desired sound field is assumed to be a superposition of plane waves, the speaker array drive signal for reproducing each plane wave is calculated, and the sum is output as a drive signal. Reproduction is possible. As a sound field reproduction technique, for example, a technique described in Non-Patent Document 1 is known.

Shoichi Koyama, 3 others, “Spatial-Time Frequency Domain Signal Conversion Method for Sound Field Recording and Reproduction”, Proceedings of the Acoustical Society of Japan, September 2011, P. 635-636

  In the prior art, it was possible to develop a plane wave using a plane, straight line, sphere, and circular array, but plane waves could not be developed when the microphone array had a cylindrical shape.

  An object of the present invention is to provide a sound field plane wave expanding method, apparatus, and program capable of expanding plane waves even if the microphone array has a cylindrical shape.

In order to solve the above-described problem, a sound field plane wave expansion method according to an aspect of the present invention is based on two pieces of a radius R _cyl centering on the axis of a cylindrical rigid baffle and having the circumferential direction of the baffle as a circumferential direction. Assume that at least two microphones are arranged in each of the above circles, ω is a frequency, c is a sound velocity, k = ω / c, and D is a predetermined positive integer in the development angle storage unit. , The discretization angle (θ _{dir, d} , φ _{dir, d} ) (d = 1,..., D) is stored, and the sound pressure signal P _mic generated based on the signal collected by the microphone is _{recorded. , ab} (k), the plane wave expansion unit uses the plane wave expansion signal P _{dir, d} (k) corresponding to each discretization angle (θ _{dir, d} , φ _{dir, d} ) read from the expansion angle storage unit. Has a plane wave expansion step in which the change of the transmission path due to the rigid baffle is taken into consideration.

  Even if the microphone array has a cylindrical shape, plane waves can be developed.

The functional block diagram which shows the example of the sound field plane wave expansion | deployment apparatus of 1st embodiment. The functional block diagram which shows the example of the sound field plane wave expansion | deployment apparatus of 2nd embodiment. The functional block diagram which shows the example of the sound field plane wave expansion | deployment apparatus of 1st embodiment. The figure for demonstrating the example of arrangement | positioning of a microphone and a speaker. The figure for demonstrating the example of arrangement | positioning of a microphone and a speaker. The flowchart which shows the example of the sound field plane wave expansion | deployment method. The figure for demonstrating the example of how to define a discretization angle.

  Embodiments of the present invention will be described below with reference to the drawings. In the following description, the symbol “˜” and the like used in the text should be described immediately above the immediately preceding character, but are described immediately after the character due to restrictions on text notation. In the formula, these symbols are written in their original positions. Further, the processing performed for each element of a vector or matrix is applied to all elements of the vector or matrix unless otherwise specified.

[First embodiment]
<Arrangement of microphone array>
The sound field plane wave expanding apparatus and method expands a sound field collected by a microphone array composed of N _a × N _b microphones arranged in a cylindrical shape with a radius R _cyl shown in FIG. 4 into a plane wave. It is.

As illustrated in FIG. 5, the microphone is fixed to a cylindrical baffle B having a radius R _b and arranged in a cylindrical shape having a radius R _cyl . The microphone is supported by, for example, a thin rod-like member that protrudes vertically from the peripheral surface of the baffle B. In the example of FIG. 5, R _cyl ≧ R _b and the microphone is disposed at a position separated from the surface of the peripheral surface of the baffle B by (R _cyl −R _b ). However, in the case of R _cyl = R _b Is highly accurate.

In other words, N _a microphones are equally spaced in each of N _b circles centering on the axis of the cylindrical rigid baffle B and having the circumferential direction of the cylindrical rigid baffle B as the circumferential direction. Be placed. N _a and N _b are predetermined integers of 2 or more. That is, by arranging two microphones in each of two circles having the circumferential direction of the baffle B as the circumferential direction, at least four microphones are arranged at a position away from the axis of the baffle B by R _cyl. .

The microphones may be arranged at any interval. That is, each of z _c and θ _c , which is an interval between adjacent microphones, can take an arbitrary value. However, plane waves can be developed with high accuracy by arranging the microphones at equal intervals, that is, by setting each of θ _c and φ _c that are the intervals between adjacent microphones to the same value.

  The microphone is arranged toward the outer side of the circumferential surface of the cylindrical rigid baffle.

The position of the microphone Ma-b is expressed as (R _cyl , θ _{mic, a} , z _{mic, b} ) (a = 1, 2,..., N _a , b = 1, 2,..., N _b ).

<Sound plane wave deployment device>
As shown in FIG. 1, the sound field plane wave expansion device includes, for example, a frequency conversion unit 1, a expansion angle storage unit 2, and a plane wave expansion unit 3, and performs processing of each step indicated by a solid line in FIG. Perform plane wave expansion.

The microphone arrays M1-1, M2-1,..., MN _a -N _b collect the sound emitted by the sound source S and generate a time domain signal. The generated signal is sent to the frequency converter 1. A signal at time t in the time domain collected by the microphone Ma-b at the position (R _cyl , θ _{mic, a} , z _{mic, b} ) is denoted as P _{mic, ab} (t).

<Frequency conversion unit 1>
The frequency converter 1 converts the signal P _{mic, ab} (t) collected by the microphone Ma-b into a frequency domain signal P _{mic, ab} (k) by Fourier transform (FIG. 6, step S1). The generated frequency domain signal P _{mic, ab} (k) is sent to the plane wave expansion unit 3. Let ω be the frequency, c be the speed of sound, and k = ω / c.

For example, the frequency domain signal P _{mic, ab} (k) is generated by short-time discrete Fourier transform. Of course, the frequency domain signal P _{mic, ab} (k) may be generated by other existing methods. Further, the frequency domain signal P _{mic, ab} (k) may be generated using a method such as overlap add. When the input signal is long or when the signal is continuously input as in real time processing, the processing is performed for each frame such as every 10 ms.

For example _{, the} frequency domain signal P _{mic, ab} (k) is defined as follows. I in the argument of the function exp is an imaginary unit.

<Development angle storage unit 2>
The development angle storage unit 2 stores discretization angles (θ _{dir, d} , φ _{dir, d} ) (d = 1,..., D), where D is a predetermined positive integer. That is, the development angle storage unit 2 includes D discretized angles (θ _{dir, 1} , φ _{dir, 1} ), (θ _{dir, 2} , φ _{dir, 2} ), ..., (θ _{dir, D} , φ _{dir , D} ) are stored.

The discretization angle (θ _{dir, d} , φ _{dir, d} ) is a pair with θ _{dir, d} and φ _{dir, d} . As shown in FIG. 4, θ _{dir, d} is an elevation angle, and φ _{dir, d} is an azimuth angle.

D discretization angles (θ _{dir, d} , φ _{dir, d} ) (d = 1,..., D) may be set in any way. For example, the discretization angles (θ _{dir, d} , φ _{dir, d} ) are equally spaced. Further, the discretization angle (θ _{dir, d} , φ _{dir, d} ) may be determined using the apex direction of the regular polyhedron. That is, the directions of a plurality of vertices of the regular polyhedron with the center of the regular polyhedron as the origin are set as the discretization angles (θ _{dir, d} , φ _{dir, d} ) (d = 1,..., D), respectively.

FIG. 7 is a conceptual diagram when the discretization angle (θ _{dir, d} , φ _{dir, d} ) is determined using an icosahedron. For example, as shown in FIG. 7, a regular icosahedron is arranged on the central axis of a cylindrical microphone array, and a predetermined distance from the central axis of the cylindrical microphone array among the vertices of the regular icosahedron. The directions of a plurality of vertices excluding the vertices at are respectively defined as discretization angles (θ _{dir, d} , φ _{dir, d} ) (d = 1,..., D).

  Setting a large value for D increases the computational cost, but increases the resolution of the sound field. The value of D is determined in consideration of calculation cost and sound field resolution.

<Plane wave expansion part 3>
The plane wave expansion unit 3 uses each sound pressure signal P _{mic, ab} (k) generated based on the signal collected by the microphone Ma-b to read each discretization angle (θ _The plane wave expansion signal P _{dir, d} (k) corresponding to _{dir, d} , φ _{dir, d} ) is calculated in consideration of the change of the transmission path due to the rigid baffle (step S2). In this example, the sound pressure signal P _{mic, ab} (k) generated based on the signal collected by the microphone Ma-b is the frequency domain signal P _{mic, ab} (k) generated by the frequency converter 1. ).

The plane wave expansion unit 3 calculates a plane wave expansion signal P _{dir, d} (k) determined by the following equation, for example.

_Let i be an imaginary unit, H _n ⁽¹⁾ (・) be an nth-order first-class Hankel function, and H _n ⁽¹⁾ '(・) be an nth-order first-class Hankel function H _n ⁽¹⁾ (・), W (k, θ _{mic, a} , z _{mic, b} , θ _{dir, d} , φ _{dir, d} ) is given as follows. N is the resolution of the sound field as described above, and is a predetermined positive integer. For example, N is a positive integer not more than a value N _MAX determined by the discretization method. In many cases, N is obtained based on numerical calculation so as to be numerically stable. The superscript + represents a pseudo inverse matrix operation.

The nth order first-class Hankel function H _n ⁽¹⁾ (x) is defined as follows using the nth-order first-order Bessel function J _n (x) and second-order Bessel function Y _n (x) Is done.

H _n ⁽¹⁾ ′ (ψ), which is a derivative of the nth-order first-class Hankel function H _n ⁽¹⁾ (•), is defined as follows.

Thus, in order to handle the signal collected by the cylindrical microphone, the plane wave developing unit 3 treats the Helmholtz equation in the helical wave spectrum region as the Helmholtz equation as an equation representing the wave equation in the frequency domain. The plane wave expansion signal P _{dir, d} (k) is calculated using the filter W (k, θ _{mic, a} , z _{mic, b} , θ _{dir, d} , φ _{dir, d} ) calculated by

In addition, a plane wave and a plane wave expansion | deployment signal are the indices showing the strength of the signal for every direction. For example, the plane wave expansion signal P _{dir, d} (k) represents the intensity of the signal in the direction of the discretization angle (θ _{dir, d} , φ _{dir, d} ).

  Thus, the sound field plane wave expanding apparatus and method of the first embodiment can expand plane waves even if the microphone array is cylindrical.

[Second Embodiment]
The sound field plane wave expansion device of the second embodiment is different from the first embodiment in the part further including the discrete spherical harmonic transformation unit 4 as shown in FIG. 2, and the other parts are the same as in the first embodiment.

  Hereinafter, the description will focus on the discrete spherical harmonic transformation unit 4 that is different from the first embodiment, and description of the same parts as in the first embodiment will be omitted.

The plane wave expansion signal P _{dir, d} (k) (d = 1,..., D) calculated by the plane wave expansion unit 3 is transmitted to the discrete spherical harmonic transformation unit 4.

The discrete spherical harmonic transformation unit 4 transforms the plane wave expansion signal P _{dir, d} (k) into the spherical harmonic spectrum signals B to _p (k) by the discrete spherical harmonic transformation (step S3).

The discrete spherical harmonic transformation unit 4 performs discrete spherical harmonic transformation, for example, according to the following equation, and generates spherical harmonic spectrum signals B to _p (k).

As index p = (n, m), A _p is a coefficient for normalization and is a predetermined real number. For example, using Furse-Malham coefficient as A _p. Note that n and m are 0 ≦ n ≦ N, −n ≦ m ≦ n and | m | ≦ M. The maximum value of the index p = (n, m) is M ² + 2N + 1.

  M is a predetermined positive integer equal to or less than N. The magnitude of the value of M also corresponds to the resolution.

Y _n ^m is a spherical harmonic function defined as follows, for example. n and m are the orders of the spherical harmonic spectrum. In the following formula, j is an imaginary unit.

P ^m _n (·) is a Legendre power function and is defined as follows. P _n (·) represents a Legendre polynomial.

As described above, the plane wave expansion signal P _{dir, d} (k) may be converted into the spherical harmonic spectrum signals B to _p (k), which are formats usable for the reproduction format such as ambisonics.

[Third embodiment]
The sound field plane wave expansion device of the third embodiment is different from the first embodiment in the part further including the frequency inverse transform unit 5 as shown in FIG. 3, and the other parts are the same as those in the first embodiment.

  Hereinafter, the frequency inverse transform unit 5 which is a different part from the first embodiment will be mainly described, and the description of the same part as the first embodiment will be omitted.

The plane wave expansion signal P _{dir, d} (k) (d = 1,..., D) calculated by the plane wave expansion unit 3 is transmitted to the frequency inverse conversion unit 5.

The frequency inverse transform unit 5 transforms the plane wave expansion signal P _{dir, d} (k) into a time domain signal P _{sp, d} (t) by inverse Fourier transform _, and converts the transformed time domain signal P _{sp, d} (t). Output to the speaker Sd (step S4). The time domain signal P _{sp, d} (t) obtained for each frame by the inverse Fourier transform is appropriately shifted to obtain a linear sum to become a continuous time domain signal. For the inverse Fourier transform, an existing method such as a short-time discrete inverse Fourier transform may be used.

The speaker arrays S1, S2,..., SD are composed of D speakers S1, S2,. Specifically, as d = 1,..., D, the speaker Sd is arranged in the direction of the discretization angle (θ _{dir, d} , φ _{dir, d} ). For example, as illustrated in FIG. 7, when the direction of each vertex of the regular polyhedron is a discretization angle (θ _{dir, d} , φ _{dir, d} ), the speaker is arranged at the position of each vertex of the regular polyhedron. The

The speaker arrays S1, S2,..., SD reproduce sound based on the time domain signals P _{sp, 1} (t), P _{sp, 2} (t) _,. Specifically, with d = 1,..., D, the speaker Sd reproduces sound based on the time domain signal P _{sp, d} (t). Thereby, the sound field picked up by the microphone arrays M1-1, M2-1,..., MN _a -N _b can be reproduced by the speaker arrays S1, S2,.

If the number of microphones is larger than the number of speakers, the reproduction signal may be thinned out. On the other hand, when the number of microphones is smaller than the number of speakers, interpolation may be performed by taking an average of the time domain signals P _{sp, d} (t). As a method for performing the interpolation, for example, linear interpolation, sinc interpolation, or the like can be applied.

[Modifications, etc.]
The sound field plane wave developing device may not include other units as long as it includes the plane wave developing unit 3.

  You may perform the process of the frequency converter 1 and the process of the plane wave expansion | deployment part 3 simultaneously. The sound field plane wave expansion device can be realized by a computer. In this case, the processing content of each part of this apparatus is described by a program. Then, by executing this program on a computer, each unit in this apparatus is realized on the computer.

  The program describing the processing contents can be recorded on a computer-readable recording medium. In this embodiment, these apparatuses are configured by executing a predetermined program on a computer. However, at least a part of these processing contents may be realized by hardware.

  The present invention is not limited to the above-described embodiment, and can be modified as appropriate without departing from the spirit of the present invention.

DESCRIPTION OF SYMBOLS 1 Frequency conversion part 2 Expansion | deployment angle memory | storage part 3 Plane wave expansion | deployment part 4 Discrete spherical harmonic conversion part 5 Frequency inverse conversion part

Claims (7)

_Assume that at least two microphones are arranged in each of two or more circles having a radius R _cyl centered on the axis of a cylindrical rigid baffle and having the circumferential direction of the baffle as a circumferential direction, and ω is a frequency. , C is the speed of sound, and k = ω / c,
In the development angle storage unit, it is assumed that D is a predetermined positive integer and discretization angles (θ _{dir, d} , φ _{dir, d} ) (d = 1,..., D) are stored,
The plane wave expansion unit uses each sound pressure signal P _{mic, ab} (k) generated based on the signal collected by the microphone to read each discretization angle (θ _{dir, d} , Φ _{dir, d} ), a plane wave expansion step for calculating a plane wave expansion signal P _{dir, d} (k) in consideration of a change in the transmission path due to the baffle of the rigid body,
Sound field plane wave expansion method including. In the sound field plane wave expansion method according to claim 1,
_Let i be an imaginary unit, H _n ⁽¹⁾ (・) be an nth-order first-class Hankel function, and H _n ⁽¹⁾ '(・) be an nth-order first-class Hankel function H _n ⁽¹⁾ (・), N is a predetermined positive integer, W (k, θ _{mic, a} , z _{mic, b} , θ _{dir, d} , φ _{dir, d} ) is As an inverse matrix operation,

The plane wave expansion unit calculates a plane wave expansion signal P _{dir, d} (k) determined by the following equation:

Sound field plane wave expansion method. In the sound field plane wave expansion method according to claim 1 or 2,
The discrete spherical harmonic transformation unit further includes a discrete spherical harmonic transformation step of transforming the plane wave expansion signal P _{dir, d} (k) into a spherical harmonic spectrum signal B to _p (k) by discrete spherical harmonic transformation,
Sound field plane wave expansion method. In the sound field plane wave expansion method according to claim 3,
M is a predetermined positive integer, Y _n ^m is a spherical harmonic function, index p = (n, m), A _p is a predetermined real number,
The discrete spherical harmonic transformation unit performs discrete spherical harmonic transformation according to the following equation:

Sound field plane wave expansion method. In the sound field plane wave expansion method according to claim 1 or 2,
The frequency inverse transform unit further includes a frequency inverse transform step of transforming the plane wave expansion signal P _{dir, d} (k) into a time domain signal by inverse Fourier transform and outputting the transformed time domain signal to a speaker.
Sound field plane wave expansion method. _Assume that at least two microphones are arranged in each of two or more circles having a radius R _cyl centered on the axis of a cylindrical rigid baffle and having the circumferential direction of the baffle as a circumferential direction, and ω is a frequency. , C is the speed of sound, and k = ω / c,
A development angle storage unit storing discretization angles (θ _{dir, d} , φ _{dir, d} ) (d = 1,..., D), where D is a predetermined positive integer;
Using the sound pressure signal P _{mic, ab} (k) generated based on the signal collected by the microphone, each discretization angle (θ _{dir, d} , φ _{dir, d} ), A plane wave expansion unit that calculates a plane wave expansion signal P _{dir, d} (k) corresponding to the rigid body baffle, and
Sound field plane wave expansion device including.   A sound field plane wave expansion program for causing a computer to execute each step of the sound field plane wave expansion method according to any one of claims 1 to 5.