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 JP2017034442 Abstract: To improve control degree of control of sound field. A plurality of high-order sound sources for reproducing an acoustic signal with a "reproduction pattern" comprising at least a part of a plurality of radiation modes independent of one another or a plurality of radiation modes having different directivity patterns. Use The plurality of high-order sound sources are arranged on the circumference. The reproduction pattern is one in which the weight of each of the radiation modes is controlled in order to generate a desired sound field in a plurality of spatial regions. [Selected figure] Figure 1 Sound field reproduction apparatus and method thereof [0001] The present invention relates to sound field reproduction technology, and more particularly to space multi-zone sound field reproduction technology. [0002] Spatial multi-zone sound field reproduction is a technology for reproducing a plurality of independent sound fields in a separated space by driving a speaker array (see, for example, NonPatent Document 1). In the prior art, in order to reproduce the sound field in a plurality of areas, a circular array is used in which nondirectional speakers are arranged in a circle at equal intervals so as to 03-05-2019 1 surround the reproduction area. In order to accurately reproduce the sound field up to wave number k within the circumference of radius R by the conventional circular array, 2kR + 1 or more huge number of speakers are required. [0003] Y. J. Wu, et al. Spatial Multizone Soundfield Reproduction: Theory and Design, "Speech and Audio Processing, IEEE Transactions on 19.6 (2011): 1711-1720. [0004] However, the conventional configuration has a problem that the degree of freedom in controlling the sound field is low. An object of the present invention is to improve the control freedom of the sound field. [0005] A plurality of high-order sound sources for reproducing an acoustic signal with a reproduction pattern are used, which are composed of any one of a plurality of mutually independent radiation modes having different directivity patterns or at least a part of a plurality of radiation modes. The plurality of high-order sound sources are arranged on the circumference. The reproduction pattern is one in which the weight of each of the radiation modes is controlled in order to generate a desired sound field in a plurality of spatial regions. [0006] In the present invention, since the weight of each of the radiation modes of the high-order sound source is controlled, it is possible to improve the control freedom of the sound field as compared to the prior art. [0007] FIG. 1 is a conceptual diagram for explaining the configuration of the sound field reproduction 03-05-2019 2 apparatus according to the first embodiment. FIG. 2 is a block diagram illustrating the control unit of the embodiment. FIG. 3 is a geometrical diagram of Theorem 1. FIGS. 4A and 4B are conceptual diagrams for explaining the configuration of the sound field reproduction apparatus according to the second and third embodiments. [0008] Hereinafter, embodiments of the present invention will be described. [Summary] In this embodiment, sound field reproduction is performed using a plurality of higher order sources arranged on the circumference. An example of a high-order sound source is a high-order speaker (for example, reference 1 M. Poletti, T. Betlehem, Design of a prototype variable directivity loudspeaker for improved surround sound reproduction in rooms, AES 52nd See International Conference, Guildford, UK, 2013, September 2-4. Each higher-order sound source reproduces an acoustic signal with a reproduction pattern consisting of at least a part of a plurality of radiation modes independent of one another or a plurality of radiation modes having different directivity patterns (linear sum) . The "reproduction pattern" is one in which the respective weights of the radiation modes are controlled to generate a desired sound field in a plurality of spatial regions. Thereby, the control freedom of the sound field can be improved as compared with the conventional case. For example, in the case of using a circular array in which high-order sound sources of order N are arranged in a circle, using the circular array of a conventional nondirectional speaker with the same radius of the circle containing the plurality of spatial regions. And the external sound field of the circular array can be sufficiently suppressed while reproducing the sound field of about N times the bandwidth with high accuracy. Further, when the external sound field is not suppressed, a sound field with a bandwidth of about 2N can be reproduced with high accuracy. [0009] In the case of controlling only the internal sound field of a circular array, for example, the solution or approximation of w <(0)> n, u (k) that satisfies for m ∈ [-MI (k), MI (k)] Let a solution pattern be a filter weight for the radiation mode m (n) at the wave number k of the high-order sound source hs (u) be a reproduction pattern . However, M I (k) is a positive integer, and [−M I (k), M I (k)] is a closed interval consisting of an integer of −M I (k) or more and M I (k) or less, "Plural higher-order sound sources" are L high-order sound sources hs (1), ..., hs (L), L is a positive integer, and "multiple radiation modes" is 2N + 1 radiation modes m (-N), ..., m (N), N is a 03-05-2019 3 positive integer, u = 1, ..., L, n =-N, ..., N, k is the wave number, and R is A value representing the magnitude of the high-order sound source hs (u) (for example, the radius of the next sound source hs (u) or its approximation value), and R L represents the radius of the circumference on which a plurality of high-order sound sources are arranged H 表 す (·) is a kind of Hankel function of the order ', H ′ ι (·) is a derivative (differential) of the Hankel function H ι (·), and i is an imaginary unit And e is The polar number coordinates of an area including a plurality of spatial areas in which a desired sound field is generated, where is the number of Ipia, θ u is a declination of the high-order sound source hs (u) with respect to the origin, and β <d> m (k) It is an expansion coefficient with respect to m of the frequency domain signal S <d> (r, θ; k) of the wavenumber k at (r, θ). [0010] In the case of controlling only the external sound field of a circular array, for example, the solution or approximation of w <(1)> n, u (k) that satisfies for m ∈ [−ME (k), ME (k)] Let a solution pattern be a filter weight for the radiation mode m (n) at the wave number k of the highorder sound source hs (u) be a reproduction pattern . However, M E (k) is a positive integer, and [−M E (k), M E (k)] is a closed interval consisting of an integer of −M E (k) or more and M E (k) or less, J ι (·) is a Bessel function of order ι, and γ <d> m (k) is the frequency domain signal S <d of wave number k at polar coordinates (r, θ) of the region where the desired sound field is generated The expansion coefficient for m of (r, θ; k). [0011] In the case of simultaneous control of the internal and external sound fields of a circular array, for example, the element w <(2)> n, u (k) for solution or approximate solution of satisfying w <(2)> (k) Let n =-N, ..., N, u = 1, ..., L) be the filter weights for the radiation mode m (n) at wave number k of the high-order sound source hs (u) as the "reproduction pattern" . Denoting G (k) w <(0)> (k) = β <d> (k) for m ∈ [-MI (k), MI (k)], G (k) It is a matrix of 2M I (k) +1) × L (2N + 1), and w <(0)> (k) is L (2N + 1) w <(0)> n, u (where n = −N, ..., N, u = 1, ..., L), and (·) <T> is the transpose of (·), and m ∈ [-M E (k), M E ( k)] is written as J (k) w <(1)> (k) = γ <d> (k), and J (k) is (2M E (k) +1) × L (2N + 1) It is a matrix, and w <(1)> (k) is L (2N + 1) w <(1)> n, u (k) (where n = −N,..., N, u = 1,..., L) and is a vertical vector. [0012] 03-05-2019 4 First Embodiment A first embodiment will be described with reference to the drawings. <Configuration> As illustrated in FIG. 1, the sound field reproduction device 1 of this embodiment includes a control unit 11 and L high-order sound sources (high-order speakers) 12-u arranged on the circumference. u = 1,..., L). Each higher-order sound source 12-u is placed, for example, under an anechoic environment or an environment close to it. However, each higher-order sound source 12-u may be arranged in a reverberant environment. As illustrated in FIG. 2, the control unit 11 includes a storage unit 111, a weight acquisition unit 112, a filtering unit 113-u, and a drive signal generation unit 114-u. The control unit 11 is, for example, a general-purpose or dedicated computer including a processor (hardware processor) such as a CPU (central processing unit) and a memory such as a RAM (random-access memory) and a ROM (read-only memory). It is configured by executing a predetermined program. The computer may have one processor or memory, or may have a plurality of processors or memory. This program may be installed in a computer or may be stored in advance in a ROM or the like. Further, instead of an electronic circuit (circuitry) that realizes a functional configuration by reading a program like a CPU, a part or all of the processing units are configured using an electronic circuit that realizes a processing function without using a program. May be Also, the electronic circuit that constitutes one device may include a plurality of CPUs. 1 and 2 are examples of L = 15, but this does not limit the present invention. [0013] << Geometrical Arrangement >> A two-dimensional global (global) space area and S twodimensional local non-overlapping desired two-dimensional space areas (circular areas) 14-1, ..., 14 Let's assume -S and the corresponding desired sound field. However, S is an integer of 2 or more. The radius and origin of the s-th (where s = 1,..., S) space region 14-s is expressed by R z <(s)> and O s, respectively. Here, O s is located at polar coordinates (r <(s0)>, θ <(s0)>) with respect to the global origin O. r <(s0)> and θ <(s0)> represent a radius of curvature and a declination, respectively. The local polar coordinates of an arbitrary observation point in the s-th space region 14-s are expressed as (R <(s)>, Ω <(s)>). (R <(s)>, Ω <(s)>) are polar coordinates centered on the local origin O s, and R <(s)> and Ω <(s)> are the radius and declination, respectively Represents The local polar coordinates (R <(s)>, Ω <(s)>) are located at polar coordinates (r, θ) with respect to the global origin O. r and θ represent the radius and the declination, respectively. All spatial regions 14-1, ..., 14-S lie in a circular region of radius R P r r around the global origin O. R p is the radius of the circular area including all spatial areas 14-1, ..., 14-S inside. The L high-order sound sources 12-u are arranged on the circumference of radius R L ≧ R P from the global origin O. The high-order sound sources 12-1, ..., 12-L may be arranged at equal intervals, or may not be arranged at equal intervals. L is a positive integer, for example, L is an integer of 2 or more. 03-05-2019 5 [0014] << Cylindrical Harmonic Expansion of Internal / External Sound Field >> In the region r <R L, the time frequency domain signal S (r, θ; k) of the internal sound field at the wavenumber k of the polar coordinate (r, θ) with respect to the origin O Deployment is as follows. However, r and θ indicate the radius and the declination, respectively. A m (k) is an expansion coefficient (sound field coefficient) for m to uniquely represent S (r, θ; k), and m is an integer. [0015] The expansion of the time frequency domain signal S (r, θ; k) of the external sound field at polar coordinates (r, θ) with respect to the origin O in the region r> R L is as follows. However, B m (k) is an expansion coefficient (sound field coefficient) for m to uniquely represent S (r, θ; k). H m (·) is a first kind of Hankel function of order m. [0016] << Plane wave expansion coefficient >> A time-frequency domain signal S <<< at wave number k in polar coordinates (R <(s)>, Ω <(s)>) representing a plane wave propagating from the direction of vector r s <→> d (s)> (R <(s)>, Ω <(s)>; k) is expressed as follows. Note that → of rs → →> should originally be written directly above rs as in equation (3), but due to the restrictions of the description notation, → should be r It is written in the upper right of "s". By the Jacobi-Anger expansion, equation (3) can be transformed as follows. Where θ s is the angle of the vector r s <→> in polar coordinates. That is, r s <→> = (rs s cos θ s, r s sin θ s), and r s <→> is expressed as polar coordinates (r s, θ s). Here, the time-frequency domain signal S <d (s)> at wave number k of polar coordinates (R <(s)>, Ω <(s)>) representing the internal sound field of the spatial region 14-s (S)>, Ω <(s)>; k) are expressed as follows by cylindrical harmonics expansion. However, β m <d> (k) is an expansion coefficient for m for uniquely expressing S <d (s)> (R <(s)>, Ω <(s)>; k). From equations (3), (4) and (5), the expansion coefficient β m <d> (k) of the plane wave is given by: [0017] 03-05-2019 6 «Linear sound source expansion coefficient» r s <→ → = (rs cos θ s, r s sin θ s) (in polar coordinates (r s, θ s)) Line sound source (point sound source in two-dimensional space domain) Time-domain signal S <d (s)> (R <(s)>, Ω at wavenumber k in polar coordinates (R <(s)>, Ω <(s)>) representing the sound field generated by <(S)>; k) is expressed as follows. However, R <→ (s)> = (R <(s)> cos Ω <(s)>, R <(s)> sin Ω <(s)>), and R <→ (s)> in polar coordinates If it represents, it will become (R <(s)>, ohm <(s)>). ¦¦ (•) ¦¦ represents the norm of (•). In addition, as shown in the equation (7), originally "→" of "R <→ (s)>" should be written right above "R", but due to the restriction of written description, "→" Write on the upper right of "R". Here, the following relations hold by the Hankel function addition theorem. Here, the time-frequency domain signal S <d (s)> at wave number k of polar coordinates (R <(s)>, Ω <(s)>) representing the internal sound field of the spatial region 14-s (S)>, Ω <(s)>; k) are represented as follows. Therefore, the expansion factor of the sound field by the linear sound source is expressed as follows. [0018] << Expansion coefficient of sound field in each space region >> A time frequency domain signal S at wave number k in polar coordinates (R <(s)>, Ω <(s)>) representing a desired sound field in the space region 14-s <d (s)> (R <(s)>, Ω <(s)>; k) is expressed as follows by cylindrical harmonics expansion. Here, J m (·) is a Bessel function of order m, and α m <d (s)> (k) is S <d (s)> (R <(s)>, Ω <(s)>; k) Expansion coefficients (sound field coefficients) for m to uniquely represent k), e is the number of Napiers (the base of natural logarithms). Equation (11) is a Fourier series expansion, which can express an arbitrary two-dimensional sound field derived from an arbitrary number of cylindrical waves and plane waves. In addition, although "d (s)" of "α m <d (s)> (k)" should be written right above "m", due to the restriction of written description, "α m <d (s It is written as "> (k)". The same notation may be applied to other symbols. [0019] Equation (11) has an infinite number of orthogonal modes. However, due to the nature of the Bessel function and the fact that the sound field is limited in the spatial domain where all the sound sources are on the outside, this series expansion can be truncated with an expansion with a finite number of orthogonal modes. In this case, S <d (s)> (R <(s)>, Ω <(s)>; k) can be approximated as follows. However, M s (k) is a positive integer. In this case, S <d (s)> (R <(s)>, Ω <(s)>; k) is expressed in at least 2M s (k) +1 modes. In the case of M s (k) = ceil (keR z <(s)> / 2), the censoring error is less than or equal to 16.1%. However, ceil (·) is a ceiling function of (·). 03-05-2019 7 [0020] << Equivalent global sound field >> An equivalent global sound field composed of the sound fields of the S space regions 14-1, ..., S (multi-zone) described above is defined. That is, the problem of the reproduction of the sound field of the plurality of space regions 14-1, ..., S is reduced to the reproduction of the global desired sound field over the entire area. The timefrequency domain signal S <d> (r, θ; k) representing the desired global sound field is approximated by cylindrical harmonics expansion as follows: However, β m <d> (k) is an expansion coefficient (sound field coefficient) for m for uniquely expressing S <d> (r, θ; k). In this case, S <d> (r, θ; k) is expressed in at least 2M 0 (k) +1 modes. For example, M 0 (k) = ceil (keR p / 2). If all multizones fall within a circular region of radius R P, then M 0 (k) ≧ (M 1 (k) to reproduce the sound field in all multizones with mode limitation by M 0 (k) ) + M 2 (k) +... + M s (k)) (14). [0021] << Spatial harmonic coefficient conversion >> Consider the sound field in the area where no sound source exists. As shown in FIG. 3, O 1 and O 2 are origins of two coordinate systems, and they have axes in the same direction, and it is assumed that O 2 is moved by a known transformation. . Polar coordinates (r <(1)>, θ <(1)>) in the coordinate system with O 1 as the origin are represented by polar coordinates in the coordinate system with O 2 as the origin (r <(2)>, It becomes θ <(2)>). Here, polar coordinates of O 2 with respect to O 1 (r <(12)>, θ <(12)>) are expressed. In addition, in the two coordinate systems where {α m <(1)> (k)} and {α m <(2)> (k)} have origin as O 1 and O 2 respectively, in the region where no sound source exists It is assumed that a set of expansion coefficients for m to uniquely represent the sound field of. In this case, the following theorem 1 and 2 hold. [0022] [Theorem 1] α m <(1)> (k) and α m <(2)> (k) are related by the following. However, * represents discrete convolution at mode order m. T m <(21)> represents a conversion operator from the origin O 2 to O 1, and T m <(12)> represents a conversion operator from the origin O 1 to O 2. 03-05-2019 8 [0023] [Theorem 2] Denoting the polar coordinates of O 1 with respect to O 2 as (r <(21)>, θ <(21)>), and applying the theorem of spatial harmonic coefficient translation, the following It is possible to derive the relationship. Here, T m <(0 s)> is a conversion operator from a global coordinate system whose origin is O to a local coordinate system whose origin is O s of the s-th space region 14-s. [0024] << Search of Global Sound Field Coefficients >> The coefficient conversion from α m <d (s)> (k) to β m <d> (k) is performed. The convolution of equation (18) can be written as a linear sum as follows. The equation (19) is written S times for s = 1,..., S, and these simultaneous equations are constructed and expressed in matrix form as follows. α <d> (k) = T (k) β <d> (k) (20) However, the following conditions are satisfied. [0025] Equation (20) can be modified as follows. β <d> (k) = T (k) <+> α <d> (k) (23) where T (k) <+> = [T (k) <H> T (k)] <− 1> T (k) <H> is a Moore-Perones pseudo-inverse of T (k), and (·) <H> represents a complex conjugate transpose of (·). [0026] << Description of High-order Sound Source >> A time-frequency signal S n (r, θ; at wave number k at polar coordinates (r, θ) representing a sound field according to the radiation mode m (n) of the high-order sound source arranged at the origin O The ideal form of k) is expressed as follows. Actual high-order loudspeakers can emit sound fields with far-field polar responses of the form cos (nθ) and sin (nθ). The responses represented by sin and cos are easily obtained from the directivity of complex values. The radial velocity r r (θ) in the direction of the angle θ based on the radiation mode m (n) of the high-order sound source of radius R located at the origin O is expressed as follows. Where V 0 is a constant, and α m is a coefficient of Fourier series expansion. Further, the external sound field at wave number k in polar coordinates (r, θ) in two dimensions is expressed in the form of the above-mentioned equation (2), from which the 03-05-2019 9 radiation velocity is derived as follows. Where ρ is a constant and c is the speed of sound. Equation (26) must be equal to equation (25) and r = R. Therefore, the sound pressure at wave number k in polar coordinates (r, θ) can be expressed by the following time frequency signal. Here, t is an index representing time, and ω is each speed. Each mode has a phase variation e <imθ> and a radiation variation H m (kr), and the scale factor is α m / H m '(kr). In the case of generating a single high-order sound source response e <inθ>, the following conditions need to be satisfied. Real higher-order sources with discrete drivers (e.g. monopole speakers) can only generate the desired response up to a finite frequency. At higher frequencies spatial aliasing occurs. [0027] << Description of high-order sound source after conversion >> Wave number in polar coordinates (r, θ) generated by radiation mode m (n) of an ideal high-order sound source arranged at polar coordinates (rs, θs) with respect to the origin O A time frequency domain signal S n (r, θ, r s, θ s; k) representing a sound field at k can be expressed as follows with respect to the origin O according to the cylinder addition theorem. And r <→> = (r cos θ, r sin θ), r s <→> = (rs cos θ s, r s sin θ s), and β s is r 0 <→> And the angle between r s <and is expressed as: Here, x rot = x cos θ s + y sin θ s (31) and y rot = −x sin θ s + y cos θ s (32). [0028] A general high-order sound source is a single speaker unit, and can generate radiation modes m (n) of all orders up to a given N-th order. An Nth-order single higher-order sound source arranged at polar coordinates (rs, θs) with radiation mode m (n) (nε [-N, N]) has the following S N (r, θ, A sound field of wave number k represented by r s, θ s; k) can be generated at polar coordinates (r, θ). Here, w n (k) represents a weight for the radiation mode m (n) and the wavenumber k. Expression (33) is expanded as follows. [0029] By superimposing the L-order high-order sound source, a sound field represented by a timefrequency domain signal S (r, θ; k) of wave number k can be generated at polar coordinates (r, θ). Here, θ u is an argument of polar coordinates (R L, θ u) of the high-order sound source 12u with respect to the origin. This can be applied to the approximation of the desired internal and 03-05-2019 10 external sound fields. [0030] << Spatial multi-zone sound field reproduction by high-order sound source >> A circular array composed of L high-order sound sources 12-1, ..., 12-L Desired for a desired space region 14-1, ..., 14-S Reproduce the sound field of For this purpose, a weight w n for each radiation mode m (n) (where n = -N,..., N) at the wave number k of each higher-order sound source 12-u (where u = 1,..., L) . We must decide u (k). Each higher-order sound source 12-u can generate radiation modes m (-N),..., M (N) up to an N-th pole response. Weight w n. u (k) is determined by minimizing the squared error. In this embodiment, only the internal sound field of the circular array is controlled without controlling the external sound field of the circular array. [0031] << Control of Internal Sound Field of Circular Array >> To control the desired internal sound field without controlling the external sound field, a linear sum of the sound fields generated by the high-order sound sources 12-1, ..., 12-L Therefore, it is necessary to generate a desired internal sound field having an arbitrary expansion coefficient. Each higher-order sound source 12-u generates pole responses up to the N-th order, and the expansion order representing the desired sound field is M I (k). However, M I (k) is a positive integer. In this case, the right side of equation (13) and the right side of equation (35) (in the case of r <R L) need to be matched. The following relationship holds from now on. [0032] The equation of equation (36) can be written in matrix-vector form as follows. G (k) w <(0)> (k) = β <d> (k) (37) where G (k) is a matrix of (2MI (k) + 1) x L (2N + 1), w <(0)> (k) is L (2N + 1) weights w <(0)> n, u (k) (where n =-N, ..., N, u = 1, ..., L) and is a vector. [0033] The vector w <(0)> (k) consisting of w <(0)> n, u (k) (approximate solution or solution) which 03-05-2019 11 minimizes the square error of each element of left side and right side of equation (37) is become that way. w <(0)> (k) = G (k) <H> [G (k) G (k) <H> + λ (k) I] <-1> β <d> (k) (38) where And I is an identity matrix of (2M I (k) +1) × (2M I (k) +1), and 2M I (k) + 1 ≦ L (2N + 1). λ (k) is a regularization parameter, and when λ (k) = 0, equation (38) is the minimum norm solution. Also, λ (k) is used to reduce the weight solution when G (k) has a small singular value. The order M I (k) required to reproduce the sound field inside a circular array is However, the right side of equation (39) represents the ceiling function value of (ekR L / 2). The order N increases with the frequency, and the order M I (k) is limited by the relational expression 2M I (k) + 1 = βL (2N + 1), β <1 (40). Therefore, the approximate value of the spatial Nyquist frequency is as follows. [0034] <Operation> w <(0)> n, u (k) obtained as described above is stored in the storage unit 111 of the control unit 11 (FIG. 2). The input signal S (k) is also stored in the storage unit 111. The weight acquisition unit 112 reads w <(0)> n, u (k) from the storage unit 111 and sends w <(0)> n, u (k) to the filtering unit 113-u (where u = 1, ..., L). The filtering unit 113-u reads the input signal S (k) from the storage unit 111, and the filter weight for the radiation mode m (ν) at the wave number k of the high-order sound source 12-u is w <(0)> n, u ( Apply the filter as k) to the input signal S (k) to obtain the output signal S v u (k). The processing of the filtering unit 113-u may be performed in the time domain or may be performed in the time frequency domain. Each highorder sound source 12-u is, for example, by Du loudspeakers sp u (χ) (where χ∈ [0, D u −1]) annularly disposed at equal intervals on the outer periphery of a cylindrical baffle. It can be configured by a circular array (e.g. reference 1). In this case, the weight of the acoustic signal of each speaker sp u (χ) emitting in the radiation mode m (ν) from the high-order sound source 12-u is W u, χ = (1 / iρcD u) e <−iνφ (χ )> However, χ∈ [0, D u −1], and φ (χ) is the angle φ (χ) = 2χπ / D u on the two-dimensional plane with respect to the center of the annular array forming the high-order sound source 12-u. It is. Also, ρ represents the density of air and c represents the speed of sound. In this example, the output signal S 信号 u (k) is as follows. S u u (k) = w <(0)> n, u (k) W u, χ S (k) [0035] The output signal S u u (k) or the combination (linear sum) thereof is sent to the drive signal generation unit 114-1, and the drive signal generation unit 114-1 outputs the drive signal S corresponding to the output signal S u u (k) or the combination thereof. 'ν u (k) or a combination thereof is generated and output to the high-order sound source 12-u. The highorder sound source 12-u emits an acoustic signal of a reproduction pattern according to the 03-05-2019 12 drive signal S ′ u u (k) or a combination thereof. Thereby, desired sound fields are generated in desired space regions 14-1, ..., 14-S, and space multi-zone sound field reproduction is realized. In this embodiment, G u u (k) controls each of the radiation modes m ()) (where ν = 1,. Do. As a result, the degree of freedom in controlling the mirror image by echo can be improved, and the number of high-order sound sources 12-u (order N V) of order N V required to reproduce accurate sound fields in multiple regions in the reverberation room L can be reduced by up to 1 / N V + 1 as compared to Non-Patent Document 1. [0036] Second Embodiment The second embodiment is a modification of the first embodiment. The difference from the first embodiment of the second embodiment is that a desired external sound field is controlled without controlling the internal sound field. The following description will focus on the differences from the first embodiment. [0037] <Configuration> As illustrated in FIG. 4A, the sound field reproduction device 2 of this embodiment includes the control unit 21 and L high-order sound sources 12-u arranged on the circumference (where u = 1,... , L). As illustrated in FIG. 2, the control unit 21 includes a storage unit 111, a weight acquisition unit 212, a filtering unit 113-u, and a drive signal generation unit 114-u. The control unit 21 is configured, for example, by the aforementioned computer executing a predetermined program. [0038] << Geometrical Arrangement >> The difference from the first embodiment is that it assumes one two-dimensional local desired space region (circular region) 24-1 and a corresponding desired sound field. (FIG. 4A). However, the space area 24-1 exists outside the circular area of radius R P> r centered on the global origin O. [0039] 03-05-2019 13 << Control of External Sound Field of Circular Array >> To control a desired external sound field without controlling the internal sound field, a linear sum of the sound fields generated by the high-order sound sources 12-1, ..., 12-L. Therefore, it is necessary to generate a desired external sound field having an arbitrary expansion coefficient. Each higher-order sound source 12-u generates pole responses up to the Nth order, and let M E (k) be a development order representing a desired sound field. However, M E (k) is a positive integer. In this case, the right side of equation (13) and the right side of equation (35) (in the case of r> R L) need to be matched. The following relationship holds from now on. The equation of equation (42) can be written in matrix-vector form as follows. J (k) w <(1)> (k) = γ <d> (k) (43) where G (k) is a matrix of (2M I (k) +1) × L (2N + 1), w <(1)> (k) is L (2N + 1) weights w <(1)> n, u (k) (where n =-N, ..., N, u = 1, ..., It is a vector consisting of L), and γ m <d> (k) = β m <d> (k). [0040] The vector w <(1)> (k) consisting of w <(1)> n, u (k) (approximate solution or solution) which minimizes the square error of each element of the left side and right side of equation (42) is become that way. w <(1)> (k) = J (k) <H> [J (k) J (k) <H> + λ (k) I] <-1> γ <d> (k) (44) yen The order M E (k) necessary to reproduce the sound field outside the matrix array is The order N increases with the frequency, and the order M E (k) is limited by the relational expression 2M E (k) + 1 = βL (2N + 1), β <1 (46). Therefore, the approximate value of the spatial Nyquist frequency is as follows. [0041] <Operation> w <(1)> n, u (k) obtained as described above is stored in the storage unit 111 of the control unit 11 (FIG. 2). The input signal S (k) is also stored in the storage unit 111. The weight acquisition unit 212 reads w <(1)> n, u (k) from the storage unit 111 and sends w <(1)> n, u (k) to the filtering unit 113-u (where u = 1, ..., L). The filtering unit 113-u reads the input signal S (k) from the storage unit 111, and the filter weight for the radiation mode m (ν) at the wave number k of the high-order sound source 12-u is w <(1)> n, u ( Apply the filter as k) to the input signal S (k) to obtain the output signal S v u (k). The subsequent processing is the same as in the first embodiment. [0042] 03-05-2019 14 Third Embodiment The third embodiment is a modification of the first embodiment. The difference from the first embodiment of the third embodiment is that both the internal sound field and the external sound field are controlled. The following description will focus on the differences from the first embodiment. [0043] <Configuration> As illustrated in FIG. 4B, the sound field reproduction device 3 of this embodiment includes a control unit 31 and L high-order sound sources 12-u arranged on the circumference (where u = 1,... , L). As illustrated in FIG. 2, the control unit 21 includes a storage unit 111, a weight acquisition unit 312, a filtering unit 113-u, and a drive signal generation unit 114-u. The control unit 11 is configured, for example, by the aforementioned computer executing a predetermined program. [0044] << Geometrical Arrangement >> The difference from the first embodiment is that S twodimensional local desired spatial regions (circular regions) 34-1,... The desired sound field corresponding to is assumed (FIG. 4A). However, the space regions 34-1, ..., 34- (S-1) exist in the circular region of radius R p <r, and the space region 34-S exists outside the circular region of the radius R p> r. [0045] Simultaneous Control of Internal and External Sound Fields of Circular Array In this embodiment, the internal sound field and the external sound field are controlled separately. In this case, in order to generate a desired internal sound field having an arbitrary expansion coefficient and a desired external sound field having an arbitrary expansion coefficient, it is necessary to take a weighted sum of sound fields generated by higher-order sound sources. Combining the abovementioned internal sound field control equation (equation (37)) and the external sound field control equation (equation (43)) results in the following. However, w <(2)> (k) is L (2N + 1) weights w <(2)> n, u (k) (where n = −N,..., N, u = 1,. .., L) is a vector. [0046] 03-05-2019 15 The vector w <(1)> (k) consisting of w <(1)> n, u (k) (approximate solution or solution) which minimizes the square error of each element of the left side and right side of equation (48) become that way. w <(2)> (k) = Ψ <H> (k) [Ψ (k) Ψ <H> (k) + λ (k) I] <-1> ζ <d> (k) (49) Frequency As the order N increases with the following equation, the approximate value of the spatial Nyquist frequency is as follows by the relational expression 2 (MI (k) + ME (k)) + 1 = βL (2N + 1), β <1 (50) become. [0047] <Operation> w <(2)> n, u (k) obtained as described above is stored in the storage unit 111 of the control unit 11 (FIG. 2). The input signal S (k) is also stored in the storage unit 111. The weight acquisition unit 312 reads w <(2)> n, u (k) from the storage unit 111 and sends w <(2)> n, u (k) to the filtering unit 113-u (where u = 1, ..., L). The filtering unit 113-u reads the input signal S (k) from the storage unit 111, and the filter weight for the radiation mode m (ν) at the wave number k of the high-order sound source 12-u is w <(2)> n, u ( Apply the filter as k) to the input signal S (k) to obtain the output signal S v u (k). The subsequent processing is the same as in the first embodiment. [0048] [A comparison of the principle limits of multi-zone sound field reproduction by nondirectionality and higher order sound source] In space multi-zone sound field reproduction, M I (k) = M 0 (k) ≧ (M 1 (k) + M The central coordinates and the radius of each space area can be obtained by 2 (k) +... + M S (k) (53). [0049] When generating the desired internal sound field using L nondirectional speakers, the approximation of the spatial Nyquist frequency is [0050] On the other hand, when the desired internal sound field is controlled without controlling the external sound field using L high-order sound sources 12-u (where u = 1, ..., L), the approximate value of the spatial Nyquist frequency is It becomes. 03-05-2019 16 When L high-order sound sources 12-u (where u = 1, ..., L) are used to control both the internal sound field and the external sound field, the approximate value of the spatial Nyquist frequency is [0051] From equation (55), when the radius R L of a circle containing a plurality of spatial regions is the same, the external sound field is not suppressed using a circular array of high-order sound sources 12-u of order N Thus, it can be seen that a sound field with a bandwidth of about 2N times that of sound field reproduction by a circular array of omnidirectional speakers can be reproduced with high accuracy. [0052] Sound field reproduction by a circular array of nondirectional speakers can not suppress the external sound field. On the other hand, in the present embodiment, the external sound field can also be suppressed. From equation (56), when suppressing an external sound field using a circular array of highorder sound sources 12-u of order N, the sound field reproduction by the circular array of nondirectional speakers is approximately N times It can be seen that the sound field of the bandwidth can be reproduced with high accuracy. [0053] [Modifications, etc.] The present invention is not limited to the above-described embodiment. For example, the processing of the control unit described above is not only performed chronologically according to the description, but may be performed in parallel or individually depending on the processing capability of the device executing the processing or the necessity. It goes without saying that other modifications can be made as appropriate without departing from the spirit of the present invention. 03-05-2019 17 [0054] When the configuration of the control unit is realized by a computer, the processing contents of the functions that these should have are described by a program. By executing this program on a computer, those processing functions are realized on the computer. The program describing the processing content can be recorded in a computer readable recording medium. An example of a computer readable recording medium is a non-transitory recording medium. Examples of such recording media are magnetic recording devices, optical disks, magneto-optical recording media, semiconductor memories and the like. [0055] This program is distributed, for example, by selling, transferring, lending, etc. a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Furthermore, this program may be stored in a storage device of a server computer, and the program may be distributed by transferring the program from the server computer to another computer via a network. [0056] For example, a computer that executes such a program first temporarily stores a program recorded on a portable recording medium or a program transferred from a server computer in its own storage device. At the time of execution of the process, this computer reads the program stored in its own recording device and executes the process according to the read program. As another execution form of this program, the computer may read the program directly from the portable recording medium and execute processing in accordance with the program, and further, each time the program is transferred from the server computer to this computer Alternatively, processing may be performed sequentially according to the received program. The configuration described above is also executed by a so-called ASP (Application Service Provider) type service that realizes processing functions only by executing instructions and acquiring results from the server computer without transferring the program to this computer. Good. [0057] In the above embodiment, the processing function of the present apparatus is realized by 03-05-2019 18 executing a predetermined program on a computer, but at least a part of these processing functions may be realized by hardware. [0058] 1 to 3 sound field reproduction device 03-05-2019 19

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