Patent Translate Powered by EPO and Google Notice This translation is machine-generated. It cannot be guaranteed that it is intelligible, accurate, complete, reliable or fit for specific purposes. Critical decisions, such as commercially relevant or financial decisions, should not be based on machine-translation output. DESCRIPTION JP2013150027 Abstract A directional speaker constituting the speaker array to provide a sound field sound collecting playback technique capable of the reproduction of the sound field even any directivity. Is A conversion filter unit 3, the filter F ~ defined by the following equation with respect to the spatial frequency domain signals P ~ when generated based on the signal collected by the microphone array (omega) the (omega) Apply to generate filtered signal D ~ (ω). The spatial frequency inverse transform unit 4 transforms the filtered signal D ~ (ω) into a frequency domain signal by inverse Fourier transform of space. The frequency inverse transform unit 5 transforms the frequency domain signal into a time domain signal by inverse Fourier transform. [Selected figure] Figure 1 Sound field sound collecting and reproducing apparatus, method and program [0001] The present invention relates to a wave field synthesis technique in which a sound signal is collected by a microphone array installed in a certain sound field, and the sound field is reproduced by a speaker array using the sound signal. [0002] For example, Non-Patent Document 1 describes a wave field synthesis technique in which a microphone array installed in a certain sound field picks up a signal and uses that signal to reproduce the sound field with a speaker array. Technology is known. [0003] 09-05-2019 1 In the technology described in Non-Patent Document 1, the filters are configured on the premise that the speakers constituting the speaker array are nondirectional. [0004] Shoichi Koyama, 3 others, "Spatio-temporal frequency domain signal conversion method for sound field collection and reproduction", Proceedings of the Acoustical Society of Japan, September 2011, P. 635-636 [0005] However, in the technology described in Non-Patent Document 1, since the filters constituting the speaker array are non-directional on the premise that the speakers constituting the speaker array are non-directional, the speakers constituting the speaker array are not non-directional. Can not apply the technology described in Non-Patent Document 1. [0006] The purpose of the present invention is to provide a sound field sound collecting and reproducing apparatus, method and program capable of directivity of speakers constituting the speaker array is applied be of any directivity. [0007] In order to solve the above problems, in the sound field collection and reproduction apparatus according to one aspect of the present invention, the microphone array is disposed on the xz plane, j is an imaginary unit, ω is a frequency, and c is a speed of sound. , K = ω / c, kx, n is the wave number in the x-axis direction, n is its index, kz, m is the wave number in the z-axis direction, m is its index, and the three-dimensional free space Green function is x The function of Fourier transform of space in the axial direction and z-axis direction is taken as function G ~, and the pre-measured transfer between the position of the loudspeaker array in the space where the sound field is reproduced and the position away from that position by yref the function of characteristics of the Fourier transform of the space x-axis direction and the z-axis direction as a function G ~ sp, a spatial frequency domain signal P ~ nm when generated based on the signal collected by the microphone array (omega) On the other hand, the filter F ~nm (ω) defined by the following equation is applied to the filtered signal D ~ a conversion filter unit that generates nm (ω); [0008] 09-05-2019 2 [0009] The inverse Fourier transform of the spatial and spatial frequency inverse converting portion for converting filtered signal after D ~ nm to (omega) to the frequency domain signal, and the frequency inverse conversion unit for converting a time domain signal by the inverse Fourier transform a frequency domain signal ,including. [0010] In the sound field collection and reproduction apparatus according to one aspect of the present invention, the microphone array is disposed on the xz plane, j is an imaginary unit, ω is a frequency, c is a speed of sound, k = ω / c, kx the n and the wave number in the x-axis direction, the n and the index, kz, and z-axis direction of the wave number m, the m and the index, 3dimensional free-space Green's function of the space in the x-axis direction and the z-axis direction A function obtained by Fourier transform is taken as a function G ~, and a function obtained by Fourier transform of space in the x-axis direction and z-axis direction is a transfer function measured in advance between the speaker array arranged on the xz plane and the position yref. As a function G ~ sp, a frequency converter for converting a signal collected by the microphone array into a frequency domain signal by Fourier transform, and a space domain frequency domain signal P ~ nm (ω) by Fourier transform of space Space frequency converter to convert to A conversion filter unit to generate a filtered signal after D ~ nm (ω) and apply a filter F ~ nm (ω) defined by the No. following expression for P ~ nm (ω), [0011] [0012] including. In the sound field collection and reproduction apparatus according to one aspect of the present invention, the arrangement direction of the microphone arrays arranged in a straight line is the x axis direction, j is the imaginary unit, ω is the frequency, c is the speed of sound, and k = ω Let / c, kx, n be the wave number in the x-axis direction, n be its index, let the two-dimensional free space Green's function be the Fourier transform of space in the x-axis direction be the function G ~ 2D, and reproduce the sound field The transfer characteristics of the previously measured transfer characteristics between the position of the speaker array in the target space and the position away from the position by yref are subjected to Fourier transform of the space in the x- 09-05-2019 3 axis direction as a function G ~ sp spatial frequency domain signals P ~ n (ω) after filtering the signal by applying a filter F ~ n (ω) which is defined by the following expression for D ~ n (ω when generated based on the sound signal A conversion filter unit that generates [0013] [0014] The inverse Fourier transform of the spatial and spatial frequency inverse converting portion for converting filtered signal after D ~ n the (omega) to the frequency domain signal, and the frequency inverse conversion unit for converting a time domain signal by the inverse Fourier transform a frequency domain signal ,including. [0015] In the sound field collection and reproduction apparatus according to one aspect of the present invention, the arrangement direction of the microphone arrays arranged in a straight line is the x axis direction, j is the imaginary unit, ω is the frequency, c is the speed of sound, and k = ω Let / c, kx, n be the wave number in the x-axis direction, n be its index, let the two-dimensional free space Green's function be the Fourier transform of space in the x-axis direction be the function G ~ 2D, and reproduce the sound field The transfer characteristics of the previously measured transfer characteristics between the position of the speaker array in the target space and the position away from the position by yref are subjected to Fourier transform of the space in the xaxis direction as a function G ~ sp a frequency conversion unit for converting a frequency domain signal by a Fourier transform a sound signal, the Fourier transform of the spatial and spatial frequency transformation unit for converting a frequency domain signal to spatio-temporal frequency domain signal P ~ n (ω), when The spatial frequency domain signal P ~n (ω) is given by A conversion filter unit that generates a filtered signal D ~n (ω) by applying the defined filter F ~n (ω); [0016] [0017] including. [0018] Beforehand by a filter using the measured transfer characteristics can be directional speakers 09-05-2019 4 constituting the speaker array is a reproduction of a sound field be any directivity. [0019] FIG. 1 is a functional block diagram showing an example of a sound field collection and reproduction device according to a first embodiment. FIG. 2 is a view for explaining an example of the arrangement of a microphone array and a speaker array of the sound field collection and reproduction device according to the first embodiment. The flowchart which shows the example of the sound field sound collection reproducing method of 1st embodiment and 2nd embodiment. The figure for demonstrating the measuring method of Gsp of 1st embodiment. The functional block diagram which shows the example of the sound field sound collection reproducing | regenerating apparatus of 2nd embodiment. The figure for demonstrating the example of arrangement | positioning of the microphone array of the sound field sound collection reproducing | regenerating apparatus of 2nd embodiment, and a speaker array. The figure for demonstrating the measuring method of Gsp of 1st embodiment. [0020] Hereinafter, embodiments of the present invention will be described with reference to the drawings. [0021] Sound field sound collection reproducing apparatus and method of the First Embodiment The 09-05-2019 5 first embodiment, as shown in FIG. 2, composed of Nx × Nz pieces of microphones arranged at a position of y = 0 in the first chamber is the two-dimensional microphone array M1-1, M2-1, ..., MNx-Nz and, second chamber composed of Nx × Nz number of speakers arranged in a twodimensional speaker array S1-1, S2-1 , ..., using the SNx-Nz, to reproduce the sound field of the first chamber formed by the sound produced by the sound source S in the second chamber. [0022] Nx and Nz are arbitrary integers. In this embodiment, the microphone array M1-1, M2-1, ..., the number and the speaker array S11 microphone constituting the MNx-Nz, S2-1, ..., the number of speakers constituting the SNx-Nz same It is. Microphone array M1-1, M2-1, ..., microphones Mi-j constituting the MNx-Nz are arranged in a lattice pattern on the xz plane of y = 0. The speakers constituting the speaker arrays S1-1, S2-1,..., SNx-Nz are also arranged in a lattice on the xz plane. Microphone array M1-1, M2-1, ..., and the size of MNx-Nz, speaker array S1-1, S2-1, ..., the magnitude of SNx-Nz is substantially the same. Microphone array M1-1 of the microphones Mi-j, M2-1, ..., position in MNx-Nz is the speaker Si-j of the speaker array S1-1 corresponding to the respective microphones Mi-j, S2-1, ... , SNx-Nz, but may be different. If the positions are the same, the sound field can be reproduced more faithfully. [0023] Let rs = (xi, 0, zj) represent the positions of the microphones constituting the microphone arrays M1-1, M2-1,.. Make it 09-05-2019 6 [0024] Sound field sound collecting and reproducing apparatus of the first embodiment, the frequency conversion unit 1 as shown in FIG. 1, the spatial frequency conversion unit 2, conversion filter unit 3, the spatial frequency inverse transform unit 4, a frequency inverse transform unit 5 and window function For example, the processing of each step illustrated in FIG. 3 is performed. [0025] First chamber of the microphone array M1-1, M2-1, ..., MNx-Nz generates collected sound to signal in the time domain the sound emitted by the sound source S of the first chamber. The generated signal is sent to the frequency converter 1. rs = (xi, 0, zj) the signal at time t in the time domain, which is picked up by the microphone Mi-j of is denoted by pij (t). [0026] The frequency converter 1 converts the signals pij (t) collected by the microphone arrays M1-1, M2-1,..., MNx-Nz into frequency domain signals Pij (.omega.) By Fourier transform (step S1). The generated frequency domain signal P ij (ω) is sent to the spatial frequency converter 2. ω is a frequency. For example, frequency domain signal P ij (ω) is generated by short time discrete Fourier transform. Of course, the frequency domain signal P ij (ω) may be generated by another existing method. 09-05-2019 7 Alternatively, the frequency domain signal Pij (ω) may be generated using a method such as overlap ad. When the input signal is long or when the signal is continuously input as in real time processing, processing is performed every frame, for example, every 10 ms. The frequency domain signal P ij (ω) is defined, for example, as follows. J in the argument of the function exp is an imaginary unit. [0027] [0028] Spatial frequency converter 2, by Fourier transform of the spatial converting frequency domain signal Pij the (omega) the spatio-temporal frequency domain signal P ~ nm (ω) (Step S2). The space-time frequency domain signal P ~nm (ω) is calculated for each ω. The converted space-time frequency domain signal P ~nm (ω) is sent to the conversion filter unit 3. Specifically, the spatial frequency transform unit 2 calculates P to nm (ω) defined by the following equation (1). [0029] [0030] kx, n is the wave number of the x-axis direction, n is the index of the wave number kx, n, kz, m is the wave number of the z-axis direction, m is the index of the wave number kz, m. The wave number is the so-called spatial frequency or angular spectrum. The above equation (1) is an example of conversion to the space-time frequency domain, and Fourier transform of space may be performed by another method. 09-05-2019 8 [0031] Conversion filter unit 3, the spatio-temporal frequency domain signal P ~ nm (omega) by applying a filter F ~ nm (omega) filtering after signal D ~ nm defined by the following equation (2) with respect to (omega) Are generated (step S3). The filtered signal D ~nm (ω) is transmitted to the spatial frequency inverse transform unit 4. [0032] [0033] In the formula (2), G ~ is a function of three-dimensional free-space Green's function to the Fourier transform of the spatial x-axis direction and the z-axis direction representing the ideal transfer characteristic. y ref is a position at which the transfer characteristics are matched. More specifically, yref, as shown in FIG. 2, the speaker array S1-1, S2-1, ..., represent the distance between the linear position to match the amplitude of the signal to reproduce the SNx-Nz. G ~ sp is the position of the speaker array of the space sound field can be reproduced with the spatial Fourier transform of the previously measured transfer characteristics in the x-axis direction and the z-axis direction between a position spaced yref from that position Function. [0034] The spatial frequency inverse transform unit 4 transforms the filtered signal D ~nm (ω) into a frequency domain signal Dij (ω) by inverse Fourier transform of space (step S 4). The converted frequency domain signal Dij (ω) is sent to the frequency inverse transform unit 5. Spatial frequency inverse transform unit 4, specifically calculated defined as a frequency domain signal Dij (omega) by the following equation (3). [0035] 09-05-2019 9 [0036] The frequency inverse transform unit 5 transforms the frequency domain signal Dij (ω) into a time domain signal P <d> ij (t) by inverse Fourier transform (step S5). The time domain signal P <d> ij (t) obtained for each frame by the inverse Fourier transform is appropriately shifted and linearly summed to be a continuous time domain signal. As the inverse Fourier transform, an existing method such as a short time discrete inverse Fourier transform may be used. The time domain signal P <d> ij (t) is sent to the window function unit 6. [0037] The window function unit 6 multiplies the time domain signal P <d> ij (t) by the window function to generate a post-window function time domain signal dij (t) (step S6). Window function after a time-domain signal dij (t) is the speaker array S1-1, S2-1, ..., sent to SNx-Nz. [0038] For example, a so-called Tukey window function wij defined by the following equation is used as a window function. Ntpr is a score to which a taper is applied, and is an integer of 1 or more and Nx and Nz or less. Of course, other window functions may be used. [0039] [0040] Speaker array S1-1, S2-1, ..., SNx-Nz reproduces sound based on the post-window function time domain signal dij (t). 09-05-2019 10 Specifically, the speaker Si-j reproduces the sound based on the time-domain signal after the window function dij (t) as i = 1,..., Nx, j = 1,. Thereby, the wave front at the position y = 0 of the first room is reproduced by the speaker arrays S1-1, S2-1,..., SNx-Nz of the second room, and the sound field of the first room is It can be reproduced in two rooms. [0041] If the number of microphones constituting the microphone array is larger than the number of speakers constituting the speaker array, the time-domain signal dij (t) may be thinned after the window function. On the other hand, when the number of microphones constituting the microphone array is smaller than the number of speakers constituting the speaker array, the interpolation may be performed by averaging the time domain signal dij (t) after the window function. . [0042] Hereinafter, the reason why the filter F to nm (ω) is expressed as the above equation (2) will be described. [0043] The position vector of the reproduction area is r = (x, y, z), and the position vector of the secondary sound source plane is r0 = (x0, 0, z0). Assuming that the sound pressure distribution of the frequency ω in the reproduction region is P (r, ω) and the drive signal of the secondary sound source is D (r0, ω), the following relational expression can be written. [0044] [0045] Here, Gsp (r−r0, ω) is a transfer function between r and r0. 09-05-2019 11 Fourier transform of space in the x-axis direction and y-axis direction of equation (4) gives the following. [0046] [0047] Here, kx and kz represent the spatial frequency in the x-axis direction and the spatial frequency in the z-axis direction, respectively. Moreover, the spatial frequency domain is shown by "<->". Here, the Fourier transform of space is defined as follows. [0048] [0049] Next, the first kind of Rayleigh integration is introduced as an ideal sound field. [0050] [0051] Here, G (r−r 0, ω) is a three-dimensional free space Green's function. [0052] [0053] Here, k = ω / c is the wave number and c is the speed of sound. 09-05-2019 12 When this equation is subjected to space Fourier transform, the following equation is obtained. [0054] [0055] ここで、 [0056] [0057] である。 By the equations (5) and (6), the drive signal of the secondary sound source is obtained as follows. [0058] [0059] At this time, G ~ sp (kx, y, kz, ω) Since it is unknown, it is necessary to obtain the actual measurement. [0060] Here, a concrete filter design method is considered. Let G be an ideal transfer characteristic from the origin to a planar grid point rij = (xi, yref, zj) (1 ≦ i ≦ Nx, 1 ≦ j ≦ Ny), and the transfer characteristic obtained by measurement be Gsp I 09-05-2019 13 assume. Here, a single frequency ω is considered as a transfer characteristic converted to the time frequency domain using FFT or the like. G, Gsp is a matrix of Nx × Ny, each element is a transfer characteristic to each point rij at frequency omega. Therefore, the (i, j) th element Gij of G can be written as follows. [0061] [0062] Similarly, the (i, j) th element Gsp, ij of Gsp can be written as follows. [0063] [0064] Gsp (rij, ω) represents the measured transfer characteristic up to rij. In the measurement of the speaker characteristics, as shown in FIG. 4, the speakers Sp are disposed at the positions of the speaker arrays S1-1, S2-1,..., SNx-Nz of the second room which is a space where the sound field is reproduced. a planar microphone array Ma placed in position in front y = yref from its position, after the measurement of the impulse response, it may be converted into the frequency domain. [0065] Then, into a spatio-temporal frequency domain representation G ~ and G ~ sp with the G and Gsp like DFT or FFT. 09-05-2019 14 [0066] [0067] DFT is an Nx × Ny two-dimensional discrete Fourier transform. Therefore, elements corresponding to the spatial frequencies of G to G can be substituted into equation (2). In this case, because only one characteristic for the filter expression is required, some speaker characteristic measured may be things like taking the average of them. Further, although the positional relationship between the microphone array and the speaker used for measurement may be any form, calculating G ~ sp and G ~ with the same positional relationship will increase the stability of the filter. Also, zero padding may be performed in each frequency conversion. [0068] As described above, by constructing the filter using the transfer characteristic measured in advance, it is possible to reproduce the sound field even if the directivity of the speaker constituting the speaker array is any directivity. [0069] Second Embodiment As shown in FIG. 6, in the sound field collection and reproduction apparatus and method of the second embodiment, Nx linearly arranged at the position of y = 0, z = 0 in the first room One-dimensional microphone arrays S1, S2,..., SNx consisting of one-dimensional microphone arrays M1, M2,..., MNx consisting of individual microphones and Nx speakers arranged linearly in the second room with bets, to reproduce the sound field of the first chamber formed by the sound produced by the sound source S in the second chamber. 09-05-2019 15 Compared to the first embodiment, it is possible to reduce the number of microphones, speakers and the number of the number of channels, implementation is relatively easy. [0070] Nx is an arbitrary integer. In this embodiment, the number of microphones configuring the microphone arrays M1, M2,..., MNx is the same as the number of speakers configuring the speaker arrays S1, S2,. Microphone array M1, M2, ..., microphone Mi constituting the MNx are equally spaced. Further, the speakers constituting the speaker arrays S1, S2,..., SNx are also arranged at equal intervals. The size of the microphone arrays M1, M2,..., MNx and the size of the speaker arrays S1, S2,. It is preferable that the positions of the microphones Mi in the microphone arrays M1, M2, ..., MNx are the same as the positions in the speaker arrays S1, S2, ..., SNx of the speakers Si corresponding to the respective microphones Mi. Also good. If the positions are the same, the sound field can be reproduced more faithfully. [0071] The positions of the microphones constituting the microphone arrays M1, M2,..., MNx arranged at the y = 0, z = 0 positions of the first room are represented by rs = (xi, 0, 0). [0072] The sound field sound collecting and reproducing apparatus according to the second embodiment includes, as shown in FIG. For example, the processing of each step illustrated in FIG. 3 is performed. 09-05-2019 16 [0073] The microphone arrays M1, M2,..., MNx arranged at the y = 0, z = 0 positions of the first room pick up the sound emitted by the sound source S of the first room and generate a time domain signal. Generate The generated signal is sent to the frequency converter 1. rs = (xi, 0,0) a signal at time t of the picked-up time domain microphone Mi of is denoted by pi (t). [0074] The frequency converter 1 converts the signal pi (t) collected by the microphone arrays M1, M2,..., MNx into a frequency domain signal Pi (ω) by Fourier transformation (step S1). The generated frequency domain signal Pi (ω) is sent to the spatial frequency converter 2. ω is a frequency. For example, the frequency domain signal Pi (ω) is generated by short time discrete Fourier transform. Of course, the frequency domain signal Pi (ω) may be generated by another existing method. Alternatively, the frequency domain signal Pij (ω) may be generated using a method such as overlap ad. When the input signal is long or when the signal is continuously input as in real time processing, processing is performed every frame, for example, every 10 ms. The frequency domain signal Pi (ω) is defined, for example, as follows. J in the argument of the function exp is an imaginary unit. [0075] [0076] The spatial frequency transform unit 2 transforms the frequency domain signal Pi (ω) into the space-time frequency domain signal P ~n (ω) by Fourier transform of space (step S 2). The space-time frequency domain signals P ~n (ω) are calculated for each ω. The converted 09-05-2019 17 space-time frequency domain signals P to n (ω) are sent to the conversion filter unit 3. Spatial frequency converter 2, in particular to calculate the P ~ n (omega) which is defined by the following equation (7). [0077] [0078] kx, n is a wave number in the x-axis direction, and n is an index of the wave number kx, n. The wave number is the so-called spatial frequency or angular spectrum. The equation (7) is an example of a conversion to the spatio-temporal frequency domain may be performed a Fourier transform of the space by the other methods. [0079] The conversion filter unit 3 applies the filter F to n (ω) defined by the following equation to the space-time frequency domain signal P to n (ω) to generate a post-filtering signal D to n (ω) (Step S3). The post-filtering signals D to n (ω) are transmitted to the spatial frequency inverse transform unit 4. [0080] [0081] In equation (8), G ~2D is a function obtained by performing Fourier transform of space in the xaxis direction on a two-dimensional free space Green's function representing an ideal transfer characteristic. y ref is a position at which the transfer characteristics are matched. More specifically, as shown in FIG. 6, yref represents the distance between the speaker array S1, S2,..., SNx and the linear 09-05-2019 18 position where the amplitude of the signal to be reproduced is adjusted. G ~ sp is a function obtained by performing Fourier transform of space in the x-axis direction on the pre-measured transfer characteristic between the position of the speaker array in the space where the sound field is reproduced and the position away from the position by yref . [0082] The spatial frequency inverse transform unit 4 transforms the post-filtering signals D to n (ω) into a frequency domain signal Di (ω) by inverse Fourier transform of space (step S 4). The converted frequency domain signal Di (ω) is sent to the frequency inverse transform unit 5. Spatial frequency inverse transform unit 4, specifically calculated defined as a frequency domain signal Di (omega) by the following equation (9). [0083] [0084] The frequency inverse transform unit 5 transforms the frequency domain signal Di (ω) into a time domain signal P <d> i (t) by inverse Fourier transform (step S5). The time domain signal P <d> i (t) obtained for each frame by the inverse Fourier transform is appropriately shifted and linearly summed to be a continuous time domain signal. As the inverse Fourier transform, an existing method such as a short time discrete inverse Fourier transform may be used. The time domain signal P <d> i (t) is sent to the window function unit 6. [0085] The window function unit 6 multiplies the time domain signal P <d> i (t) by the window function to generate a post-window function time domain signal di (t) (step S6). The post-window function time domain signal di (t) is sent to the loudspeaker arrays S1, S2, ..., SNx. [0086] 09-05-2019 19 For example, a so-called Tukey window function wi defined by the following equation is used as a window function. Ntpr is a score to which a taper is applied, and is an integer of 1 or more and Nx or less. Of course, other window functions may be used. [0087] [0088] The speaker arrays S1, S2,..., SNx reproduce sound based on the window function after time domain signal di (t). Specifically, the speaker Si reproduces a sound based on the window function after time domain signal di (t) as i = 1,..., Nx. [0089] Thereby, the wave front at the position y = 0 of the first room is reproduced by the speaker arrays S1, S2, ..., SNx of the second room, and the sound field of the first room is reproduced in the second room be able to. [0090] At this time, the amplitudes of the reproduced signals match at the position on the straight line represented by yref. Specifically, as shown in FIG. 6, the speaker array S1, S2,..., SNx has the same height, and is spaced from the speaker array S1, S2,. The amplitudes coincide at positions on a straight line parallel to the straight line where S2, ..., SNx are arranged. [0091] 09-05-2019 20 When the number of microphones constituting the microphone array is larger than the number of speakers constituting the speaker array, the time-domain signal di (t) may be thinned after the window function. On the other hand, when the number of microphones constituting the microphone array is smaller than the number of speakers constituting the speaker array, interpolation may be performed by averaging the time domain signal di (t) after the window function. . [0092] Hereinafter, the reason why the filters F to n (ω) are expressed as the above equation (8) will be described. [0093] Consider reproducing only on the xy plane using a linear array. The position vector of the reproduction region is r = (x, y, 0), and the position vector of the secondary sound source plane is r0 = (x 0, 0, 0). Assuming that the sound pressure distribution of the frequency ω in the reproduction region is P (r, ω) and the drive signal of the secondary sound source is D (r0, ω), the following relational expression can be written. [0094] [0095] Here, Gsp (r−r0, ω) is a transfer function between r and r0. Fourier transform of space in the x-axis direction of equation (10) gives the following. [0096] 09-05-2019 21 [0097] Here, kx represents the spatial frequency in the x-axis direction. Moreover, the spatial frequency domain is shown by "<->". Here, the Fourier transform of space is defined as follows. [0098] [0099] Next, we introduce a two-dimensional first-class Rayleigh integral. [0100] [0101] ここで、 [0102] [0103] である。 k = ω / c is the wave number and c is the speed of sound. H0 <(2)> is a second Hankel function of n = 0. The second Hankel function Hn <(2)> is defined as follows using the first Bessel function Jn (x) and the second Bessel function Yn (x). 09-05-2019 22 [0104] [0105] By applying equation (12) to space Fourier transform, the following equation is obtained. [0106] [0107] ここで、 [0108] [0109] である。 Therefore, the drive signal of the secondary sound source is obtained as follows. [0110] [0111] At this time, since G ~sp (kx, y, ω) is unknown, it needs to be obtained by measurement as in the case of the planar array. [0112] Here, a concrete filter design method is considered. 09-05-2019 23 An ideal transfer characteristic from the origin to a linear grid point ri = (xi, yref, 0) (1 ≦ i ≦ Nx) is G2D, and a transfer characteristic obtained by measurement is Gsp. Here, a single frequency ω is considered as a transfer characteristic converted to the time frequency domain using FFT or the like. Gsp is a vector of 1 × Nx, and each element is a transfer characteristic up to each point ri at the frequency ω. Therefore, the ith element G2D, i of G2D can be written as follows. [0113] [0114] Similarly, the ith element Gsp, i of Gsp can be written as follows. [0115] [0116] Gsp (ri, ω) represents the measured transfer characteristic up to ri. In the measurement of the speaker characteristics, as shown in FIG. 7, the speakers Sp are arranged at the positions of the speaker arrays S1, S2,..., SNx of the second room which is a space in which the sound field is reproduced. A linear microphone array Ma may be installed at the position of yref, and the impulse response may be measured and then converted to the frequency domain. [0117] Next, G2D and Gsp are converted into space-time frequency domain representations G2D and 09-05-2019 24 Gsp ~ using DFT, FFT, or the like. [0118] [0119] DFT is Nx one-dimensional discrete Fourier transform. Therefore, elements corresponding to the spatial frequencies G to 2D and Gsp ~ may be substituted into equation (8). At this time, since only one characteristic is required in the filter equation, some speaker characteristics may be measured and their average may be taken. Further, although the positional relationship between the microphone array and the speaker used for measurement may be any form, calculating G ~2D and G ~sp with the same positional relationship increases the stability of the filter. Moreover, you may perform zero padding etc. in each frequency conversion. As described above, by constructing the filter using the transfer characteristic measured in advance, it is possible to reproduce the sound field even if the directivity of the speaker constituting the speaker array is any directivity. [0120] [Modifications, etc.] In the first embodiment, the microphone arrays M1-1, M2-1, ..., MNx-Nz and the speaker arrays S1-1, S2-1, ..., SNx-Nz are not arranged in a straight line. It does not have to be on the plane if it is. [0121] 09-05-2019 25 The number of microphones constituting the microphone array may be different from the number of speakers constituting the speaker array. If the number of microphones constituting the microphone array is larger than the number of speakers constituting the speaker array, the output signals of the speakers may be thinned out. On the other hand, when the number of speakers constituting the speaker array is larger than the number of microphones constituting the microphone array, interpolation may be performed such as averaging the output signals of the speakers. [0122] Each part constituting the sound field sound collecting and reproducing apparatus may be provided in either the sound collecting apparatus arranged in the first room or the reproducing apparatus arranged in the second room. In other words, processing of each of the frequency conversion unit 1, the space frequency conversion unit 2, the conversion filter unit 3, the space frequency inverse conversion unit 4, the frequency inverse conversion unit 5, and the window function unit 6 is arranged in the first room It may be performed by the sound collection apparatus, or may be performed by the reproduction apparatus arranged in the second room. The signal generated by the sound collection device is transmitted to the reproduction device. [0123] The positions of the first room and the second room are not limited to those shown in FIGS. 2 and 6. The first room and the second room may be adjacent or separated from each other. Also, the orientation of the first room and the second room may be any. [0124] 09-05-2019 26 The processing of the window function by the window function unit 6 may be performed at any stage, or may be performed in multiple stages. That is, the window function unit 6 is between the microphone array and the frequency conversion unit 1, between the frequency conversion unit 1 and the spatial frequency conversion unit 2, between the spatial frequency conversion unit 2 and the conversion filter unit 3, and a conversion filter unit It may be provided between at least one of the space frequency inverse transform unit 4 and the space frequency inverse transform unit 5. When processing of the window function is performed on the signal input to each part of each part of the sound field collection and reproduction device, processing of the window function is performed in the same manner as described above instead of the input signal. Process the signal after the [0125] In addition, the window function unit 6 may be omitted. In this case, in the first embodiment, the speaker Si-j reproduces the sound based on the time domain signal P <d> ij (t) as i = 1,..., Nx, j = 1,. In the second embodiment, the speaker Si reproduces sound based on the time domain signal P <d> i (t) as i = 1,. [0126] As long as the sound field sound collecting and reproducing apparatus includes the conversion filter unit 3, it does not have to include other units. For example, the sound field sound collection and reproduction apparatus may be configured of the conversion filter unit 3, the spatial frequency inverse conversion unit 4, and the frequency inverse conversion unit 5. Further, the sound field sound collecting and reproducing apparatus may be configured of the frequency conversion unit 1, the spatial frequency conversion unit 2, and the conversion filter unit 3. [0127] The processing of the frequency conversion unit 1 and the processing of the spatial frequency conversion unit 2 may be performed simultaneously. Similarly, the process of the spatial frequency inverse transform unit 4 and the process of the frequency inverse transform unit 5 may be performed simultaneously. Also, the space frequency conversion unit 2 and the space 09-05-2019 27 frequency inverse conversion unit 4 may be interchanged. [0128] The sound field sound collecting and reproducing apparatus can be realized by a computer. In this case, the processing content of each part of this apparatus is described by a program. And each part in this apparatus is implement | achieved on a computer by running this program by computer. [0129] The program describing the processing content can be recorded in a computer readable recording medium. Further, in this embodiment, these devices are configured by executing a predetermined program on a computer, but at least a part of the processing contents may be realized as hardware. [0130] 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. [0131] Reference Signs List 1 frequency conversion unit 2 space frequency conversion unit 3 conversion filter unit 4 space frequency inverse conversion unit 5 frequency inverse conversion unit 6 window function unit 09-05-2019 28

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