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 JP2014150416 Abstract: The present invention provides a sound field collection and reproduction technique capable of reproducing a sound field with higher accuracy than in the prior art when using a circular microphone array / speaker array. SOLUTION: At least two microphones are arranged on a circumference of a radius R of a first space centering on an axis of a cylindrical rigid baffle of radius R and circumferential direction of the baffle circumferential direction, Assuming that at least two speakers are disposed on the circumference of a virtual cylinder of radius R of a second space different from the first space, the circle in which the speakers are disposed is a secondary sound source circle, and R is a secondary sound source Defined as a distance from the center of a circle to a point on the circumference where amplitudes are matched, for a space-time frequency domain signal P ~ (ω) generated based on a signal collected by a microphone Filter F (ω) is generated to generate a filtered signal D ~ (ω). [Selected figure] Figure 1 Sound field sound collecting and reproducing apparatus, method and program [0001] This invention is a technology of Wave Field Synthesis, Ambisonics, which picks up a sound signal with a microphone installed in a certain sound field and reproduces the sound field with a speaker using the sound signal. About. [0002] Wavefront synthesis and ambisonics are techniques for virtually reproducing the sound field of a remote place using a plurality of microphones and speakers. 03-05-2019 1 As such technology, for example, the technology described in Non-Patent Document 1 is known. Since applications such as remote communication systems require real-time sound collection and reproduction, the sound pressure collected by a general microphone array is unique to a sound field reproduction signal for output by a general speaker array. Need to be convertible to [0003] Oyama, Furuya, Kazukazu Kazukazu, Haneda, Suzuki, “Wavefront Reconstruction Filter for Cylindrical Microphone-Speaker Array”, September 2012, Proceedings of the Fall Meeting of the Acoustical Society of Japan, pp. 605-608 [0004] In the technique described in Non-Patent Document 1, assuming that a cylindrical microphone array / speaker array is used, a filter for conversion has been derived. Therefore, if this filter is applied to a circular microphone array / speaker array, the sound field can not be reproduced with high accuracy, and the sound field can be reproduced with high accuracy such that sound comes from all directions around the listener. There was a possibility that could not. [0005] It is an object of the present invention to reproduce a sound field with higher accuracy than in the prior art when using a circular microphone array / speaker array, and to increase the sound field such that sound comes from all directions around the listener. Abstract: A sound field sound collecting and reproducing apparatus, method, and program that can be reproduced with accuracy. [0006] In order to solve the above-mentioned subject, sound field sound collection playback device by one mode of this invention is the 1st space which makes the circumferential direction of the baffle circumferential direction centering on the axis of baffle of cylindrical rigid body of radius Rb. Assuming that at least two microphones are arranged around the radius Rm of R, Rm R Rb, the circumferential direction of the baffle is φ direction, j is an imaginary unit, ω is a frequency, 03-05-2019 2 c is a speed of sound, k = ω / c, m is the order in the φ direction, H <(1)> m (·) is the first kind Hankel function of the m order, Jm (·) is the Bessel function of the m order, H <( 1) Let> m '(.) Be the derivative of the first-class Hankel function H <(1)> m (.) Of the m-th, Jm' (.) Be the derivative of the Bessel function Jm (.) Of the m-th, Let wm be a weight determined on the basis of m, A (ω) be a complex number determined on the basis of ω, and at least two speakers be disposed on the circumference of a virtual cylinder having a radius Rs of a second space different from the first space Have been The circle on which the signal is placed is the secondary sound source circle, and Rref is the distance from the center of the secondary sound source circle to the point on the circumference where the amplitudes are matched, generated based on the signal collected by the microphone A conversion filter unit that generates a filtered signal D ~ m (ω) by applying a filter F ~ m (ω) defined by the following equation to the space-time frequency domain signal P ~ m (ω); [0007] [0008] A space-frequency inverse transform unit that transforms the filtered signal D to m (ω) into a frequency domain signal by inverse Fourier transform of space, and a time domain signal that is transformed into a time domain signal by inverse Fourier transform And a frequency inverse converter for outputting the area signal to the speaker. [0009] According to another aspect of the present invention, there is provided an acoustic field sound collecting and reproducing apparatus comprising: a cylinder-shaped rigid baffle having a radius Rb and a radius of Rm in a first space whose circumferential direction is a circumferential direction of the baffle; Assuming that at least two microphones are arranged, Rm ≧ Rb, the circumferential direction of the baffle is φ direction, j is an imaginary unit, ω is a frequency, c is a speed of sound, k = ω / c, m Is an order in the φ direction, H <(1)> m (·) is a first kind Hankel function of the m order, Jm (·) is a Bessel function of the m order, H <(1)> m ′ (· Let m) be the derivative of the Hank function H <(1)> m (.) Of the m-th, Jm '(.) Be the derivative of the Bessel function Jm (.) Of the m-th, and wm be determined based on m Assuming that A (ω) is a complex number determined based on ω, and at least two speakers are disposed on the circumference of a virtual cylinder having a radius Rs of a second space different from the first space Two placed circles A frequency converter configured to convert a signal collected by the microphone into a frequency domain signal by Fourier transform, where R so is the distance from the center of the secondary sound source circle to the point on the circumference where the amplitude is matched. A spatial frequency conversion unit that converts a frequency domain signal to a space-time frequency domain signal P ~ m (ω) by the Fourier transform of A conversion filter unit that 03-05-2019 3 generates filtered signal D ~ m (ω) by applying F ~ m (ω); [0010] [0011] including. [0012] According to another aspect of the present invention, there is provided a sound field collection and reproduction apparatus, in which at least two microphones are arranged around a circle of radius Rm of a first space centered on the center of a spherical rigid baffle of radius Rb. It is assumed that Rm 円 Rb, the circle in which the microphone is disposed is the receiving circle, the circumferential direction of the receiving circle is the φ direction, and the circumference of the large circle of the plane perpendicular to the receiving circle and the baffle Let the direction be the θ direction, j be the imaginary unit, ω be the frequency, c be the speed of sound, k = ω / c, m be the order in the φ direction, n be the order in the θ direction, H <(1) > Let m (·) be the first kind Hankel function of order m, Jm (·) be the Bessel function of order m, h <(1)> n (·) be the first kind of sphere Hankel function of order n, Let jn (·) be the n-th-order spherical Bessel function, h <(1)> n '(.) be the derivative of the n-th-order first-class sphere Hankel function h <(1)> n (·), jn' Let (·) be the derivative of the n-th-order spherical Bessel function jn (·), and P <m> n (·) be a regende Let 陪 be a function, w m be a weight determined based on m, A (ω) be a complex number determined based on ω, and at least two speakers be virtual spheres of a second space radius Rs different from the first space It is assumed that the circle is arranged on the circumference of the great circle, the circle on which the speaker is arranged is the secondary sound source circle, and Rref is the distance from the center of the secondary sound source circle to the point on the circumference where the amplitudes are matched. A filter F ~m (ω) defined by the following equation is applied to a space-time frequency domain signal P ~m (ω) generated based on a collected signal, and a post-filtering signal D ~m ( a conversion filter unit that generates ω), [0013] [0014] A space-frequency inverse transform unit that transforms the filtered signal D to m (ω) into a frequency domain signal by inverse Fourier transform of space, and a time domain signal that is transformed into a time domain signal by inverse Fourier transform And a frequency inverse 03-05-2019 4 converter for outputting the area signal to the speaker. [0015] According to another aspect of the present invention, there is provided a sound field collection and reproduction apparatus, in which at least two microphones are arranged around a circle of radius Rm of a first space centered on the center of a spherical rigid baffle of radius Rb. It is assumed that Rm 円 Rb, the circle in which the microphone is disposed is the receiving circle, the circumferential direction of the receiving circle is the φ direction, and the circumference of the large circle of the plane perpendicular to the receiving circle and the baffle Let the direction be the θ direction, j be the imaginary unit, ω be the frequency, c be the speed of sound, k = ω / c, m be the order in the φ direction, n be the order in the θ direction, H <(1) > Let m (·) be the first kind Hankel function of order m, Jm (·) be the Bessel function of order m, h <(1)> n (·) be the first kind of sphere Hankel function of order n, Let jn (·) be the n-th-order spherical Bessel function, h <(1)> n '(.) be the derivative of the n-th-order first-class sphere Hankel function h <(1)> n (·), jn' Let (·) be the derivative of the n-th-order spherical Bessel function jn (·), and P <m> n (·) be a regende Let 陪 be a function, w m be a weight determined based on m, A (ω) be a complex number determined based on ω, and at least two speakers be virtual spheres of a second space radius Rs different from the first space It is assumed that the circle is arranged on the circumference of the great circle, the circle on which the speaker is arranged is the secondary sound source circle, and Rref is the distance from the center of the secondary sound source circle to the point on the circumference where the amplitudes are matched. A frequency conversion unit that converts the collected signal into a frequency domain signal by Fourier transform; a spatial frequency conversion unit that converts the frequency domain signal into a space-time frequency domain signal P to m (ω) by Fourier transform of space; A conversion filter unit that generates a filtered signal D ~ m (ω) by applying a filter F ~ m (ω) defined by the following equation to the space-time frequency domain signal P ~ m (ω); [0016] [0017] including. [0018] The filter for the circular microphone array and the speaker array can be used to convert the sound pickup signal of the circular microphone array into a drive signal of the circular speaker array to reproduce the sound field. It becomes possible to reproduce with high precision a sound field in which sound comes from all directions. 03-05-2019 5 [0019] The figure for demonstrating the example of arrangement | positioning of a microphone and a speaker. FIG. 2 is a functional block diagram showing an example of a sound field sound collecting and reproducing apparatus. The flowchart which shows the example of the sound field sound collection reproduction method. The figure for demonstrating the example of arrangement | positioning of a microphone and a speaker. [0020] First Embodiment Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In the following description, the symbols "~", "<->", etc. used in the text should originally be written directly above the previous character, but due to the limitations of the text notation Described in. In the formula, these symbols are described at their original positions. Moreover, the processing performed in each element unit of a vector or a matrix is applied to all elements of the vector or the matrix unless otherwise noted. [0021] 03-05-2019 6 <Regarding Arrangement of Microphone Array and Speaker Array> As shown in FIG. 1, in the sound field collection and reproduction apparatus and method of the first embodiment, the axis of the cylindrical rigid body baffle of the radius Rb of the first space is centered. And a microphone array composed of Nch microphones M1, M2,..., MNch arranged on the circumference of a circle of radius Rm whose circumferential direction is the circumferential direction of the baffle, and the radius Rs of the second space A speaker array formed of Nch speakers S1, S2,..., SNch arranged on the circumference of a virtual cylinder of The sound field of the space of is reproduced in the second space. The circumference of the imaginary cylinder means the circumference of a circle which is a common part of a plane perpendicular to the axis of the imaginary cylinder and the imaginary cylinder. The first space and the second space are mutually different spaces. In FIG. 1, the sound source S reproduced in the second space is expressed as a sound source S '. The circle formed by the microphone array is also referred to as a reception circle, and the circle formed by the speaker array is also referred to as a secondary sound source circle. In other words, a circle in which the microphone array is arranged is called a receiving circle, and a circle in which the speaker array is arranged is called a secondary sound source circle. The axial direction of the baffle is the z direction, and the circumferential direction of the baffle of radius Rb is the φ direction. In other words, the φ direction is the circumferential direction of the receiving circle. The number of microphones disposed in the first space and the number of speakers disposed in the second space may be different. When the number of microphones is larger than the number of speakers disposed in the second space, the reproduction signal may be thinned. On the other 03-05-2019 7 hand, when the number of microphones is smaller than the number of speakers arranged in the second space, the reproduction signal may be interpolated by averaging the channels. As a method of performing interpolation, for example, linear interpolation or sinc interpolation can be applied. [0022] The microphone array uses two or more microphones to form a circle. For example, as shown in FIG. 1, Nch microphones are equally spaced on the circumference of a circle of radius Rm whose center is the axis of the cylindrical rigid body baffle and whose circumferential direction is the circumferential direction of the baffle. . Nch is a predetermined integer of 2 or more. [0023] The radius Rb of the cylindrical rigid body baffle and the distance Rm between the axis of the baffle and the microphone may be any value as long as Rm ≧ Rb. In the case of Rm = Rb, the microphone will be disposed on the surface of the circumferential surface of the cylindrical baffle of radius Rb (= Rm). In the case of Rm> Rb, as shown in FIG. 1, the microphone is disposed at a position Rm away from the axis of the cylindrical baffle of radius Rb. In other words, the microphone is placed at a position (Rm-Rb) away from the surface of the peripheral surface of the baffle. For example, the microphone is disposed by being supported by a thin rod-like member that protrudes vertically from the circumferential surface of the baffle. [0024] Note that the filters F to m (ω) used in the conversion filter unit 4 are derived on the assumption that the cylinder of the baffle has an infinite length (for details, see <Regarding Derivation of Filter>). Therefore, (1) the cylinder of the baffle is preferably long, and (2) the installation position of the microphone is preferably the center of the cylinder length of the baffle. In the present embodiment, the length of the baffle and the installation position of the microphone are not limited to (1) and (2), but in the case of (1) and (2), the wavefront closest to the sound collecting field is synthesized. can do. [0025] 03-05-2019 8 The Nch microphones arranged on the circumference of a circle of radius Rm are located at intervals of φcradian, with φc being a predetermined angle. The microphones do not have to be strictly arranged at equal intervals as long as they are arranged at approximately equal intervals. That is, it is not necessary that the values of φc, which are the distances to the adjacent microphones, be strictly the same value, but may be approximately the same value. Also, the microphones may be arranged at any intervals. That is, the distance between adjacent microphones φc can take an arbitrary value. However, the sound field can be reproduced with high accuracy by arranging the microphones at substantially equal intervals, that is, by setting φc, which is the distance between adjacent microphones, to substantially the same value. [0026] The speakers are also arranged in the same manner as the microphones. That is, the speaker array uses two or more speakers to form a circle. For example, as shown in FIG. 1, Nch speakers are equally spaced around the circumference of the virtual cylinder. Nch is a predetermined integer of 2 or more. [0027] The Nch speakers arranged on the circumference of the virtual cylinder are located at intervals of φcradian, where φc is a predetermined angle. The speakers do not have to be strictly arranged at equal intervals as long as they are arranged at approximately equal intervals. That is, it is not necessary that the values of φc, which are the distances to the adjacent speakers, be exactly the same value, and it may be approximately the same value. Also, the speakers may be arranged at any intervals. That is, an interval φc between adjacent speakers can take an arbitrary value. However, the sound field can be reproduced with high accuracy by arranging the speakers at substantially equal intervals, that is, by setting φc, which is an interval between adjacent speakers, to substantially the same value. [0028] The positional relationship of the Nch microphones on the circumference of the receiving circle is preferably the same as the position of the corresponding Nch speakers of the secondary sound 03-05-2019 9 source circle, but may be different. If the positions are the same, the sound field can be reproduced more faithfully. [0029] The radius Rm of the receiving circle is, for example, about 0.2 m. The radius Rs of the secondary sound source circle is, for example, about 1.5 m. Although it is assumed in the present embodiment that RsRRm, the same processing can be applied even if this is not satisfied (that is, also in the case of Rs <Rm). However, when Rs ≧ Rm, the accuracy of sound field reproduction is improved. The larger the value of the radius Rm of the circle formed by the microphone array and the radius Rs of the virtual cylinder, the larger the area can be reproduced, but more microphones and speakers are required. It is desirable that the radius Rm of the circle formed by the microphone array and the radius Rs of the virtual cylinder be set experimentally in consideration of the frequencies of the signals to be collected and reproduced, respectively. Also, the microphones are arranged outside the sound receiving circle, and the speakers are arranged inside the secondary sound source circle. The sound collection range targeted by the microphone array is outside the sound receiving circle, and the reproduction range targeted by the speaker array is inside the secondary sound source circle. [0030] The speaker may be disposed in the air of the second space in an acoustically transparent state, or may be disposed in the second space in an acoustically non-transparent state. The acoustically transparent state is a state in which the same transfer characteristic as the transfer characteristic of the second space in which the speaker is not disposed is maintained. For example, if it is desired to place the speaker in the air of the second space in an acoustically transparent state, the speaker may be placed in the air of the second space by being suspended by a thread or fixed by a thin rod. Be done. [0031] The position of the microphone Mi (i = 1, 2,..., Nch) in the first space is expressed as r <−> m, i = (Rm, φm, i, 0) in a cylindrical coordinate system. The position of the speaker Si (i = 1, 2,..., Nch) in the second space is expressed as r <−> s, i = (Rs, φs, i, 0) in a cylindrical coordinate system. 03-05-2019 10 [0032] <Sound Field Sound Collection Reproduction Device> As shown in FIG. 2, the sound field sound collection reproduction device according to the first embodiment includes a frequency conversion unit 1, a space frequency conversion unit 3, a conversion filter unit 4, a space frequency inverse conversion unit 5, and For example, the frequency inverse transform unit 6 is included to perform the processing of each step illustrated in FIG. 3. [0033] The microphones M1, M2,..., And MNch arranged in the first space pick up the sound emitted by the sound source S in the first space to generate a time domain signal. The generated signal is sent to the frequency converter 1. A signal at time t collected in the microphone Mi located at r <−> m, i = (Rm, φm, i, 0) is denoted as pi (t). [0034] <Frequency Converter 1> The frequency converter 1 converts the signal pi (t) collected by the microphone Mi 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 3. ω is a frequency. A value k = ω / c obtained by dividing ω by the speed of sound c is defined as a wave number. The wave number is the so-called spatial frequency or angular spectrum. 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 Pi (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 as, for example, equation (1). J in the argument of the function exp is an imaginary unit. [0035] [0036] 03-05-2019 11 <Spatial Frequency Transform Unit 3> The spatial frequency transform unit 3 transforms the frequency domain signal Pi (ω) into the space-time frequency domain signal P ~m (ω) by Fourier transform of space (step S3). The space-time frequency domain signal P ~m (ω) is calculated for each frequency ω. The converted space-time frequency domain signal P ~m (ω) is sent to the conversion filter unit 4. The spatial frequency transform unit 3 calculates, for example, P ~m (ω) defined by the equation (2). [0037] [0038] m is an order in the φ direction. Here, −M ≦ m ≦ M, and m is an integer. Equation (2) is an example of conversion to the spacetime frequency domain, and Fourier transform of space may be performed by another method. Also, a method may be used in which equations (1) and (2) are combined to perform a twodimensional DFT. [0039] <Transformation Filter Unit 4> The conversion filter unit 4 applies a predetermined filter F to m (ω) to the space-time frequency domain signal P to m (ω) according to the following equation to apply filtered signals D to m ω) is generated (step S4). The post-filtering signal D ~m (ω) is sent to the spatial frequency inverse transform unit 5. [0040] [0041] 03-05-2019 12 Rref is the distance from the center of the secondary sound source circle to a point on the circumference (which is coplanar with the secondary sound source circle) that matches the amplitude. Therefore, when Rref = 0, the amplitudes coincide at the center of the secondary sound source circle, and when Rref ≠ 0, the amplitudes coincide on the concentric circle of the secondary sound source circle of the radius Rref. In addition, in the case of Rref = 0, a set of points whose amplitudes coincide with each other from the center of the secondary sound source circle does not form a circle but becomes a point (the center of the secondary sound source circle). It shall be included in the expression "circle around which the amplitude is matched from the center of". In addition, Rref may be rephrased as a distance from the center of the secondary sound source circle to a point on the same plane as the secondary sound source circle whose amplitude is matched. In the case of Equation (4), the target sound field coincides with the target sound field on the circumference of the concentric circle of the secondary sound source circle whose amplitude is determined by Rref, while in the case of Equation (5) The amplitudes match in). A (ω) is a complex number (an arbitrary complex number depending on ω) determined based on ω, and is a value for performing an equalizing operation such as lowering the high frequency gain, for example. In the case of the equation (5), specifically, the amplitude is the same height as the speaker array, and is located at the center of the secondary sound source circle or at the circumferential position of the concentric circle of the secondary sound source circle of radius Rref. Match wm is a weighting function, and is defined, for example, as follows. [0042] [0043] [0044] Γ (z) and Yv (z) represent the gamma function and the Neumann function, respectively. The conversion filter is obtained by numerically calculating the above equation. 03-05-2019 13 The integral value or the like of equation (4) may be approximately calculated, for example, discretized as in the following equation. [0045] [0046] Here, i is the index of discretization, Δkz is the discretization interval, and I is the range of the sum. Expression (11) is an example of a method of discretizing and approximately obtaining an integral value, and may be discretized by another method. It can be discretized using various approximation formulas used in the definition of the piecewise quadrature method. [0047] Further, when Rb = Rm, that is, when the microphone is disposed on the surface of the peripheral surface of the cylindrical baffle of radius Rb (= Rm), the equations (4) and (5) are respectively as follows: It can be simplified. [0048] [0049] It is reproduced in the second space by applying the filter F to m (ω) defined by the equation (4) or the equation (5), or the equation (4-2) or the equation (5-2) Since the amplitudes of the signals can be matched on a predetermined circumference, the amplitudes of the reproduced signals are matched in a wider range than in the past. [0050] <Spatial Frequency Inverse Transform Unit 5> The spatial frequency inverse transform unit 5 converts the filtered signal D ~m (ω) into a frequency domain signal Di (ω) by inverse Fourier transform of space (step S5). 03-05-2019 14 The converted frequency domain signal Di (ω) is sent to the frequency inverse transform unit 6. The spatial frequency inverse transform unit 5 calculates, for example, the frequency domain signal Di (ω) defined by equation (12). [0051] [0052] <Frequency Inverse Transform Unit 6> The frequency inverse transform unit 6 converts the frequency domain signal Di (ω) into a time domain signal di (t) by inverse Fourier transform (step S6). The time domain signal di (t) obtained for each frame by the inverse Fourier transform is appropriately shifted and a linear sum is taken 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 di (t) is sent to the speakers S1, S2, ..., SNch. [0053] The speaker Si reproduces sound based on the time domain signal di (t). For example, as i = 1,..., Nch, the speaker Si located at r <−> s, i = (Rs, φs, i, 0) reproduces a sound based on the time domain signal di (t). Thereby, the sound field of the first space can be reproduced in the second space. [0054] 03-05-2019 15 As mentioned above, if the number of microphones is greater than the number of speakers, the time domain signal di (t) may be decimated. On the other hand, when the number of microphones is smaller than the number of speakers, interpolation may be performed by averaging the time domain signal di (t). As a method of performing interpolation, for example, linear interpolation or sinc interpolation can be applied. [0055] <Effects> Since it is possible to convert the sound pickup signal of a circular microphone array into a drive signal of a circular speaker array by using a filter for a circular microphone array / speaker array and reproduce the sound field, It becomes possible to reproduce with high precision a sound field in which sound comes from all directions around the listener. Therefore, the sound field can be reproduced with higher accuracy than in the prior art. [0056] <Regarding Derivation of Filter> Hereinafter, the reason why the filters F to m (ω) are represented as Expression (4) and Expression (5) will be described. [0057] Here, the cylindrical coordinate system r <-> = (r, φ, z) is considered. The sound field on the xy plane is reproduced using the secondary sound source circle arranged in the reproduction area from the sound pressure distribution acquired by the sound receiving circle arranged in the sound collection area. [0058] A synthetic sound field Psyn (r <->, ω) by secondary sound sources continuously arranged on the circumference is a secondary sound source drive signal D (r <-> s, ω), a secondary sound source and a target sound. Using the transfer function G (r <->-r <-> s, ω) between the field, it can be expressed as follows. [0059] 03-05-2019 16 [0060] Since this can be regarded as a convolution with respect to φ of D (·) and G (·), it can be expressed in the form of a product in the circular harmonic spectrum region as follows. [0061] [0062] On the other hand, the sound pressure distribution Prcv (Rm, 0, φ, ω) obtained on the circumference of the radius Rm of the sound collection field Prcv (r <->, ω) of the target sound field Pdes (r <->, ω) It is necessary to express using. Assuming that an infinite-length rigid cylinder of radius Rb (≦ Rm) is installed centered on the same position as the receiving circle, the sound collection field Prcv (r <−>, ω) is the incident sound as in the following equation It can be expressed by the sum of the field Pinc (r <->, ω) and the scattered sound field Psct (r <->, ω). Prcv (r <->, ω) = Pinc (r <->, ω) + Psct (r <->, ω) (15) Further, from the boundary condition on the rigid cylinder, [0063] [0064] Is true. Also, Pinc (r <->, ω) and Psct (r <->, ω) can be written as follows in the helical wave spectral region. 03-05-2019 17 [0065] [0066] したがって、 [0067] [0068] となる。 From the above, assuming that the sound collection field is invariable in the z-axis direction, the relational expression between the incident sound field and the sound collection field can be derived as follows. [0069] [0070] Because the target sound field is equal to the incident sound field, [0071] [0072] となる。 Since it is sufficient if the synthetic sound field Psyn (r <->, ω) and the target sound field Pdes (r <->, ω) coincide with each other, 03-05-2019 18 [0073] [0074] Here, for simplicity, it is assumed that G (r <->-r <-> s, ω) is a monopole characteristic. [0075] [0076] Although the conversion equation of the secondary sound source drive signal has been obtained from the sound pressure distribution on the sound receiving circle above, it is necessary to give in advance a circle whose amplitude matches the target sound field as r = Rref. [0077] Assuming that the secondary sound source is a line sound source, the conversion equation can be further simplified. [0078] [0079] であることより、 [0080] [0081] となる。 However, an actual speaker is close to monopole characteristics, and a correction for linear sound source approximation is required. 03-05-2019 19 [0082] [0083] Because of this, the following frequency characteristics are corrected for each output signal. [0084] [0085] The case of Rb = Rm can be simplified using the following relational expression. [0086] [0087] Second Embodiment A description will be made focusing on parts different from the first embodiment. [0088] <Regarding Arrangement of Microphone Array and Speaker Array> As shown in FIG. 4, in the sound field collecting and reproducing apparatus and method according to the second embodiment, a first space centering on the center of the spherical rigid baffle of radius Rb is used. A microphone array composed of Nch microphones M1, M2, ..., MNch arranged on the circumference of a circle of radius Rm, and arranged on the circumference of a great circle of a virtual sphere of radius Rs of the second space The sound field of the first space formed by the sound generated by the sound source S of the first space using the Nch speakers S1, S2,. Reproduce in the space of. The circle formed by the microphone array is also called a receiving circle, and the great circle of the virtual sphere formed by the speaker array is also called a secondary sound source circle. A direction perpendicular to the receiving circle and the secondary sound source circle is the z direction, a circumferential direction of the receiving circle and the secondary sound source 03-05-2019 20 circle is the φ direction, and a large circle of a plane perpendicular to the receiving circle and the baffle The circumferential direction of the great circle of the plane perpendicular to the secondary sound source circle and the virtual sphere is taken as the θ direction. [0089] In the first embodiment, the microphone and the speaker are respectively arranged on a circle of radius Rm and a virtual cylinder of radius Rs whose center is the axis of the cylindrical rigid baffle of radius Rb and whose circumferential direction is the circumferential direction of the baffle. It is arranged. On the other hand, in the second embodiment, the microphone and the speaker are respectively disposed around the circle of the radius Rm of the first space and the circle of the imaginary sphere of the radius Rs centered on the center of the spherical rigid baffle of the radius Rb. It is done. [0090] The position of the microphone Mi (i = 1, 2,..., Nch) in the first space is expressed as r <−> m, i = (Rm, π / 2, φm, i) in a spherical coordinate system. The position of the speaker Si (i = 1, 2,..., Nch) in the second space is expressed as r <−> s, i = (Rs, π / 2, φs, i) in a spherical coordinate system. [0091] <Transformation Filter Unit 4> The conversion filter unit 4 applies a predetermined filter F to m (ω) to the space-time frequency domain signal P to m (ω) according to the following equation to apply filtered signals D to m ω) is generated (step S4). The post-filtering signal D ~m (ω) is sent to the spatial frequency inverse transform unit 5. 03-05-2019 21 [0092] [0093] Rref is the distance from the center of the secondary sound source circle to a point on the circumference (which is coplanar with the secondary sound source circle) that matches the amplitude. n is an order in the θ direction. h <(1)> n (.), jn (.), h <(1)> n '(.), jn' (.), P <m> n (.) are each n-th first Seed sphere Hankel function, nth sphere Bessel function, nth first class sphere Hankel function h <(1)> differentiation of n (·), nth sphere Bessel function jn (•) differentiation, Legendre function And is defined as follows. [0094] [0095] Pn (·) represents a Legendre polynomial. The conversion filter is obtained by numerically calculating the above equation. [0096] Further, when Rb = Rm, that is, when the microphone is disposed on the surface of the peripheral surface of the cylindrical baffle of radius Rb (= Rm), the equations (31) and (32) are respectively as follows: It can be simplified. [0097] 03-05-2019 22 [0098] Reproduced in the second space by applying the filter F to m (ω) defined by the equation (31) or the equation (32), or the equation (31-2) or the equation (32-2) Since the amplitudes of the signals can be matched on a predetermined circumference, the amplitudes of the reproduced signals are matched in a wider range than in the past. [0099] With such a configuration, the same effect as that of the first embodiment can be obtained. [0100] <Regarding Derivation of Filter> Hereinafter, the reason why the filters F to m (ω) are represented as Expression (31) and Expression (32) will be described. [0101] Here, the spherical coordinate system r <-> = (r, θ, φ) is considered. The sound field on the xy plane is reproduced using the secondary sound source circle arranged in the reproduction area from the sound pressure distribution acquired by the sound receiving circle arranged in the sound collection area. [0102] A synthetic sound field Psyn (r <->, ω) by secondary sound sources continuously arranged on the circumference can be written as follows in the circular harmonic spectrum region as in the case of the first embodiment. [0103] [0104] On the other hand, the sound pressure distribution P (Rm, π / 2, φ) obtained on the circumference of the radius Rm of the sound collection field Prcv (r <->, ω) of the target sound 03-05-2019 23 field Pdes (r <->, ω) , ω) is required to be represented. Assuming that a rigid sphere with radius Rb (≦ Rm) is installed at the same position and center as the receiving circle, the sound collection field Prcv (r <−>, ω) is the incident sound field Pinc (r <−>, It can be expressed by the sum of ω) and the scattered sound field Psct (r <−>, ω). Prcv (r <->, ω) = Pinc (r <->, ω) + Psct (r <->, ω) (38) Also, according to the boundary condition on a hard sphere, [0105] [0106] Is true. Also, Pinc (r <->, ω) and Psct (r <->, ω) can be written as follows in the spherical harmonic spectrum region. [0107] [0108] Here, Y <m> n (θ, φ) represents a spherical harmonic function. したがって、 [0109] [0110] 03-05-2019 24 となる。 From the above, assuming that the sound collection field is universal in the z-axis direction, the relational expression between the incident sound field and the sound collection field can be derived as follows. [0111] [0112] Furthermore, [0113] [0114] であり、 [0115] [0116] であることから、 [0117] [0118] となる。 Since it is sufficient if the synthetic sound field Psys (r <->, ω) and the target sound field Pdes (r 03-05-2019 25 <->, ω) coincide with each other, [0119] [0120] Here, for simplicity, it is assumed that G (r <->-r <-> s, ω) is a monopole characteristic. [0121] [0122] As described above, the conversion equation of the secondary sound source drive signal is obtained from the sound pressure distribution on the sound receiving circle, but it is necessary to give in advance a circle whose amplitude matches the target sound field as r = Rref. [0123] Assuming that the secondary sound source is a line sound source, the conversion equation can be further simplified. [0124] [0125] であることより、 [0126] [0127] となる。 However, an actual speaker is close to monopole characteristics, and a correction for linear 03-05-2019 26 sound source approximation is required. From the equation (26), the following frequency characteristics are corrected for each output signal. [0128] [0129] In the case of Rb = Rm, it can be derived using the following relational expression. [0130] [0131] [Modifications, Etc.] Each part constituting the sound field sound collecting and reproducing apparatus may be provided in either the sound collecting apparatus arranged in the first space or the reproduction apparatus arranged in the second space. In other words, the processing of each of the frequency conversion unit 1, the space frequency conversion unit 3, the conversion filter unit 4, the space frequency inverse conversion unit 5, and the frequency inversion unit 6 is performed by the sound collection device disposed in the first space. It may be executed or may be executed by a playback device located in the second space. The signal generated by the sound collection device is transmitted to the reproduction device. [0132] The positions of the first space and the second space are not limited to those shown in FIGS. 1 and 4. 03-05-2019 27 The first space and the second space may be adjacent to or separated from each other. Also, the orientation of the first space and the second space may be any. [0133] As long as the sound field sound collecting and reproducing apparatus includes the conversion filter unit 4, it may not include other units. For example, the sound field sound collecting and reproducing apparatus may be configured of the conversion filter unit 4, the spatial frequency inverse conversion unit 5, and the frequency inverse conversion unit 6. Further, the sound field sound collecting and reproducing apparatus may be configured of the frequency conversion unit 1, the spatial frequency conversion unit 3, and the conversion filter unit 4. [0134] The processing of the frequency conversion unit 1 and the processing of the spatial frequency conversion unit 3 may be performed simultaneously. Similarly, the process of the spatial frequency inverse transform unit 5 and the process of the frequency inverse transform unit 6 may be performed simultaneously. Further, the space frequency conversion unit 3 and the space frequency inverse conversion unit 5 may be interchanged. [0135] 03-05-2019 28 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. [0136] 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. [0137] 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. [0138] Reference Signs List 1 frequency conversion unit 3 space frequency conversion unit 4 conversion filter unit 5 space frequency inverse conversion unit 6 frequency inverse conversion unit 03-05-2019 29

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