Acoustic field reproduction device and program

Abstract

To improve the ease of speaker installation and mitigate restrictions on an arrival direction of a sound wave when reproducing a desired acoustic field.SOLUTION: An acoustic field reproduction device 1 generates a drive signal for reproducing a desired acoustic field by using one or a plurality of cylindrical array speakers 101 and one or a plurality of spherical array speakers 102. A drive signal calculation unit 10 multiplies a cylindrical harmonious spectrum of the desired acoustic field to a pseudo-inverse matrix T+ of a preliminarily set transmission matrix T(ω) so as to determine a cylindrical harmonious spectrum of the drive signal and a spherical harmonious spectrum of the drive signal. The transmission matrix T(ω) is derived by conversion of a spherical harmonious spectrum representing an acoustic field of a spherical sound source corresponding to the spherical array speaker 102 into a cylindrical harmonious spectrum, assuming that a total acoustic field by a cylindrical sound source and the spherical sound source can be expressed by the cylindrical harmonious spectrum.SELECTED DRAWING: Figure 5

Description

[Technical field]

[0001] The present invention relates to a sound field reproducing device and a program using a cylindrical array speaker and a spherical array speaker. [Background technology]

[0002] Research has been conducted on sound field reproduction technology that uses multiple speakers to create an arbitrary sound field in a certain space. Known technologies for sound field reproduction include Wave Field Synthesis (WFS), Boundary Surface Control (BoSC), Higher Order Ambisonics (HOA), and Spectral Division Method (SDM).

[0003] 9 is a diagram showing an example of speaker array arrangement in wave field synthesis (WFS). WFS is a method based on the Rayleigh integral, and uses a speaker array 100-1 arranged linearly or planarly to reproduce the sound pressure or sound pressure gradient on the boundary plane of a desired sound field, thereby forming a wavefront due to a sound source arriving from outside the boundary.

[0004] Fig. 10 shows an example of speaker array placement in boundary sound field control (BoSC). BoSC is a method based on the Kirchhoff-Helmholtz integral equation. BoSC places speaker array 100-2 outside the area where the sound field is to be reproduced so as to surround the listener toward the inside of the area, and reproduces the desired sound field inside the area by controlling the sound pressure and sound pressure gradient on the boundary surface of the area using an inverse system.

[0005] Fig. 11 is a diagram showing an example of speaker array arrangement in higher order Ambisonics (HOA). HOA is a method of expressing a desired sound field using spherical harmonic functions, and reproducing the sound field by matching the spherical harmonic coefficients of the reproduced sound field with the spherical harmonic coefficients of the desired sound field using a spherical speaker array 100-3 arranged to surround the listener toward the inside of the sphere. For details of HOA, see, for example, Non-Patent Document 1.

[0006] Fig. 12 is a diagram showing an example of speaker array arrangement in the spectral division method (SDM). SDM is a method for expressing a desired sound field using an angular spectrum, and reproducing the sound field by matching the angular spectrum of the reproduced sound field with the angular spectrum of the desired sound field using a speaker array 100-4 arranged in a line or a plane. For details of SDM, see, for example, Non-Patent Document 2.

[0007] [Calculation method of drive signal in SDM] A typical sound field reproduction method using SDM will be explained below. Figure 13 shows the arrangement of speaker arrays and the reproduced sound field in SDM.

[0008] Speakers are densely arranged on a straight line y=y0 on the z=0 plane in the xyz space (hereinafter referred to as a "line array speaker"), and the driving signal of the sound source with angular frequency ω arranged at the coordinate r0=(x0,y0,0) is defined as D(r0,ω). ref The sound pressure P(r,ω) at the point (r, 0) is expressed by the following equation:

number

[0009] Here, G(r-r0,ω) is the transfer function of direction and distance expressed by the vector r-r0. If a free sound field is assumed as the reproduced sound field and each speaker can be regarded as a point sound source, G(r-r0,ω) is expressed by the three-dimensional free-field Green's function and is expressed by the following formula.

number

[0010] The sound pressure P(r,ω) can be interpreted as the convolution of the drive signal D(r0,ω) and the transfer function G(r-r0,ω) placed at the point r0 in space along r0, and y=y ref By performing a Fourier transform along the x-axis direction in x ,y ref ,ω) is obtained. In the following explanation, it is assumed that everything is on the same plane (z=0 plane), and the notation of z coordinates is omitted.

number

[0011] P^(k x ,y ref ,ω) is the sound pressure P(r,ω) at y=y ref The angular spectrum is obtained by performing a spatial Fourier transform on D^(k x ,y0,ω) is the angular spectrum obtained by spatial Fourier transform of the driving signal D(r0,ω) on y=y0. Furthermore, G^(k x ,y ref -y0,ω) is the transfer function G(r-r0,ω) as y=y ref This is the angular spectrum obtained by performing the spatial Fourier transform on the x is the wave number along the x-axis.

[0012] Here, the angular spectrum G^(k x ,y ref -y0,ω) is expressed by the following formula.

number

[0013] H0 (2) is the second kind of Hankel function of degree 0, and K0 is the 0th order modified Bessel function. 2 -k x 2When , it represents an evanescent wave that propagates only near the sound source. Since the reproduction of evanescent waves is prone to numerical instability, it is generally omitted. In the following, 0≦k 2 -k x 2 The following explanation will be given on the assumption that:

[0014] Here, the wavefront of the desired sound field to be reproduced is y=y des The angular spectrum obtained by spatial Fourier transform of the sound pressure distribution at d (k x ,y des ,ω), the angular spectrum D^(k x , y0,ω) are expressed by the following equation.

number

[0015] From the above, the desired boundary y = y des Angular spectrum of sound pressure P^ at d (k x ,y des , ω), it is possible to obtain the angular spectrum of the driving signal for synthesizing a desired sound field using a line array speaker.

[0016] An example of reproducing a simple sound field in which a point sound source is placed at a certain point in the desired sound field will be described. s =(x s ,y s ) driven by S(ω) at angular frequency ω, the desired sound field y=y des Angular spectrum P^ at d (k x ,y des ,ω) is expressed by the following formula:

number

[0017] Therefore, the angular spectrum of the drive signal D^(kx , y0,ω) are expressed by the following equation.

number

[0018] Furthermore, the angular spectrum of this drive signal D^(k x , y0,ω) in the x-axis spatial direction and the frequency direction to obtain a time series representation of the driving signals for each point sound source that constitutes the line array speaker.

[0019] According to the above example, by using SDM, it is possible to reproduce a sound field formed by a point sound source placed at coordinates specified by the user. The derived drive signal is assumed to reproduce a sound field on a horizontal plane at the same height as the speaker using a line array speaker. However, the above-mentioned Non-Patent Document 2 explains that it is possible to reproduce a sound field including the vertical direction by assuming a planar array speaker in which a sound source is placed on a plane and extending the derivation method of the drive signal to three dimensions.

[0020] [How to calculate the drive signal in HOA] Next, we will explain the sound field reproduction method using HOA. Figure 14 shows the speaker array arrangement and reproduced sound field in HOA.

[0021] In a three-dimensional space, speakers are densely arranged on a sphere of radius R0 (hereafter referred to as a "spherical array speaker"), and the driving signal of angular frequency ω for the speaker arranged at polar coordinate r0 = (Θ0, φ0, R0) is defined as D(r0, ω). In this case, the sound pressure P(r, ω) at polar coordinate r = (Θ, φ, r) in the space inside the spherical array speaker is expressed by the following formula.

number

[0022] Here, dA(r0) represents the surface element on the sphere at point r0, and G(r-r0, ω) represents the transfer function of direction and distance expressed by vector r-r0.

[0023] If we assume a free field to reproduce the sound field and each speaker is considered as a point sound source, G(r-r0,ω) is expressed by the three-dimensional free-field Green's function, as shown in the following equation.

number

[0024] The above formula (8) can be interpreted as the convolution of the driving signal D(r0,ω) on a sphere and the transfer function G(r-r0,ω) on a sphere. When the sound pressure P(r,ω) is expanded in a series using spherical harmonic functions, the spherical harmonic spectrum is given by the convolution theorem. TIFF2025039295000011.tif14170 is expressed by the following formula.

number

[0025] n and m are the degree and order of the spherical harmonic expansion, respectively. TIFF2025039295000013.tif15170 represents the spherical harmonic spectrum of the driving signal D(r0,ω). TIFF2025039295000014.tif13170 is the north pole of the spherical array speaker N = (0,0,R0) is expanded into a series using spherical harmonic functions at the origin of the coordinate system, and is expressed specifically by the following equation.

number

[0026] Here, the spherical harmonic spectrum obtained by expanding the sound pressure distribution of the desired sound field to be reproduced spherically around the origin of the coordinate system is called P nm(ω), the spherical harmonic spectrum of the driving signal to reproduce the wavefront of the desired sound field is TIFF2025039295000016.tif16170 is expressed by the following formula.

number

[0027] An example of reproducing a simple sound field in which a point sound source is placed at a certain point in the desired sound field will be described. s =(Θ s ,φ s ,r s ) driven by S(ω) at angular frequency ω, the spherical harmonic spectrum of the desired sound field is TIFF2025039295000018.tif14170 is expressed by the following formula.

number

[0028] Therefore, the spherical harmonic spectrum of the drive signal at this time is TIFF2025039295000020.tif16170 can be expressed by the following formula.

number

[0029] Furthermore, the spherical harmonic spectrum of this driving signal By inversely expanding TIFF2025039295000022.tif15170 in the spatial direction using spherical harmonic functions and performing an inverse Fourier transform in the frequency direction, a time series representation of the driving signals for each point sound source that makes up the spherical array speaker can be obtained.

[0030] According to the above example, by using HOA, it is possible to reproduce a sound field formed by a point sound source placed at coordinates specified by the user.

[0031] There are also known methods for reproducing a sound field using methods other than the above-mentioned SDM, HOA, etc. For example, there is a method of capturing a sound field using a cylindrically arranged microphone array and reproducing the captured sound field using a one-dimensional linear speaker array (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0032] [Patent Document 1] JP 2014-116821 A [Non-patent literature]

[0033] [Non-Patent Document 1] J.Ahrens and S.Spors, “A Modal Analysis of Spatial Discretization of Spherical Loudspeaker Distributions Used for Sound Field Synthesis”, IEEE Trans. Audio, Speech, Lang. Process., vol. 20, no.9, pp.2564-2574, Nov.2012. [Non-Patent Document 2] J.Ahrens and S.Spors, “Sound field reproduction using planar and linear arrays of loudspeakers”, IEEE Trans. Audio, Speech, Lang. Process., vol.18, no.8, pp.2038-2050, Nov.2010. Summary of the Invention [Problem to be solved by the invention]

[0034] By using the sound field reproduction method using the SDM described above or the sound field reproduction method using the HOA described above, it is possible to realize sound field reproduction in a three-dimensional space.

[0035] However, in the sound field reproduction method using SDM, the desired sound field is reproduced using loudspeakers densely arranged on a plane, but arranging the loudspeakers on a plane increases the size of the equipment, and there is also the problem that the reproduced sound waves are limited to those arriving from the side of the plane on which the planar array loudspeakers are arranged.

[0036] On the other hand, in the sound field reproduction method using HOA, the speaker array is placed on a sphere surrounding the listener, so there are no restrictions on the direction from which the reproduced sound waves come, but there is a problem in that it is difficult to install the speaker array.

[0037] Therefore, the present invention has been made to solve the above-mentioned problems, and its object is to provide a sound field reproduction device and program that improves speaker installation ease and relaxes restrictions on the direction of arrival of sound waves when reproducing a desired sound field. [Means for solving the problem]

[0038] In order to solve the above-mentioned problems, the sound field reproduction device of claim 1 generates drive signals for reproducing a sound field formed by a desired sound source using one or more cylindrical array speakers distributed in parallel to the longitudinal direction on a cylinder, and one or more spherical array speakers distributed in parallel to the longitudinal direction on a cylinder, the sound field reproduction device including: a drive signal calculation unit that inputs a cylindrical harmonic spectrum of the desired sound field and calculates a cylindrical harmonic spectrum of a drive signal for the cylindrical array speaker and a spherical harmonic spectrum of a drive signal for the spherical array speaker by a predetermined arithmetic expression; a cylindrical harmonic inverse expansion unit that obtains a drive signal in the time-frequency domain of the cylindrical array speaker by performing cylindrical harmonic inverse expansion on the cylindrical harmonic spectrum of the drive signal for the cylindrical array speaker calculated by the drive signal calculation unit; and a cylindrical harmonic inverse expansion unit that obtains a drive signal in the time-frequency domain of the cylindrical array speaker by performing spherical harmonic inverse expansion on the spherical harmonic spectrum of the drive signal for the spherical array speaker calculated by the drive signal calculation unit. a spherical harmonic inverse expansion unit that calculates a time-frequency domain drive signal for the cylindrical array speaker, and a time-frequency domain inverse Fourier transform unit that performs a discrete inverse Fourier transform in the frequency direction on the time-frequency domain drive signal for the cylindrical array speaker calculated by the cylindrical harmonic inverse expansion unit and the time-frequency domain drive signal for the spherical array speaker calculated by the spherical harmonic inverse expansion unit to calculate the time-domain drive signal for the cylindrical array speaker and the time-domain drive signal for the spherical array speaker, wherein the drive signal calculation unit calculates the predetermined arithmetic expression: D=T, † P(D) is the cylindrical harmonic spectrum of the driving signal of the cylindrical array speaker and the spherical harmonic spectrum of the driving signal of the spherical array speaker, T †is the pseudo-inverse matrix of the transfer matrix, and P is the cylindrical harmonic spectrum of the desired sound field.) is used to calculate the cylindrical harmonic spectrum of the drive signal for the cylindrical array speaker and the spherical harmonic spectrum of the drive signal for the spherical array speaker.

[0039] The sound field reproduction device of claim 2 is the sound field reproduction device of claim 1, wherein the drive signal calculation unit defines a global cylindrical coordinate system in space as (X, Φ, R) (X is the distance in the axial direction of the cylinder, Φ is the angle in the radial direction of the cylinder, and R is the radial distance from the axis of the cylinder), and calculates the distance between the point (0, φ l1 ,R l1 ) and parallel to the X-axis with radius a l1 The cylindrical sound source is placed at the point (0,φ l1 ,R l1 ) is the origin of the local cylindrical coordinate system (x l1 ,φ l1 ,r l1 ), where l1 is the number of the cylindrical sound source, i is the imaginary unit, ρ is the density of air, k is the wave number, and k x is the wave number in the x-axis direction, ω is the angular frequency, TIFF2025039295000023.tif14170 is the cylindrical harmonic spectrum of the radiation sound field of the cylindrical sound source, m is the order, H m (2) m is the second kind of Hankel function, H m (2) ' is the derivative of the second Hankel function, J m is the mth order Bessel function, Let TIFF2025039295000024.tif14170 be the cylindrical harmonic spectrum of the vibration velocity of the cylindrical sound source. Let the global spherical coordinate system in space be (Θ, Φ, R) (Θ is the elevation angle, Φ is the azimuth angle, and R is the radial distance from the origin). l2 SP =(Θ l2 ,Φ l2 ,R l2 ) with radius a l2 The spherical sound source is placed at point R l2 SP The local spherical coordinate system with the origin at (θ l2 ,φ l2 ,r l2), where l2 is the number of the spherical sound source, TIFF2025039295000025.tif14170 is the spherical harmonic spectrum of the radiation sound field of the spherical sound source, n is the order, m is the rank, h n (2) 'n' is the derivative of the two-kind spherical Hankel function, TIFF2025039295000026.tif15170 is the spherical harmonic spectrum of the vibration velocity of the spherical sound source, h q (2) q is a two-kind spherical Hankel function, j q (2) is the qth order spherical Bessel function, Y nm is a spherical harmonic function of degree n and order m, TIFF2025039295000027.tif19170 is the complex conjugate of the spherical harmonic function, TIFF2025039295000028.tif11170, Gaunt coefficient, and wave number k x When ∈[-k,k] is divided into Q parts, the q-th element is k x q year, TIFF2025039295000029.tif14170 is the wave number k of the driving signal of the cylindrical array speaker. x q Cylindrical harmonic spectrum for (q∈[1,Q]), TIFF2025039295000030.tif12170 is a spherical harmonic spectrum of the driving signal of the spherical array speaker, and the cylindrical harmonic spectrum of the internal sound field when the desired sound field is divided into an internal sound field and an external sound field by a predetermined cylindrical boundary. TIFF2025039295000031.tif10170, Cylindrical harmonic spectrum of external sound field TIFF2025039295000032.tif10170, and the cylindrical harmonic spectrum of the radiation sound field of the cylindrical sound source corresponding to the cylindrical array speaker is expressed by the following formula: The sound field formed by the spherical sound source corresponding to the spherical array speaker is divided into an internal sound field and an external sound field at a predetermined spherical boundary, and the spherical harmonic spectrum is expressed by the following formulas: TIFF2025039295000034.tif29170 (where TIFF2025039295000035.tif13170TIFF2025039295000036.tif13170.) and the formula for converting the spherical harmonic spectrum of the radiation sound field of the spherical sound source into a cylindrical harmonic spectrum is: The predetermined arithmetic expression derived so as to minimize the difference between the sound field obtained by converting the radiation sound field of the cylindrical sound source and the radiation sound field of the spherical sound source into cylindrical harmonic spectra and adding them together and the desired sound field when the predetermined arithmetic expression is represented by TIFF2025039295000037.tif13170, The cylindrical harmonic spectrum of the desired sound field is input as TIFF2025039295000038.tif59170, and the cylindrical harmonic spectrum of the drive signal of the cylindrical array speaker and the spherical harmonic spectrum of the drive signal of the spherical array speaker are calculated by the arithmetic formula.

[0040] Furthermore, a program according to claim 3 causes a computer to function as the sound field reproduction device according to claim 1. Effect of the Invention

[0041] As described above, according to the present invention, when reproducing a desired sound field, it is possible to improve the ease of installation of speakers and to alleviate restrictions on the direction from which sound waves arrive. [Brief description of the drawings]

[0042] [Figure 1] 1A and 1B are diagrams illustrating examples of speaker arrangement in an embodiment of the present invention. [Diagram 2] FIG. 2 is a diagram illustrating a radiation sound field of a cylindrical sound source. [Diagram 3] FIG. 2 is a diagram illustrating a radiation sound field of a spherical sound source. [Figure 4] FIG. 2 is a diagram illustrating the direction in which a plane wave arrives. [Diagram 5] 1 is a block diagram showing an example of the configuration of a sound field reproduction device according to an embodiment of the present invention. [Figure 6] 4 is a block diagram showing an example of the configuration of a drive signal calculation unit; FIG. [Figure 7] 10 is a flowchart showing an example of processing by a drive signal calculation unit. [Figure 8] FIG. 13 is a block diagram showing an example of the configuration of a sound field reproduction device according to another embodiment of the present invention. [Figure 9] FIG. 1 is a diagram showing an example of speaker array arrangement in wave field synthesis (WFS). [Figure 10] FIG. 1 is a diagram showing an example of speaker array arrangement in boundary sound field control (BoSC). [Figure 11] FIG. 1 is a diagram showing an example of speaker array arrangement in Higher Order Ambisonics (HOA). [Figure 12] FIG. 1 is a diagram showing an example of speaker array arrangement in the spectral division method (SDM). [Figure 13] 1A and 1B are diagrams showing the arrangement of speaker arrays and the reproduced sound field in SDM. [Figure 14] 1 is a diagram showing the arrangement of speaker arrays in an HOA and the reproduced sound field. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0043] Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings. In the embodiment of the present invention, a plurality of cylindrical array speakers are distributed in a cylindrical shape so as to surround a listener, and a plurality of spherical array speakers are distributed to synthesize an arbitrary sound field.

[0044] 1 is a diagram showing an example of speaker arrangement in an embodiment of the present invention. The same applies to other embodiments of the present invention described later. The speakers used in the embodiment of the present invention are configured by distributing one or more cylindrical array speakers 101 on a cylinder, and distributing one or more spherical array speakers 102.

[0045] One or more cylindrical array speakers 101 are distributed on a cylinder and arranged parallel to the longitudinal direction of the cylinder.

[0046] The cylindrical array speaker 101 is configured as a unit in which a plurality of speakers are arranged on a cylinder, and the spherical array speaker 102 is configured as a unit in which a plurality of speakers are arranged on a spherical surface.

[0047] As shown in Figure 1, by distributing one or more unitized cylindrical array speakers 101 on a cylinder and distributing one or more unitized spherical array speakers 102 on a cylinder, a desired sound field can be reproduced, which improves the ease of installation of the speakers and relaxes restrictions on the direction from which sound waves arrive.

[0048] Specifically, it is possible to improve the ease of speaker installation compared to the conventional sound field reproduction method using HOA in which a single speaker is arranged on a spherical surface as shown in Fig. 11. Also, compared to the sound field reproduction method using SDM as shown in Fig. 12, it is possible to relax the restrictions on the arrival direction of reproducible sound waves.

[0049] [Sound field reproduction method / radiation field of a cylindrical sound source] First, a radiation sound field of a cylindrical sound source will be described for the sound field reproduction method according to the embodiment of the present invention. The same applies to other embodiments of the present invention described later. This cylindrical sound source corresponds to one cylindrical array speaker 101 shown in FIG.

[0050] Fig. 2 is a diagram explaining the radiation sound field of a cylindrical sound source. In a space represented by the X-axis, Y-axis, and Z-axis, the global cylindrical coordinate system is (X, Φ, R). X is the distance in the axial direction of the cylinder, Φ is the angle in the radial direction of the cylinder, and R is the radial distance from the X-axis, which is the axis of the cylinder.

[0051] In the global cylindrical coordinate system (X,Φ,R), point R l1 =(0,Φ l1 ,R l1 ) and parallel to the X-axis with radius a l1 There are L1 cylindrical sound sources 104 (l∈[1,L]) arranged at point R l1 =(0,Φ l1 ,R l1The local cylindrical coordinate system around the cylindrical sound source 104 with the origin at (x l1 ,φ l1 ,r l1 ) This cylindrical sound source 104 corresponds to one cylindrical array speaker 101 shown in FIG.

[0052] Local cylindrical coordinate system (x l1 ,φ l1 ,r l1 ) on the cylindrical sound source surface (x l1 ,φ l1 ,a l1 ) the vibration velocity of the cylindrical sound source 104 at angular frequency ω is D l1 (x l1 ,φ l1 ,ω), and then x l1 The cylindrical harmonic spectrum around the axis is Let the file name be TIFF2025039295000039.tif16170. m is the order of the cylindrical harmonic spectrum.

[0053] In this case, any sound receiving point r in the local cylindrical coordinate system l1 =(x l1 ,φ l1 ,r l1 ) sound pressure p l1 (r l1 ,ω) is expressed as follows:

number

[0054] Also, any sound receiving point r in the local cylindrical coordinate system l1 =(x l1 ,φ l1 ,r l1 ) in the global cylindrical coordinate system, l1=R=(X,Φ,R), then by coordinate transformation using the addition theorem of the Hankel function, the sound pressure p l1 (R,ω) is expressed as follows.

number

[0055] The above formula (16) means a formula in which the radiation sound field of the cylindrical sound source 104 is expanded into a cylindrical harmonic spectrum around the X axis at the sound receiving point (X, Φ, R) in the global cylindrical coordinate system. TIFF2025039295000042.tif13170 is represented as follows:

number

[0056] In the above equation (17), the first equation represents the sound field inside the cylindrical sound source 104 in the global cylindrical coordinate system, and the second equation represents the external sound field.

[0057] [Sound field reproduction method / sound field radiation from a spherical sound source] Next, a radiation sound field of a spherical sound source will be described. This spherical sound source corresponds to one spherical array speaker 102 shown in FIG.

[0058] Fig. 3 is a diagram explaining the radiation sound field of a spherical sound source. In a space represented by the X-axis, Y-axis, and Z-axis, the global spherical coordinate system is (Θ, Φ, R). Θ is the elevation angle, Φ is the azimuth angle, and R is the radial distance from the origin.

[0059] In the global spherical coordinate system (Θ,Φ,R), point R l2 SP =(Θ l2 ,Φ l2 ,R l2 ) with radius a l2 There are L2 spherical sound sources 105 (l∈[1,L]) arranged at point R l2 SP =(Θ l2 ,Φl2 ,R l2 The local spherical coordinate system with the origin at (θ l2 ,φ l2 ,r l2 ) This spherical sound source 105 corresponds to one spherical array speaker 102 shown in FIG.

[0060] Local spherical coordinate system (θ l2 ,φ l2 ,r l2 ) on the spherical sound source surface (θ l2 ,φ l2 ,a l2 ) the vibration velocity of the spherical sound source 105 at angular frequency ω is D l2 (θ l2 ,φ l2 ,ω), and the spherical harmonic spectrum around the origin is Let TIFF2025039295000044.tif13170, where n is the degree of the spherical harmonic spectrum and m is the order of the spherical harmonic spectrum.

[0061] In this case, any sound receiving point r in the local spherical coordinate system l2 =(θ l2 ,φ l2 ,r l2 ) sound pressure p l2 (r l2 ,ω) is expressed as follows:

number

[0062] Also, any sound receiving point r in the local spherical coordinate system l2 =(θ l2 ,φ l2 ,r l2 ) in the global spherical coordinate system, l2If =R=(Θ,Φ,R), the sound pressure p l2 (R,ω) is expressed as follows.

number

[0063] In the above formula (19), the transformation coefficient S nν mμ (ω,b),S^ nν mμ The function of (ω, b) is expressed by the following equation.

number

number

[0064] Where: TIFF2025039295000049.tif15170 is the Gaunt coefficient, TIFF2025039295000050.tif15170 is the complex conjugate of the spherical harmonic function.

[0065] The above formula (19) means a formula in which the radiated sound field of the spherical sound source 105 is expanded into a spherical harmonic spectrum around the origin of the global spherical coordinate system at the sound receiving point R=(Θ,Φ,R). TIFF2025039295000051.tif15170 is represented as follows:

number

[0066] In the above formula (22), the first formula represents the sound field inside the spherical sound source 105 in the global spherical coordinate system, and the second formula represents the external sound field. In other words, the above formula (22) represents the spherical harmonic spectrum when the sound field formed by the spherical sound source 105 is divided into an internal sound field and an external sound field at a predetermined spherical boundary.

[0067] (Conversion of spherical harmonic spectrum to cylindrical harmonic spectrum) Here, the spherical harmonic spectrum expressed in the above formula (22) can be converted to a cylindrical harmonic spectrum. The cylindrical harmonic spectrum after conversion is expressed as follows.

number

[0068] For details, please refer to the following non-patent document, which shows that a spherical harmonic spectrum about the origin of a coordinate system can be transformed into a cylindrical harmonic spectrum about the X-axis in a cylindrical coordinate system with the same origin. [Non-patent literature] T. Okamoto, “Angular spectrum decomposition-based 2.5D higher-order spherical harmonic sound field synthesis with a linear loudspeaker array”, 2017 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), New Paltz, NY, USA, 2017, pp. 180-184, doi: 10.1109 / WASPAA.2017.8170019.

[0069] According to the above formulas (22) and (23), the sound field radiated by the spherical sound source 105 having an arbitrary vibration velocity distribution can also be expressed by a cylindrical harmonic domain in the global cylindrical coordinate system.

[0070] [When a sound field containing multiple cylindrical sound sources and multiple spherical sound sources is represented by a cylindrical harmonic domain] Next, we will explain the case where a sound field in which there are multiple cylindrical sound sources 104 shown in Fig. 2 and multiple spherical sound sources 105 shown in Fig. 3 is expressed by a cylindrical harmonic domain. The sound fields formed by each cylindrical sound source 104 and spherical sound source 105 can be unified by a cylindrical coordinate system, and expressed by a cylindrical harmonic domain in the cylindrical coordinate system with the same origin, and can be expressed by the sum of them.

number

[0071] Regarding the above equation (17) which represents the cylindrical harmonic spectrum of the sound field formed by the cylindrical sound source 104, if the order is truncated at m∈[-M,M],m'∈[-M',M'] and expressed as a matrix, it can be expressed as follows.

number

[0072] Where: TIFF2025039295000056.tif25170JPEG2025039295000057.jpg37170JPEG2025039295000058.jpg37170TIFF2025039295000059.tif24170.

[0073] In addition, the above-mentioned equation (22) representing the spherical harmonic spectrum of the sound field formed by the spherical sound source 105 can be expressed as follows when the order is truncated at n∈[0,N],ν∈[0,N'] and expressed as a matrix.

number

[0074] Where: TIFF2025039295000061.tif46170TIFF2025039295000062.tif47170JPEG2025039295000063.jpg90170JPEG2025039295000064.jpg90170.

[0075] Furthermore, the above-mentioned equation (23) representing the cylindrical harmonic spectrum of the sound field formed by the spherical sound source 105 can be expressed as follows when the order is truncated at n∈[0,N],m∈[-M,M] and expressed as a matrix.

number

[0076] From the above formulas (26) and (27), it can be seen that the spherical sound source 105 has a spherical harmonic spectrum centered on the spherical sound source 105. The cylindrical harmonic spectrum in the global coordinate system of the radiated sound field when vibrating with the distribution represented by TIFF2025039295000069.tif12170 can be expressed as follows.

number

[0077] In a radiated sound field in which there are multiple cylindrical sound sources 104 and multiple spherical sound sources 105, the cylindrical harmonic spectrum in the global cylindrical coordinate system can be expressed as follows. This formula is derived from the above formula (24) expressed by the sum of the cylindrical harmonic regions, the above formula (25) expressing the cylindrical harmonic spectrum of the radiated sound field formed by the cylindrical sound sources 104, and the above formula (28) expressing the cylindrical harmonic spectrum of the radiated sound field formed by the spherical sound source 105.

number

number

[0078] Here, equation (29) represents an internal sound field in which sound waves propagate toward the origin of the coordinate system, and equation (30) represents an external sound field in which sound waves propagate in the opposite direction to the origin of the coordinate system.

[0079] Also, the wave number k in the x-axis direction x ∈[-π,π] into Q elements, and the qth element is k x q (q∈[1,Q]). In this case, the above equations (29) and (30) are respectively expressed as k x q The simultaneous equation for (q∈[1,Q]) is as follows.

number

number

[0080] The cylindrical harmonic spectrum of the internal sound field of the desired sound field to be reproduced is TIFF2025039295000075.tif12170, and the cylindrical harmonic spectrum of the external sound field Let's say TIFF2025039295000076.tif12170.

[0081] Vibration distribution of the cylindrical sound source 104 and the spherical sound source 105 that minimizes the square error between the sound field expressed by the above equations (31) and (32) and the desired sound field. TIFF2025039295000077.tif12170 is represented as follows:

number

[0082] The transfer matrix T(ω) is a matrix expressed as follows: TIFF2025039295000079.tif60170

[0083] According to the above equation (33), the vibration velocity distribution of L1 cylindrical sound sources 104 is TIFF2025039295000080.tif13170 and the vibration velocity distribution of L2 spherical sound sources 105 The result is TIFF2025039295000081.tif14170.

[0084] By performing a cylindrical harmonic inverse expansion on the cylindrical sound source 104, the cylindrical sound source surface (x l1 ,φ l1 ,a l1 ) the vibration velocity D of the cylindrical sound source 104 at angular frequency ω l1 (x l1 ,φ l1 In addition, by performing a spherical harmonic inverse expansion on the spherical sound source 105, the spherical sound source surface (θ l2 ,φ l2 ,a l2 ) the vibration velocity D of the spherical sound source 105 at angular frequency ω l2 (θ l2 ,φ l2 ,ω) is obtained.

[0085] The actual cylindrical sound source 104 is made by arranging speakers, which are assumed to be point sound sources, in a cylindrical shape to form a cylindrical array speaker 101.These speakers are regarded as cylindrical sound sources, and a sound field can be reproduced by playing back the vibration velocity corresponding to the coordinates of each speaker element as a driving signal.

[0086] In addition, the actual spherical sound source 105 can also be reproduced by arranging speakers, each of which is assumed to be a point sound source, in a spherical shape to form a spherical array speaker 102, which can be regarded as a spherical sound source and reproduced as a drive signal the vibration velocity corresponding to the coordinates of each speaker element.

[0087] The inverse cylindrical harmonic expansion and the inverse spherical harmonic expansion at the angular frequency ω are expressed by the following equations, respectively, and are expressed in cylindrical coordinates (x l1 ,φ l1 ,a l1 ) and spherical coordinates (θ l2 ,φ l2 ,a l2 ) can be obtained according to the following equation:

number

number

[0088] Here, φ in the cylindrical array speaker 101 l1 The directional resolution depends on the order m of the cylindrical harmonic spectrum, but φ l1 When reproducing a sound field only on the φ = 0 plane, the order m of the cylindrical harmonic spectrum is sufficient as the 0th order (M = 0). In this case, the speaker elements constituting the cylindrical array speaker 101 are φ l1 There is no need to line them up in the x direction. l1 You only need to line them up in the direction.

[0089] That is, the cylindrical array speaker 101 has a frequency of x l1 This can be substituted with a line array speaker in which speaker elements are arranged in the direction, and since M=0, the above equation (34) can be simplified as follows.

number

[0090] The formula (36) is x l1 can be interpreted as the spatial frequency domain inverse Fourier transform of the x direction. In this case, the cylindrical harmonic inverse expansion is l1 can be replaced by the spatial frequency domain inverse Fourier transform of the

[0091] (Example of reproducing a sound field from a point sound source) Next, the desired sound field is defined as point R in the global cylindrical coordinate system. s=(X s ,Φ s ,R s ) will be described as an example of reproducing a sound field in which point sound sources are arranged.

[0092] For a point sound source driven by S(ω) at frequency ω, the cylindrical harmonic spectrum of the desired sound field is given by:

number

[0093] Then, by calculating the cylindrical harmonic spectrum of the drive signal for the cylindrical array speaker 101 and the spherical harmonic spectrum of the drive signal for the spherical array speaker 102 using equation (33), the sound field of a point sound source can be reproduced.

[0094] (Example of reproducing a sound field with incoming plane waves) Next, the desired sound field is in a certain direction Θ s ∈[-π,π],Φ s We will explain an example of reproducing a sound field where a plane wave arrives from ∈[0,2π].

[0095] 4 is a diagram for explaining the direction in which a plane wave arrives. As shown in FIG. 4, in a space represented by the X-axis, the Y-axis, and the Z-axis, the plane wave arrives at an azimuth angle Θ s and elevation angle Φ s It is assumed that the incident light comes from the direction of

[0096] For a plane wave source driven by S(ω) at frequency ω, the cylindrical harmonic spectrum of the desired sound field is given by:

number

[0097] Then, by calculating the cylindrical harmonic spectrum of the drive signal for the cylindrical array speaker 101 and the spherical harmonic spectrum of the drive signal for the spherical array speaker 102 using equation (33), it is possible to reproduce a sound field in which plane waves arrive.

[0098] The above explanation has been given by formulating in continuous time, but when considering implementation on an actual speaker array and computer, it is necessary to perform discretization and truncation to a finite length, and the Fourier transform and inverse transform are replaced with DFT (discrete Fourier transform) (FFT (fast Fourier transform)) and IDFT (inverse discrete Fourier transform) (IFFT (inverse fast Fourier transform)) as appropriate. Also, the order m of the cylindrical harmonic spectrum needs to be handled up to an infinite order in theory, but in practice it is truncated to a finite order.

[0099] The sound pressure signal discretized in the time direction is assumed to be acquired by buffering at a predetermined sampling frequency and buffer size. The sound pressure signal acquired by buffering is windowed with a certain predetermined DFT (FFT) length, and then DFT (FFT) is performed to convert it into the frequency domain. Here, the DFT (FFT) length is set to be longer than the buffer size.

[0100] When a signal is acquired in a stream, the signal may be processed by overlap-adding a predetermined length for each successively acquired buffer size signal. In addition, the shape of the window function is appropriately selected according to the overlap length.

[0101] [Sound field reproduction device] Next, a sound field reproduction device according to an embodiment of the present invention will be described. Fig. 5 is a block diagram showing an example of the configuration of a sound field reproduction device according to an embodiment of the present invention. This sound field reproduction device 1 is a device that realizes the sound field reproduction method described in Fig. 2 and Fig. 3 in the speaker arrangement example shown in Fig. 1, and includes a drive signal calculation unit 10, a cylindrical harmonic inverse expansion unit 11, a spherical harmonic inverse expansion unit 12, and a time-frequency domain inverse Fourier transform unit 13.

[0102] The drive signal calculation unit 10 receives an input of a cylindrical harmonic spectrum about a predetermined axis (x-axis) of a desired sound field truncated at an arbitrary order M. Then, based on the above equation (33), the drive signal calculation unit 10 calculates the cylindrical harmonic spectrum of the drive signal of the cylindrical array speaker 101 and the spherical harmonic spectrum of the drive signal of the spherical array speaker 102. The orders of the cylindrical harmonic spectrum of the drive signal and the spherical harmonic spectrum of the drive signal are set to be the same as the order M of the cylindrical harmonic spectrum of the input desired sound field.

[0103] The drive signal calculation unit 10 outputs the cylindrical harmonic spectrum of the drive signal (cylindrical array speaker drive signal) to the cylindrical harmonic inverse development unit 11, and outputs the spherical harmonic spectrum of the drive signal (spherical array speaker drive signal) to the spherical harmonic inverse development unit 12.

[0104] The cylindrical harmonic inverse development unit 11 inputs the cylindrical harmonic spectrum of the drive signal (cylindrical array speaker drive signal) from the drive signal calculation unit 10. Then, the cylindrical harmonic inverse development unit 11 performs cylindrical harmonic inverse development based on the positions of the sound sources that constitute the cylindrical array speaker 101, thereby calculating the drive signals of the individual sound sources that constitute one or more cylindrical array speakers 101 expressed in the time-frequency domain.

[0105] Specifically, the cylindrical harmonic inverse development unit 11 calculates a φ l1 Direction and x l1 By performing IDFT (Inverse Discrete Fourier Transform) in the direction, driving signals of individual sound sources constituting one or more cylindrical array speakers 101 expressed in the time-frequency domain are calculated.

[0106] The cylindrical harmonic inverse expansion unit 11 outputs the driving signals in the time-frequency domain (cylindrical array speaker driving signals in the time-frequency domain) for each individual sound source constituting one or more cylindrical array speakers 101 to the time-frequency domain inverse Fourier transform unit 13.

[0107] The spherical harmonic inverse expansion unit 12 inputs the spherical harmonic spectrum of the drive signal (spherical array speaker drive signal) from the drive signal calculation unit 10. Then, the spherical harmonic inverse expansion unit 12 performs spherical harmonic inverse expansion on the multiple speakers constituting one or more spherical array speakers 102 based on the positions of the sound sources constituting each of the spherical array speakers 102, thereby calculating the drive signals of the individual sound sources constituting one or more spherical array speakers 102 expressed in the time-frequency domain.

[0108] The spherical harmonic inverse expansion unit 12 outputs the time-frequency domain driving signals (spherical array speaker driving signals in the time-frequency domain) for each individual sound source constituting one or more spherical array speakers 102 to the time-frequency domain inverse Fourier transform unit 13.

[0109] The time-frequency domain inverse Fourier transform unit 13 inputs the time-frequency domain drive signals (cylindrical array speaker drive signals in the time-frequency domain) for each individual sound source that constitutes one or more cylindrical array speakers 101 from the cylindrical harmonic inverse expansion unit 11, and inputs the time-frequency domain drive signals (spherical array speaker drive signals in the time-frequency domain) for each individual sound source that constitutes one or more spherical array speakers 102 from the spherical harmonic inverse expansion unit 12.

[0110] The time-frequency domain inverse Fourier transform unit 13 performs a discrete inverse Fourier transform in the frequency direction on these time-frequency domain drive signals based on a preset sampling frequency and DFT tap number, to calculate time domain speaker drive signals for each individual sound source that constitutes one or more cylindrical array speakers 101, and time domain speaker drive signals for each individual sound source that constitutes one or more spherical array speakers 102.

[0111] The time-frequency domain inverse Fourier transform unit 13 outputs a time-domain speaker drive signal (time-domain cylindrical array speaker drive signal) for each individual sound source constituting one or more cylindrical array speakers 101 to a corresponding speaker unit constituting one or more (L1) cylindrical array speakers 101. In addition, the time-frequency domain inverse Fourier transform unit 13 outputs a time-domain speaker drive signal (time-domain spherical array speaker drive signal) for each individual sound source constituting one or more spherical array speakers 102 to a corresponding speaker unit constituting one or more (L2) spherical array speakers 102.

[0112] (Drive signal calculation unit 10) Next, a detailed description will be given of the drive signal calculation section 10 shown in Fig. 5. Fig. 6 is a block diagram showing an example of the configuration of the drive signal calculation section 10, and Fig. 7 is a flowchart showing an example of the processing performed by the drive signal calculation section 10.

[0113] The drive signal calculation unit 10 includes memories 20 and 21 and a multiplication unit 22. An input unit (not shown) of the drive signal calculation unit 10 receives a cylindrical harmonic spectrum of a desired sound field. TIFF2025039295000087.tif15170 is input (step S701) and stored in the memory 20. The cylindrical harmonic spectrum of the desired sound field is the cylindrical harmonic spectrum of the internal sound field when the sound field is divided into an internal sound field and an external sound field with a predetermined cylindrical boundary as the boundary. TIFF2025039295000088.tif14170 and cylindrical harmonic spectrum of external sound field It consists of TIFF2025039295000089.tif14170.

[0114] The memory 21 also stores the pseudo-inverse matrix T † The pseudo-inverse matrix T of this transfer matrix T(ω) is † is calculated using the transfer matrix T(ω). As mentioned above, the transfer matrix T(ω) is int1 (k x 1 ,ω),···,Tint1 (k x Q ,ω),T int2 (k x 1 ,ω) ,···,T int2 (k x Q ,ω) ,T ext1 (k x 1 ,ω),···,T ext1 (k x Q ,ω),T ext2 (k x 1 ,ω) ,···,T ext2 (k x Q ,ω), is a matrix with 0 as an element.

[0115] And the wave number k in the x-axis direction x 1 ,···,k x Q k x As shown in the above equation (29), the element of the transfer matrix T(ω) is int1 (k x ,ω) is T1(R1,k x ,ω),···,T1(R L1 ,k x ,ω), and T int2 (k x ,ω) is T5(k x ,ω)T3(R1 SP ,ω),···,T5(k x ,ω)T3(R L2 SP , ω). Also, as shown in the above formula (30), T ext1 (k x ,ω) is T2(R1,k x ,ω),···,T2(R L1 ,k x ,ω), and T ext2 (k x ,ω) is T5(k x ,ω)T4(R1 SP ,ω),···,T5(k x ,ω)T4(R L2SP ,ω). Also, T1(R l1 ,k x ,ω),T2(R l1 ,k x ,ω),T3(R l2 SP ,ω),T4(R l2 SP ,ω),T5(k x ,ω) are as described above.

[0116] The multiplication unit 22 proceeds from step S701 to read out the cylindrical harmonic spectrum of the desired sound field from the memory 20 and also reads out the pseudo inverse matrix T of the transfer matrix T(ω) from the memory 21. † is read out (step S702).

[0117] The multiplication unit 22 multiplies the cylindrical harmonic spectrum of the driving signal of the cylindrical array speaker 101 and the spherical harmonic spectrum of the driving signal of the spherical array speaker 102 by D and the cylindrical harmonic spectrum of the desired sound field by P, as shown in the above formula (33): D=T † Using P, we obtain the pseudo-inverse matrix T of the transfer matrix T(ω). † is multiplied by the cylindrical harmonic spectrum P of the desired sound field to obtain the cylindrical harmonic spectrum of the driving signal (wave number k of the driving signal of the cylindrical array speaker 101). x q (Cylindrical harmonic spectrum for q∈[1,Q]) TIFF2025039295000090.tif13170 and the spherical harmonic spectrum of the driving signal TIFF2025039295000091.tif12170 is obtained (step S703).

[0118] Here, the above formula (33) is derived so as to minimize the difference between the sound field of the sum of the cylindrical sound source and the spherical sound source and the desired sound field, by converting the spherical harmonic spectrum representing the sound field of the cylindrical sound source corresponding to the cylindrical array speaker 101 into a cylindrical harmonic spectrum (see the above formula (23)), and by assuming that the sound field of the sum of the cylindrical sound source and the spherical sound source is represented by a cylindrical harmonic spectrum (see the above formula (24)).

[0119] In other words, the above formula (33) is derived so as to minimize the difference between the total sound field due to the cylindrical sound source and the spherical sound source (the sound field obtained by converting the radiation sound field of the cylindrical sound source and the radiation sound field of the spherical sound source into cylindrical harmonic spectra and adding them up) and the desired sound field when the sound field of the cylindrical sound source corresponding to the cylindrical array speaker 101 is expressed by the cylindrical harmonic spectrum shown in the above formula (17), the sound field of the spherical sound source corresponding to the spherical array speaker 102 is expressed by the spherical harmonic spectrum shown in the above formula (22), and the spherical harmonic spectrum of the sound field of the spherical sound source shown in the above formula (22) is expressed by the above formula (23) which is converted into a cylindrical harmonic spectrum.

[0120] In other words, the pseudo-inverse matrix T of the transfer matrix T(ω) † is a matrix derived when the sound field of a cylindrical sound source corresponding to the cylindrical array speaker 101 is represented by a cylindrical harmonic spectrum, and the spherical harmonic spectrum representing the sound field of a spherical sound source corresponding to the spherical array speaker 102 is converted into a cylindrical harmonic spectrum (see equation (23) above), thereby resulting in the sum of the sound field due to the cylindrical sound source and the spherical sound source being represented by a cylindrical harmonic spectrum.

[0121] In other words, the pseudo-inverse matrix T of the transfer matrix T(ω) † is a matrix derived when the sound field of a cylindrical sound source corresponding to the cylindrical array speaker 101 is expressed by the cylindrical harmonic spectrum shown in the above formula (17), the sound field of a spherical sound source corresponding to the spherical array speaker 102 is expressed by the spherical harmonic spectrum shown in the above formula (22), and the spherical harmonic spectrum of the sound field of the spherical sound source shown in the above formula (22) is converted into the cylindrical harmonic spectrum and expressed by the above formula (23).

[0122] The multiplication unit 22 outputs the cylindrical harmonic spectrum of the drive signal (cylindrical array speaker drive signal) to the cylindrical harmonic inverse development unit 11, and outputs the spherical harmonic spectrum of the drive signal (spherical array speaker drive signal) to the spherical harmonic inverse development unit 12 (step S704).

[0123] As described above, according to the sound field reproduction device 1 of the embodiment of the present invention, when generating a drive signal for reproducing a sound field formed by a desired sound source using one or more cylindrical array speakers 101 distributed parallel to the longitudinal direction of a cylinder, and one or more spherical array speakers 102 distributed, the spherical harmonic spectrum representing the sound field of the spherical sound source corresponding to the spherical array speaker 102 is converted into a cylindrical harmonic spectrum, so that the total sound field of the cylindrical sound source corresponding to the cylindrical array speaker 101 and the spherical sound source corresponding to the spherical array speaker 102 is represented by a cylindrical harmonic spectrum, and the cylindrical harmonic spectrum of the drive signal and the spherical harmonic spectrum of the drive signal are calculated using the above equation (33).

[0124] Specifically, the drive signal calculation unit 10 inputs the cylindrical harmonic spectrum of the desired sound field, and calculates the pseudo-inverse matrix T of the preset transfer matrix T(ω) using the above-mentioned equation (33). † by the cylindrical harmonic spectrum of the desired sound field to obtain the cylindrical harmonic spectrum of the drive signal and the spherical harmonic spectrum of the drive signal.

[0125] The cylindrical harmonic inverse expansion unit 11 performs cylindrical harmonic inverse expansion on the cylindrical harmonic spectrum of the drive signal based on the positions of the sound sources that make up one or more cylindrical array speakers 101, specifically by performing a discrete inverse Fourier transform in the x-axis direction and the Φ direction, to obtain drive signals in the time-frequency domain for each individual sound source that makes up one or more cylindrical array speakers 101.

[0126] The spherical harmonic inverse expansion unit 12 performs spherical harmonic inverse expansion on the spherical harmonic spectrum of the drive signal based on the positions of the sound sources that make up the one or more spherical array speakers 102, thereby obtaining drive signals in the time-frequency domain for each of the sound sources that make up the one or more spherical array speakers 102.

[0127] The time-frequency domain inverse Fourier transform unit 13 performs a discrete inverse Fourier transform in the frequency direction on these time-frequency domain drive signals to obtain time domain speaker drive signals for each individual sound source that constitutes one or more cylindrical array speakers 101, and time domain speaker drive signals for each individual sound source that constitutes one or more spherical array speakers 102.

[0128] This improves the ease of speaker installation and relaxes the restrictions on the sound wave arrival direction when reproducing a desired sound field. For example, compared to a conventional sound field reproduction method using HOA in which a single speaker is arranged on a spherical surface, the ease of speaker installation can be improved. Also, compared to a sound field reproduction method using SDM in which the sound wave arrival direction is restricted to the side of the surface on which the planar array speaker is arranged, the restrictions on the sound wave arrival direction that can be reproduced can be relaxed.

[0129] [Sound field reproduction devices / other examples] Next, a sound field reproduction device according to another embodiment of the present invention will be described. In the sound field reproduction device 1 shown in Fig. 5, the cylindrical harmonic spectrum of the desired sound field input to the drive signal calculation unit 10 can be obtained in two ways: by measurement using a microphone array, or by analytical or numerical calculation using a computer.

[0130] A sound field reproduction device according to another embodiment of the present invention is applied to a case where a cylindrical harmonic spectrum is calculated using a computer. The sound field reproduction device according to another embodiment of the present invention has a component for calculating the cylindrical harmonic spectrum of a desired sound field (cylindrical harmonic spectrum calculation unit 14 shown in FIG. 8, which will be described later) provided in front of the drive signal calculation unit 10 shown in FIG.

[0131] Fig. 8 is a block diagram showing an example of the configuration of a sound field reproduction device according to another embodiment of the present invention. This sound field reproduction device 2 is a device that realizes the sound field reproduction method described in Fig. 2 and Fig. 3 in the speaker arrangement example shown in Fig. 1, and includes a cylindrical harmonic spectrum calculation unit 14, a drive signal calculation unit 10, a cylindrical harmonic inverse expansion unit 11, a spherical harmonic inverse expansion unit 12, and a time-frequency domain inverse Fourier transform unit 13.

[0132] Comparing the sound field reproduction device 1 shown in FIG. 5 with the sound field reproduction device 2 shown in FIG. 8, both sound field reproduction devices 1 and 2 have in common the fact that they are equipped with a drive signal calculation unit 10, a cylindrical harmonic inverse expansion unit 11, a spherical harmonic inverse expansion unit 12 and a time-frequency domain inverse Fourier transform unit 13.

[0133] On the other hand, the sound field reproduction device 2 differs from the sound field reproduction device 1 which does not include a cylindrical harmonic spectrum calculation unit 14 in that the sound field reproduction device 2 further includes a cylindrical harmonic spectrum calculation unit 14 in addition to a drive signal calculation unit 10, a cylindrical harmonic inverse expansion unit 11, a spherical harmonic inverse expansion unit 12 and a time-frequency domain inverse Fourier transform unit 13. In Fig. 8, parts common to Fig. 5 are given the same reference numerals as in Fig. 5 and detailed explanations thereof will be omitted.

[0134] When reproducing a sound field due to a point sound source as a desired sound field, the cylindrical harmonic spectrum calculation unit 14 calculates the position R of the point sound source. s =(X s ,Φ s ,R s ), and the sound source signal S(ω) are input, and the cylindrical harmonic spectrum of the desired sound field is calculated based on the above equation (37).

[0135] On the other hand, when reproducing a sound field in which a plane wave arrives, the cylindrical harmonic spectrum calculation unit 14 calculates the direction of arrival of the plane wave (Θ s ,φ s ), and the sound source signal S(ω), and calculates the cylindrical harmonic spectrum of the desired sound field based on the above equation (38). The cylindrical harmonic spectrum calculation unit 14 then outputs the cylindrical harmonic spectrum of the desired sound field to the drive signal calculation unit 10.

[0136] When reproducing a sound field in which a plurality of point sound sources coexist, the cylindrical harmonic spectrum of the desired sound field is determined by adding up the cylindrical harmonic spectra calculated for each condition.

[0137] As described above, according to the sound field reproduction device 2 of another embodiment of the present invention, when reproducing a sound field caused by a point sound source as the desired sound field, the cylindrical harmonic spectrum calculation unit 14 calculates the cylindrical harmonic spectrum of the desired sound field using the above-mentioned equation (37), and when reproducing a sound field where a plane wave arrives, it calculates the cylindrical harmonic spectrum of the desired sound field using the above-mentioned equation (38).

[0138] The drive signal calculation unit 10 , the cylindrical harmonic inverse expansion unit 11 , the spherical harmonic inverse expansion unit 12 and the time-frequency domain inverse Fourier transform unit 13 perform the same processes as those performed by the sound field reproduction device 1 .

[0139] As a result, similar to the above-mentioned sound field reproducing device 1, when reproducing a desired sound field, it is possible to improve the installation of speakers and ease the constraints on the direction of arrival of sound waves. Furthermore, when reproducing a sound field of a point sound source or a sound field where a plane wave arrives, it is possible to obtain the cylindrical harmonic spectrum of the desired sound field by calculating the above formula (37) or (38) using a computer without actually performing measurements using a microphone array. This saves the effort of obtaining the cylindrical harmonic spectrum of the desired sound field.

[0140] Although the present invention has been described above with reference to the embodiments, the present invention is not limited to the above-described embodiments and can be modified in various ways without departing from the technical concept thereof.

[0141] In the above examples, the case of reproducing a sound field of a point sound source, the case of reproducing a sound field where a plane wave arrives, etc. are described. In addition to these, the present invention is also applicable to the case of reproducing a sound field where a plurality of sound sources exist, or the case of reproducing a sound field where a point sound source and a plane wave coexist, and the cylindrical harmonic spectrum of the desired sound field can be obtained by adding up the cylindrical harmonic spectra calculated under each condition.

[0142] The cylindrical array speaker 101 shown in FIG. 1 is configured as a unit in which multiple speakers are arranged on a cylinder. As described above, the cylindrical array speaker 101 is configured as the x l1 In the present invention, the cylindrical array speaker 101 includes a line array speaker.

[0143] A normal computer can be used as the hardware configuration of the sound field reproduction device 1 according to the embodiment of the present invention and the sound field reproduction device 2 according to another embodiment of the present invention. The sound field reproduction devices 1 and 2 are configured by a computer equipped with a CPU, a volatile storage medium such as a RAM, a non-volatile storage medium such as a ROM, an interface, etc.

[0144] The functions of the drive signal calculation unit 10, the cylindrical harmonic inverse expansion unit 11, the spherical harmonic inverse expansion unit 12 and the time-frequency domain inverse Fourier transform unit 13 provided in the sound field reproduction device 1 are each realized by having a CPU execute a program in which these functions are written.

[0145] In addition, each function of the cylindrical harmonic spectrum calculation unit 14, the drive signal calculation unit 10, the cylindrical harmonic inverse expansion unit 11, the spherical harmonic inverse expansion unit 12 and the time-frequency domain inverse Fourier transform unit 13 provided in the sound field reproduction device 2 is realized by having a CPU execute a program describing these functions.

[0146] These programs are stored in the storage medium and are read and executed by the CPU. These programs can also be distributed by storing them in a storage medium such as a magnetic disk (floppy disk, hard disk, etc.), an optical disk (CD-ROM, DVD, etc.), or a semiconductor memory, and can also be transmitted and received via a network. [Explanation of symbols]

[0147] 1,2 Sound field reproduction device 10 Drive signal calculation unit 11 Cylindrical harmonic reverse development section 12 Spherical harmonic inverse expansion part 13 Time-frequency domain inverse Fourier transform section 14 Cylindrical harmonic spectrum calculation section 20,21 Memory 22 Multiplication section 100 Speaker Array 101 Cylindrical array speaker 102 Spherical array speaker 104 Cylindrical Sound Source 105 Sphere sound source

Claims

1. A sound field reproduction device that generates a drive signal for reproducing a sound field formed by a desired sound source using one or more cylindrical array speakers that are distributed in parallel to the longitudinal direction of a cylinder, and one or more spherical array speakers that are distributed in parallel to the longitudinal direction of a cylinder, comprising: a drive signal calculation unit that inputs a cylindrical harmonic spectrum of a desired sound field and calculates a cylindrical harmonic spectrum of a drive signal for the cylindrical array speaker and a spherical harmonic spectrum of a drive signal for the spherical array speaker by a predetermined arithmetic expression; a cylindrical harmonic inverse expansion unit that performs cylindrical harmonic inverse expansion on the cylindrical harmonic spectrum of the driving signal of the cylindrical array speaker calculated by the driving signal calculation unit to obtain a driving signal in a time-frequency domain of the cylindrical array speaker; a spherical harmonic inverse expansion unit that performs a spherical harmonic inverse expansion on the spherical harmonic spectrum of the driving signal of the spherical array speaker calculated by the driving signal calculation unit to obtain a driving signal in a time-frequency domain of the spherical array speaker; a time-frequency domain inverse Fourier transform unit that performs a discrete inverse Fourier transform in the frequency direction on the time-frequency domain drive signals of the cylindrical array speaker obtained by the cylindrical harmonic inverse expansion unit and the time-frequency domain drive signals of the spherical array speaker obtained by the spherical harmonic inverse expansion unit to obtain the time-domain drive signals of the cylindrical array speaker and the time-domain drive signals of the spherical array speaker, The drive signal calculation unit The sound field radiated by a cylindrical sound source corresponding to the cylindrical array speaker is represented by a cylindrical harmonic spectrum, and the spherical harmonic spectrum representing the sound field radiated by a spherical sound source corresponding to the spherical array speaker is converted into a cylindrical harmonic spectrum, so that the total sound field due to the cylindrical sound source and the spherical sound source is represented by a cylindrical harmonic spectrum, The predetermined equation derived to minimize the difference between the sum sound field and the desired sound field: D=T † P(D) is the cylindrical harmonic spectrum of the driving signal of the cylindrical array speaker and the spherical harmonic spectrum of the driving signal of the spherical array speaker, T † is a pseudo-inverse matrix of a transfer matrix, and P is the cylindrical harmonic spectrum of the desired sound field.

2. 2. The sound field reproduction device according to claim 1, The drive signal calculation unit The global cylindrical coordinate system in space is (X, Φ, R) (X is the distance in the axial direction of the cylinder, Φ is the angle in the radial direction of the cylinder, and R is the radial distance from the axis of the cylinder), and the point (0, φ l1 , R l1 ) and parallel to the X-axis with radius a l1 The cylindrical sound source is placed at the point (0, φ l1 , R l1 A local cylindrical coordinate system with the origin at (x l1 , φ l1 , r l1 ) and l1 is the number of the cylindrical sound source, i is the imaginary unit, ρ is the density of air, k is the wave number, k x is the wave number in the x-axis direction, ω is the angular frequency, is the cylindrical harmonic spectrum of the radiation sound field of the cylindrical sound source, m is the order, H m (2) The second kind of Hankel function, H m (2) ' is the derivative of the second Hankel function, J m is the mth order Bessel function, is the cylindrical harmonic spectrum of the vibration velocity of the cylindrical sound source, The global spherical coordinate system in space is (Θ, Φ, R) (Θ is the elevation angle, Φ is the azimuth angle, and R is the radial distance from the origin). l2 SP = (Θ l2 , Φ l2 , R l2 ) with radius a l2 The spherical sound source is disposed at point R l2 SP The local spherical coordinate system with the origin at (θ l2 , φ l2 , r l2 ) and l2 is the number of the spherical sound source, is the spherical harmonic spectrum of the radiated sound field of the spherical sound source, n is the order, m is the rank, h n (2) ' is the derivative of the n-th spherical Hankel function, is the spherical harmonic spectrum of the vibration velocity of the spherical sound source, h q (2) Let q be the two-kind spherical Hankel function, j q (2) is the qth order spherical Bessel function, Y nm is a spherical harmonic function of degree n and order m, the complex conjugate of the spherical harmonic function, is the Gaunt coefficient, and the wave number k x When ∈[-k, k] is divided into Q parts, the q-th element is k x q year, The wave number k of the driving signal of the cylindrical array speaker x q Cylindrical harmonic spectrum for (q ∈ [1,Q]), is a spherical harmonic spectrum of the driving signal of the spherical array speaker, and is a cylindrical harmonic spectrum of the internal sound field when the desired sound field is divided into an internal sound field and an external sound field at a predetermined cylindrical boundary. , the cylindrical harmonic spectrum of the external sound field is The cylindrical harmonic spectrum of the radiation sound field of the cylindrical sound source corresponding to the cylindrical array speaker is expressed by the following formula: The spherical harmonic spectrum when the sound field formed by the spherical sound source corresponding to the spherical array speaker is divided into an internal sound field and an external sound field at a predetermined spherical boundary is expressed by the following formula: (where: (Assuming that.) The spherical harmonic spectrum of the radiated sound field of the spherical sound source is converted into a cylindrical harmonic spectrum as follows: The predetermined arithmetic expression derived so as to minimize the difference between the sound field obtained by converting the radiation sound field of the cylindrical sound source and the radiation sound field of the spherical sound source into cylindrical harmonic spectra and adding them together and the desired sound field, when expressed as As, a cylindrical harmonic spectrum of the desired sound field is input, and a cylindrical harmonic spectrum of a drive signal for the cylindrical array speaker and a spherical harmonic spectrum of a drive signal for the spherical array speaker are calculated by the arithmetic formula.

3. A program for causing a computer to function as the sound field reproduction device according to claim 1.

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