Sound pressure estimation device, sound pressure estimation method, and program

Abstract

To provide a technique capable of estimating a sound pressure to an ear source from a sound pressure observed by using a plurality of microphone arranged at a neighbor of a bead part without a conversion to a frequency region.SOLUTION: A sound pressure estimation device includes: a weighting addition part that calculates weighting sums q0, ..., qN of sound pressures p1, ..., pL at a point arranged on a spherical surface at a neighbor of a head part of L microphones from the sound pressure p1, ..., pL to dimension of 0 to N; and a sound pressure calculation part that calculates a sound pressure ^p of an ear source by using IIR filters η0, ..., ηN from the dimension of 0 to N from the weighting sums q0, ..., qN from the dimension of 0 to N. In the device, a point is that the L microphones is arranged in (re, Ω1), ..., (re, ΩL) (where, re is a radius of the spherical surface at the neighbor of the head part), and a point (where, a is a radial of the spherical surface in which the ear source is positioned) is that a position of the ear source of (a, Ωa) expresses, and the IIR filter ηn of the dimension of n is a time region filter designed on the basis of a predetermined function Hn(kr) in the frequency region.SELECTED DRAWING: Figure 7

Description

[Technical field]

[0001] The present invention relates to a technology for active noise control near the head, and in particular to a technology for estimating sound pressure at a desired control point using multiple microphones. [Background technology]

[0002] There is an active noise control technology that uses a reference microphone, an error microphone, and a cancellation speaker to suppress noise at a specific position (see Non-Patent Document 1).

[0003] In order to ensure the noise suppression performance at the ears in the seat-mounted active noise control system, a method of estimating the sound pressure at the ears using a microphone placed near the head is being considered. For example, it is possible to estimate the sound pressure at the ears by using a spherical harmonic expansion and an interpolation relationship of sound pressure using microphones placed on a sphere that includes the head, which is assumed to be a hard sphere. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Yoshinobu Kajikawa, "Recent Topics and Applications of Active Noise Control," IPSJ Technical Report, Vol.2015-MUS-107, No.3, pp.1-6, 2015. Summary of the Invention [Problem to be solved by the invention]

[0005] However, since the above-mentioned method uses calculations in the frequency domain, it is necessary to convert a time domain signal into a frequency domain signal. Therefore, when attempting to apply the above-mentioned method to an active noise control system that requires highly immediate processing, it may not be possible to satisfy the required processing performance.

[0006] Therefore, an object of the present invention is to provide a technology for estimating sound pressure at the ear from sound pressure observed using multiple microphones placed near the head, without transforming into the frequency domain. [Means for solving the problem]

[0007] In one aspect of the present invention, L is the number of microphones arranged on a spherical surface near the head (where L is an integer equal to or greater than 2), p1, ..., p L Let p1, …, p be the sound pressure at the points where the L microphones are placed. L , the sound pressures p1, …, p for orders 0 to N L The weighted sum of q0, …, q N and a weighted sum q0, …, q N to IIR filters η0, …, η of orders 0 to N N A sound pressure estimation device including a sound pressure calculation unit that calculates the sound pressure ^p at the ear using (r e , Ω1), …, (r e , Ω L ) (where r e is the radius of the sphere near the head) are the points where L microphones are placed, (a, Ω a ) is the point that represents the position of the ear (where a is the radius of the sphere on which the ear is located), and an IIR filter η of order n is n (n=0, …, N) is the function H in the frequency domain that represents the interpolation relationship of sound pressure. n (kr) (n=0, …, N, where k is the wavenumber). Effect of the Invention

[0008] According to the present invention, it is possible to estimate the sound pressure at the ear without using calculations in the frequency domain. [Brief description of the drawings]

[0009] [Figure 1] FIG. 1 is a diagram showing a state in which multiple microphones are arranged on a spherical surface near the head. [Diagram 2]FIG. 1 is a diagram showing the outline of a function H0(kr). [Diagram 3] FIG. 1 is a diagram showing the state of a frequency fk that becomes a pole of a function Hn(kr). [Figure 4] FIG. 13 is a diagram showing an estimated waveform and an observed waveform for a band-limited pulse (before correction). [Diagram 5] FIG. 13 is a diagram showing an estimated waveform and an observed waveform for a band-limited pulse (after correction). [Figure 6] FIG. 13 shows the estimated waveform and observed waveform for white noise (after correction). [Figure 7] FIG. 1 is a block diagram showing a configuration of a sound pressure estimation device 100. [Figure 8] 4 is a flowchart showing an operation of the sound pressure estimation device 100. [Figure 9] FIG. 2 is a diagram illustrating an example of a functional configuration of a computer that realizes each device according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Hereinafter, an embodiment of the present invention will be described in detail. Note that components having the same functions are given the same reference numbers and duplicated explanations will be omitted.

[0011] Before describing each embodiment, the notation used in this specification will be described.

[0012] ^ (caret) represents a superscript. For example, x y^z Yes z is a superscript to x, and x y^z Yes z is a subscript to x. Also, _ (underscore) represents a subscript. For example, x y_z Yes z is a superscript to x, and x y_z Yes z is a subscript on x.

[0013] The superscripts "^" and "~" such as ^x and ~x for a certain letter x should actually be written directly above the "x", but due to the constraints of the description in the specification, they are written as ^x and ~x.

[0014] <Technical background> In an embodiment of the present invention, the head is assumed to be a hard sphere, and the sound pressure at the ear is estimated by convolving an IIR filter, which is a time domain filter designed to estimate the sound pressure at the ear, with a weighted sum of sound pressures of signals observed using multiple microphones arranged on a spherical surface near the head. Here, the spherical surface near the head means a spherical surface that can include the head. FIG. 1 is a diagram showing a state in which multiple microphones are arranged on a spherical surface near the head. The sound pressure estimation process in the embodiment of the present invention and a method for deriving an IIR filter used in the process will be described below.

[0015] <<1: Sound pressure estimation process in the time domain>> First, we consider estimating the sound pressure at the ear in the frequency domain from the sound pressure of a signal observed using two or more microphones arranged on a sphere near the head. Hereafter, we express points in space using polar coordinates (r, Ω) (where Ω represents two arguments θ and φ). Let L be the number of microphones, and let (r e , Ω1), …, (r e , Ω L ) at the points where L microphones are placed (where r e is the radius of the sphere around the head on which the L microphones are placed), (a, Ω a ) is the point that represents the position of the ear (where a is the radius of the sphere on which the ear is located). Also, p1, …, p L Let be the sound pressure at the points where the L microphones are placed.

[0016] The point (a, Ω) represents the position of the ear. a ) sound pressure ^p(a, Ω a ) can be expressed by the following equation using spherical harmonic expansion:

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[0017] Equation (1) can be transformed into the following by using the interpolation relationship of sound pressure:

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[0018] As can be seen from equation (2), the term H n The IIR filter η n If it is possible to use the above, it is possible to estimate the sound pressure in the time domain. The sound pressure estimation process in the time domain at this time is performed as follows.

[0019] (1) Sound pressures p1, …, p at the points where L microphones are placed L The input is the sound pressure p1, …, p L The weighted sum of q n Calculate (n=0, …, N).

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[0020] (2) Weighted sums q0, …, q from degree 0 to N N The input is an IIR filter η0, …, η of orders 0 to N. N Using this, the sound pressure at the ear is calculated using the following formula:

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[0021] <<2: How to derive an IIR filter>> Here, the term H n The IIR filter η n We will explain how to derive the following two methods.

[0022] (1) Method using sz transformation (2) Function H n How to use the numerical calculation of the poles of (kr) Both methods (1) and (2) are derived using the z-plane. Therefore, before starting the explanation of methods (1) and (2), let us consider the relationship between the transfer function H(z) on the z-plane and the filter coefficients of the IIR filter. In general, the output signal y(i) (where i represents the sampling time) of an IIR filter can be expressed by the following equation, with x(i) as the input signal.

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[0023] By z-transforming both sides of the above equation and considering the transfer function H(z) on the z-plane, we obtain the following equation.

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[0024] <<<2-1: Method using sz conversion>>> Function H in the frequency domain n (kr) is a function H on the z plane n The steps to convert to (z) are as follows:

[0025] (1) Function H n By expressing (kr) in the s domain, the function H n To do this, we use the fact that the frequency domain corresponds to a set on the imaginary axis of the s-plane.

[0026] (2) Function H on the s-plane n By expressing (s) on the z-plane, the function H n To do this, we use the sz transformation, which is a transformation method that maps a function on the s plane to the z plane.

[0027] First, we will explain step (1). Function H nTo express (kr) on the s domain, we use the function H n (kr) is considered as a function of s = jω (where j is the imaginary unit and ω (= 2πf) is the angular frequency). As an example of considering a function in the frequency domain as a function of s = jω, the 0th order second kind spherical Hankel function h0 (2) (kr) to function h0 (2) Here is an example of obtaining (s). First, function h0 (2) Transform (kr) as follows:

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[0028] The first kind of spherical Hankel function h n (1) (s), the second kind of spherical Hankel function h n (2) If we calculate (s) for n=0, 1, 2, we get the following.

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[0029] Using the above results, the function H0(s) is calculated as follows:

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[0030] Therefore, r = r e Then, when u=7, the filter coefficient a m , b m The values ​​shown in the table below are calculated. [Table 1] however,

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[0031] In particular, (r e -a) / cT is an integer, so that radius r e By selecting the value of m , b m can be simplified as follows:

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[0032] <<<2-2: Function H n How to use the numerical calculation of poles of (kr)>>> Here, the function H n We focus on the fact that (kr) is a real-valued function. Figure 2 shows the outline of the function H0(kr). Figure 2 is a graph with frequency on the horizontal axis. As can be seen from Figure 2, the frequency characteristic of the function H0(kr) diverges periodically, and the poles are dominant. Therefore, we will use the IIR filter as the function H n (kr) is derived as a filter with poles on the unit circle. To do this, the function H n The pole locations of (kr) are calculated numerically. The procedure for deriving the IIR filter is as follows:

[0033] (1) Pole frequency f w function H n It is found from the zero points of the reciprocal function f of (kr) (see Figure 3).

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[0034] (2) The frequency f of the obtained pole w The transfer function H n (z) is calculated. The pole frequency f w The deviation angle on the z plane is θ w =2πf w / f s , coordinate is v w =r×exp(jθ w ) (where r is a value close to 1, for example 0.999). Therefore, if W is the number of frequencies with poles obtained, the transfer function H n (z) is given by the following formula:

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[0035] (3) Transfer function H n (z) is expanded, and the IIR filter coefficients η n (w) (w=1, …, 2W) is calculated. Specifically, the IIR filter coefficient η n The transfer function H expressed using (w) (w=1, …, 2W) n Using (z) and equation (7), the IIR filter coefficient η n (w) (w=1, …, 2W) can be found.

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[0036] The noise to be estimated for sound pressure is band-limited pulse (100Hz to 700Hz) and white noise (100Hz to 700Hz). The experimental conditions are as follows:

[0037] (1) The noise is assumed to come from the left side of the left ear. Therefore, we estimate the observed waveform on the left surface of the sphere.

[0038] (2) The radius of the hard sphere representing the head is 0.10 m, and the radius of the sphere on which the 12 microphones are placed is 0.15 m.

[0039] (3) The order n of the spherical harmonic function is 2 or less, and the IIR filter length is 14. Note that the IIR filter length is a result dependent on the number of poles being 7.

[0040] Under the above experimental conditions, the estimated waveform and observed waveform are obtained. Figure 4 shows the estimated waveform and observed waveform for a band-limited pulse. From Figure 4, it can be seen that when calculation is performed using equation (8), a time lag of several samples occurs between the estimated waveform and the observed waveform, and the amplitudes of the estimated waveform and the observed waveform do not match. This shows that it is necessary to take into account the advancement due to reflected noise and adjust the filter gain. Therefore, equation (8) is corrected as follows.

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[0041] Fig. 5 shows the estimated waveform and observed waveform for a band-limited pulse when the corrected formula (8)' is used. It can be seen from Fig. 5 that the deviation is eliminated and the estimation is stable. Fig. 6 shows the estimated waveform and observed waveform for white noise when the corrected formula (8)' is used. It can be seen from Fig. 6 that the estimation is stable even for white noise.

[0042] First Embodiment As explained in the <Technical Background>, the sound pressure estimation device 100 estimates the sound pressure at the ear from the sound pressure of a signal observed using two or more microphones arranged on a spherical surface near the head. Let L be the number of microphones arranged on a spherical surface near the head (where L is an integer equal to or greater than 2), and p1, ..., p L Let L be the sound pressure at the point where the microphones are placed, (r e , Ω1), …, (r e , Ω L ) (where r e is the radius of the sphere near the head) are the points where L microphones are placed, (a, Ω a) is the point that represents the position of the ear (where a is the radius of the sphere on which the ear is located).

[0043] The sound pressure estimation device 100 will be described below with reference to Figs. 7 and 8. Fig. 7 is a block diagram showing the configuration of the sound pressure estimation device 100. Fig. 8 is a flowchart showing the operation of the sound pressure estimation device 100. As shown in Fig. 7, the sound pressure estimation device 100 includes a weighting addition unit 110, a sound pressure calculation unit 120, and a recording unit 190. The recording unit 190 is a component that appropriately records information necessary for the processing of the sound pressure estimation device 100. The recording unit 190 records, for example, sound pressure p λ Weight γ of degree n for λn Record (λ=1, …, L, n=0, …, N).

[0044] The operation of the sound pressure estimation device 100 will be described with reference to FIG.

[0045] In S110, the weighting addition unit 110 calculates the sound pressures p1, . . . , p L The input is sound pressure p1, …, p L , the sound pressures p1, …, p for orders 0 to N L The weighted sum of q0, …, q N Specifically, the weighting addition unit 110 calculates and outputs a weighting sum q of degree n by the following formula: n Calculate (n=0, …, N).

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[0046] A specific design example is shown below. (Example 1) The IIR filter η0 of order 0 is obtained by sz transforming the function H0(s), which is the expression of the function H0(kr) in the s domain, into the coefficient a of the following function H0(z): m (m=1, 2, 3, 2u, 2u+1, 2u+2, 2u+3, where u=floor((r e -a) / c×1 / T)), b m (m=0, 1, 2, 3), where u is preferably an integer equal to or greater than 2.

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[0047] <Additional Notes> The processing of each unit of each of the above-mentioned devices may be realized by a computer, in which case the processing contents of the functions that each device should have are described by a program. Then, this program is loaded into the recording unit 2020 of the computer 2000 shown in Fig. 9, and the arithmetic processing unit 2010, the input unit 2030, the output unit 2040, the auxiliary recording unit 2025, etc. are operated, whereby the processing functions of each of the above-mentioned devices are realized on the computer.

[0048] The device of the present invention, for example, as a single hardware entity, has an input unit capable of inputting a signal from outside the hardware entity, an output unit capable of outputting a signal to the outside of the hardware entity, a communication unit to which a communication device (e.g., a communication cable) capable of communicating with the outside of the hardware entity can be connected, a CPU (Central Processing Unit, which may have a cache memory or a register, etc.) which is an arithmetic processing unit, RAM and ROM which are memories, an external storage device which is a hard disk, and a bus which connects the input unit, output unit, communication unit, CPU, RAM, ROM, and external storage device so that data can be exchanged between them. If necessary, the hardware entity may be provided with a device (drive) capable of reading and writing a recording medium such as a CD-ROM. A physical entity equipped with such hardware resources is, for example, a general-purpose computer.

[0049] The external storage device of the hardware entity stores the programs required to realize the above-mentioned functions and the data required in the processing of these programs (not limited to the external storage device, but for example the programs may be stored in a ROM, which is a read-only storage device). Data obtained by the processing of these programs is stored appropriately in the RAM, the external storage device, etc.

[0050] In the hardware entity, each program stored in an external storage device (or ROM, etc.) and data required for processing each program are loaded into memory as necessary, and interpreted, executed, and processed by the CPU as appropriate. As a result, the CPU realizes a predetermined function (each component represented as the above, "unit," "means," etc.). In other words, each component of the embodiment of the present invention may be configured by a processing circuit.

[0051] As described above, when the processing functions of the hardware entities (the devices of the present invention) described in the above embodiments are realized by a computer, the processing contents of the functions that the hardware entities should have are described by a program. Then, by executing this program on a computer, the processing functions of the hardware entities are realized on the computer.

[0052] The program describing the processing contents can be recorded on a computer-readable recording medium. The computer-readable recording medium is, for example, a non-transitory recording medium, specifically, a magnetic recording device, an optical disk, or the like.

[0053] The program may be distributed, for example, by selling, transferring, lending, etc. portable recording media such as DVDs and CD-ROMs on which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of a server computer and transferring the program from the server computer to other computers via a network.

[0054] A computer that executes such a program, for example, first stores a program recorded on a portable recording medium or a program transferred from a server computer in the auxiliary recording unit 2025, which is a non-transient storage device of the computer. Then, when executing a process, the computer reads the program stored in the auxiliary recording unit 2025, which is a non-transient storage device of the computer, into the recording unit 2020, and executes a process according to the read program. As another execution form of the program, the computer may read the program directly from the portable recording medium into the recording unit 2020 and execute a process according to the program, or may execute a process according to the received program each time a program is transferred from the server computer to the computer. Alternatively, the server computer may not transfer the program to the computer, but may execute the above-mentioned process by a so-called ASP (Application Service Provider) type service that realizes a processing function only by issuing an execution instruction and obtaining a result. Note that the program in this embodiment includes information used for processing by an electronic computer and equivalent to a program (data that is not a direct instruction to a computer but has a nature that specifies the processing of a computer, etc.).

[0055] In addition, in this embodiment, the present device is configured by executing a specific program on a computer, but at least a part of the processing contents may be realized by hardware.

[0056] The present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the spirit of the present invention.

Claims

1. L is the number of microphones arranged on a spherical surface near the head (where L is an integer greater than or equal to 2), and p 1 , …, p L Let be the sound pressure at the point where L microphones are placed, Sound pressure p 1 , …, p L From the sound pressure p of orders 0 to N, 1 , …, p L The weighted sum q 0 , …, q N a weighting addition unit that calculates Weighted sum q of degrees 0 to N 0 , …, q N to IIR filters η of orders 0 to N 0 , …, η N A sound pressure calculation part calculates the sound pressure ^p at the ear using A sound pressure estimation device comprising: (r e , Ω 1 ), …, (r e , Ω L ) (where r e is the radius of the sphere near the head) are the points where L microphones are placed, (a, Ω a ) is the point that represents the position of the ear (where a is the radius of the sphere on which the ear is located), IIR filter η of order n n (n=0, …, N) is the function H in the frequency domain that represents the interpolation relationship of sound pressure. n (kr) (n=0, …, N, where k is the wavenumber) Sound pressure estimation device.

2. The sound pressure estimation device according to claim 1, The weighting addition unit calculates a weighted sum q of order n by the following formula: n (n=0, …, N) [Equation 40] [Equation 41] (However, Y n m represents a spherical harmonic function.) The sound pressure calculation unit calculates the sound pressure ^p using the following formula: [0.001] A sound pressure estimation device characterized by:

3. The sound pressure estimation device according to claim 1, Function H n (kr)(n=0, …, N) is expressed by the following equation [Equation 43] [0.0000] (However, j n is the nth order spherical Bessel function, h n (2) represents the nth-order spherical Hankel function of the second kind.) A sound pressure estimation device characterized by:

4. The sound pressure estimation device according to claim 3, IIR filter η of order 0 0 is the function H 0 The function H, which is the representation of (kr) on the s domain 0 The following function H obtained by sz-transforming (s) 0 Coefficient a of (z) m (m=1, 2, 3, 2u, 2u+1, 2u+2, 2u+3), b m (m=0, 1, 2, 3) is a time domain filter designed using [Equation 45] A sound pressure estimation device characterized by:

5. The sound pressure estimation device according to claim 3, IIR filter η of order n n (n=0, …, N) is the function H n (kr) pole frequency f w (w=1, …, W, W is a function H n The function H is expressed by the following equation using the number of poles (kr) n (z) IIR filter coefficients η n (w) is a time domain filter designed using (w=1, …, 2W) [Equation 46] (However, v w =r×exp(jθ w ), θ w =2πf w / f s where r is approximately equal to 1 and f s represents the sampling frequency.) A sound pressure estimation device characterized by:

6. L is the number of microphones arranged on a spherical surface near the head (where L is an integer greater than or equal to 2), and p 1 , …, p L Let be the sound pressure at the point where L microphones are placed, The sound pressure estimation device measures the sound pressure p 1 , …, p L From the sound pressure p of orders 0 to N, 1 , …, p L The weighted sum q 0 , …, q N a weighted summation step for calculating The sound pressure estimation device calculates a weighted sum q of orders 0 to N. 0 , …, q N to IIR filters η of orders 0 to N 0 , …, η N A sound pressure calculation step to calculate the sound pressure ^p at the ear using A sound pressure estimation method comprising: (r e , Ω 1 ), …, (r e , Ω L ) (where r e is the radius of the sphere near the head) are the points where L microphones are placed, (a, Ω a ) is the point that represents the position of the ear (where a is the radius of the sphere on which the ear is located), IIR filter η of order n n (n=0, …, N) is the function H in the frequency domain that represents the interpolation relationship of sound pressure. n (kr) (n=0, …, N, where k is the wavenumber) Sound pressure estimation method.

7. A program for causing a computer to function as the sound pressure estimation device according to any one of claims 1 to 5.

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