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 JP2015060007 The present invention provides an inverse system design method, an inverse system design apparatus, and a program capable of presenting a signal with an accuracy according to a priority to control points arranged in a control target system. An inverse system design apparatus 1 sets a basis on an output side of an inverse matrix G # after truncation for an inverse matrix G by truncation singular value decomposition for each set of control points corresponding to a desired order of approximation accuracy priority. Calculate V #, singular value matrix ## and basis U # on the input side. The truncated matrices in the set of control points are then combined to form the overall inverse matrix G. Specifically, processing is started from an initial set of control points, and a set of control points is added recursively. In the processing for each set of control points, the inverse matrix G # for obtaining a desired approximation accuracy is formed by changing the threshold on which the priority of the approximation accuracy is reflected. After the iterative recursion is complete, the inverse matrix G is formed. [Selected figure] Figure 8 Reverse system design method, reverse system design apparatus and program [0001] The present invention relates to a technology for constructing a control system such as an acoustic system, and more particularly to a method, an apparatus and a program for designing an inverse system having characteristics opposite to those of a system to be controlled. [0002] Conventionally, it is known to use an inverse system to build a control system such as an acoustic 07-05-2019 1 system. An inverse system is a system having the inverse characteristic of the system to be controlled. A desired control system can be constructed by appropriately designing an inverse system according to a predetermined purpose. [0003] [Inverse System] FIGS. 13 and 14 are conceptual diagrams for explaining the inverse system. 13 and 14, the system 100 receives the signal X in and outputs the signal X out, and the system 101 receives the signal Y in and outputs the signal Y out. System (control target system) B. [0004] Referring to FIG. 13, system 101, which is controlled system B, inputs signal X out output from system 100 as signal Y in. In such a system 100, 101, when the signal Y out output by the system 101 is matched or approximated to the signal X in input to the system 100, the system 100 is a reverse system of the system 101 which is the controlled system B. It becomes A. [0005] Further, referring to FIG. 14, system 100 receives signal Y out output by system 101 which is controlled system B as signal X in. In such a system 100, 101, even when the signal X out output by the system 100 is matched or approximated to the signal Y in input to the system 101, the system 100 is the reverse of the system 101 being the controlled system B. It becomes system A. [0006] FIG. 15 is a conceptual diagram for explaining a multi-input multi-output inverse system. FIG. 15 is an expansion of the one-input one-output system 100, 101 shown in FIG. 13 into a multipleinput multiple-output system. The system 102 inputs the signals X in1, X in2,..., X inN and outputs the signals X out1, X out2,..., X out M, and the system 103 outputs the signals Y in1, Y 07-05-2019 2 in2,. .., Y inM are input to output signals Y out1, Y out2,..., Y outN, and the system 103 is set as a control target system B. [0007] As shown in FIG. 15, the system 103 which is the control target system B is configured to output signals X out1, X out2,..., X outM output from the system 102 as signals Y in1, Y in2,. Enter as each. In these systems 102 and 103, the signals Y out1, Y out2,..., Y out N output by the system 103 are matched with the signals X in1, X in2,. Or when making it approximate, system 102 turns into reverse system A of system 103 which is controlled object system B. [0008] In FIG. 13, the purpose of designing the reverse system is to match the signal Y out output by the system 101 as the controlled system B with the signal X in input to the system 100 as the reverse system. The point at which the output in this case is observed is called a control point. In FIG. 13, a point at which the signal Y out output by the system 101 which is the control target system B is observed is a control point. Similarly, in FIG. 15, control points are points at which the signals Y out1, Y out2,..., Y outN outputted by the system 103 which is the control target system B are observed. Here, an input point of the system 101 which is the control target system B shown in FIG. 13, that is, a point at which the signal Y in is presented to the control point is set as a presentation point. The point at which the signals Y in1, Y in2,..., Y inM are presented to each input point of the system 103 which is the control target system B shown in FIG. [0009] [Sound System] Next, a controlled system and a reverse system will be described by taking an example of a sound system. In acoustic systems, inverse systems are used for processing such as sound field reproduction or room dereverberation. The control target system is a sound field in which sound field reproduction is performed or a room sound field in which reverberation is removed. [0010] 07-05-2019 3 FIG. 16 is a conceptual diagram for explaining a control target system and an inverse system in the case of using a listening sound field as a control target system in an acoustic system, corresponding to the multi-input multi-output systems 102 and 103 shown in FIG. ing. As shown in FIG. 16, in the case of constructing a control system for performing processing of sound field reproduction, the listening sound field is the control target system B. A system 103 which is a control target system B is a listening sound field, and five speakers 104-1 to 104-5 and two microphones 105-1 and 105-2 are arranged. The listening position (the position of the microphones 105-1 and 105-2) to be controlled is the control point. [0011] Assuming that the control is performed by the acoustic signals reproduced from the speakers 104-1 to 104-5 disposed in the listening sound field, the acoustic signals input to these speakers 104-1 to 104-5 are controlled system B It becomes an input signal to [0012] In the sound field reproduction, the system 104, which is the speaker 104-1 to 104-5 is referred to as a secondary sound source and the control target system B, is approximated by a transfer function which is an index indicating the sound propagation from each secondary sound source to the control point. Modeled. In this case, the control target system B is expressed as a matrix (transfer function matrix) of transfer functions of control point × secondary sound source. In the example of FIG. 16, the number of control points (the number of microphones 105-1 and 105-2) is two, and the number of speakers 104-1 to 104-5 which are secondary sound sources is five. The system B is represented as a transfer function matrix with two rows and five columns, each of which has 2 × 5 = 10 elements. [0013] If desired acoustic signals are presented to these control points, the desired acoustic signal may be input to the inverse system A after properly designing the system 102 which is the inverse system A. When the control target system B is modeled as a transfer function matrix, the inverse system A is designed using the inverse of the transfer function matrix. In general, when the 07-05-2019 4 control target system B is modeled as a matrix, the inverse system A is designed using the inverse matrix of that matrix. In particular, when the element is a real number, the inverse matrix can be obtained by numerical calculation. [0014] In order to uniquely determine the inverse system A, the matrix serving as a model of the control target system B needs to be square, that is, the number of input signals and the number of output signals are the same in the control target system B. In the case of the acoustic system shown in FIG. 16, the secondary sound sources and the control points need to have the same number. In other words, when the number of secondary sound sources is fixed, it means that only the acoustic signal at the same number of control points can be controlled. [0015] In the case where the number of output signals is larger than the number of input signals in the control target system B, there is generally no solution. In order to design an inverse system approximately to such a controlled system, a least squares method or the like is used. Such a system is called overdetermined system. [0016] On the other hand, as shown in FIG. 16, when the number of input signals is larger than the number of output signals in the control target system B, the solution is not unique. In order to design an inverse system for such a controlled system, a least squares norm solution or the like is usually used. Such a system is called an underdetermined system. [0017] The inverse matrix obtained in such over-determined or under-determined system is called pseudo-inverse. For example, in order to locally reproduce an acoustic signal, there has been proposed a local reproduction apparatus which obtains an inverse matrix of a transfer function matrix by calculating a pseudo inverse matrix (see Patent Document 1). In addition, when 07-05-2019 5 controlling a listening area set corresponding to a plurality of speakers, an acoustic signal processing apparatus has been proposed which represents the relationship between a target sound and an input signal as a matrix and calculates a pseudo inverse matrix. (See Patent Document 2). [0018] JP, 2013-110495, A JP, 2013-102389, A [0019] As described above, in the overdetermined system in which the number of output signals is larger than the number of input signals in the controlled system, the least squares method or the like is used to calculate the inverse matrix of the transfer function matrix of the controlled system. The conventional least squares method provides an approximate solution that minimizes the sum of squares of errors at all control points. This means that the errors are substantially evenly distributed for the entire control point (the entire control range), and the approximation accuracy is the same. [0020] However, instead of designing an inverse system that presents signals of the same approximate accuracy to the entire control point, it has been desired to design an inverse system that can present signals of different approximate accuracy for each control point. That is, an inverse system capable of giving priority to each control point, presenting a signal with high approximation accuracy to a control point with high priority, and presenting a signal with low approximation accuracy to a control point with low priority It was desired to design. The conventional least squares method can not calculate the inverse matrix considering the priority, and as a result, there is a problem that the inverse system can not be designed considering the priority for each control point. [0021] 07-05-2019 6 For example, in the control target system B of sound field reproduction in the acoustic system shown in FIG. 16, at control points near the center of the room, the acoustic signal is presented as directly as possible, that is, as accurately as possible. At the control point, there is a desire to design an inverse system to present the acoustic signal with reasonable accuracy. However, when the inverse matrix is calculated using the conventional least squares method, the acoustic signal is presented to all control points with the same approximate accuracy, so it is not possible to design an inverse system meeting the above-mentioned requirements. . [0022] Therefore, the present invention has been made to solve the above problems, and an object thereof is to provide an inverse system design method capable of presenting a signal with an accuracy according to a priority to a control point in a control target system, reverse A system design apparatus and program are provided. [0023] According to a first aspect of the present invention, there is provided an inverse system design method comprising a predetermined number of control points and a predetermined number of presentation points each presenting a signal to the predetermined number of control points. In an inverse system design method by an inverse system design apparatus which forms a transfer function matrix and forms an inverse matrix of the transfer function matrix, the inverse system design apparatus includes a storage unit, a transfer function matrix formation unit, a singular value decomposition unit, an inverse A matrix singular value calculation unit, a threshold processing / termination number determination unit, a truncation unit, an additional control point determination unit, and an inverse matrix formation unit, and the storage unit is configured to interpose the predetermined number of presentation points for each control point A transfer function table in which a transfer function of the above is set, and a threshold table in which a threshold is set for each of a single control point and a plurality of control points included in the predetermined number of control points are stored; function A column formation unit reads transfer functions for the same number of control points as the predetermined number of presentation points from the transfer function table stored in the storage unit, and the initial number of control points is the initial control point. A first step of forming a square transfer function matrix between a control point and the predetermined number of presentation points, and the singular value decomposition unit performing singular value decomposition on the basis of the output side in the transfer function matrix, singular A second step of generating a value matrix and an input-side basis, and the inverse matrix singular value calculation unit is configured to calculate the transfer function based on the output-side basis, the singular value matrix and the input-side basis of the transfer function matrix The third step of generating an output-side basis, a singular value matrix and an input-side basis in an inverse matrix of the 07-05-2019 7 matrix, and the threshold processing / termination number determination unit uses the threshold table stored in the storage unit to generate the initial value. Control of A fourth step of reading a threshold for a set of points, and determining a truncation number by thresholding each singular value constituting the singular value matrix in the transfer function matrix, and the truncation unit outputs an output in the inverse matrix Truncation processing is performed on each of the side base, singular value matrix and input side basis according to the number of truncations, and the output side base, singular value matrix and input side base in the inverse matrix after truncation are the above Among the control points not included in the transfer function matrix formed in the predetermined number of control points, the fifth step of storing in the storage unit, and the additional control point determination unit are the same number as the number of terminations A sixth step of determining a control point of the second control point as an additional control point, and the transfer function matrix formation unit further adds the transfer function table from the transfer function table stored in the storage unit. Reading a transfer function of the additional control point, and forming a transfer function matrix between the additional control point and the predetermined number of presentation points, and By repeating the seventh step, additional control points are increased, and for each additional control point, in the fifth step, the basis on the output side, the singular value matrix, and the basis on the input side in the inverse matrix after truncation. Are stored in the storage unit, and in the fourth step, when there is no truncation by the threshold processing, the truncation unit generates the transfer function matrix generated in the immediately preceding third step. Storing the outputside basis, singular value matrix and input-side basis of the inverse matrix of the inverse matrix in the storage unit as the output-side basis, singular value matrix and input-side basis of the truncated inverse matrix When The inverse matrix formation unit reads, from the storage unit, the output-side base, the singular value matrix and the input-side base of the truncated inverse matrix, and the output-side base, the singular value matrix and the input-side base And ninth step of respectively combining and forming an inverse matrix of the whole. [0024] Also, in the inverse system design method according to claim 2, in the inverse system design method according to claim 1, the fourth step includes: singular values and threshold values constituting singular value matrices in the transfer function matrix. Are determined, and the number of singular values smaller than the threshold is determined as the censoring number. [0025] The inverse system design method according to claim 3 is the inverse system design method according to claim 1, wherein the fourth step is the largest singularity among the singular values constituting the singular value matrix in the transfer function matrix. A value is specified, the largest singular value is divided by each singular value constituting the singular value matrix, each of the division results is compared with the threshold, and the number of division results 07-05-2019 8 larger than the threshold is calculated. It is characterized in that it is determined as a censoring number. [0026] Further, in the inverse system design method according to claim 4, in the inverse system design method according to any one of claims 1 to 3, in the threshold value table stored in the storage unit, a signal is transmitted to the control point. A threshold value reflecting the accuracy of the signal is set for each set of control points according to the accuracy of the signal at the time of presentation. [0027] In the inverse system design method according to claim 5, in the inverse system design method according to any one of claims 1 to 4, the control target system is an acoustic system, and the presentation point is a speaker. It is characterized in that the control point is a listening position or a place where a microphone is disposed. [0028] Furthermore, the inverse system design apparatus according to claim 6 forms a transfer function matrix of a controlled system including a predetermined number of control points and a predetermined number of presentation points for presenting signals to the predetermined number of control points, respectively. In the inverse system design apparatus for forming the inverse matrix of the transfer function matrix, the storage unit includes a transfer function table in which a transfer function between the control point and the predetermined number of presentation points is set for each control point, A threshold table in which a threshold is set for each set of one or more control points included in the predetermined number of control points is stored, and from the transfer function table stored in the storage unit, the predetermined number of presentation points are stored. The transfer functions for the same number of control points are read out, and the same number of control points as an initial control point form a square transfer function matrix between the initial control point and the predetermined number of presentation points. Transmission of A matrix forming unit, a singular value decomposition unit generating a base on the output side of the transfer function matrix, a singular value matrix and a base on the input side by singular value decomposition of the transfer function matrix, and the singular value decomposition unit Inverse matrix singular value calculation for generating an output side base, a singular value matrix and an input side base in the inverse matrix of the transfer function matrix based on the output side base, the singular value matrix and the input side base in the transfer function matrix The threshold value for the initial control point or the set of additional control points is read out from the threshold value table stored in the storage unit and the storage unit, and the singular value matrix in the transfer function matrix generated 07-05-2019 9 by the singular value decomposition unit is constructed. When threshold processing is performed on each singular value and the predetermined processing is satisfied by the threshold processing, the number of censors is determined, and the predetermined processing is not satisfied by the threshold processing. And a thresholding / cutoff number determination unit that determines not to abort, and an output side of the inverse matrix generated by the inverse matrix singular value calculation unit when the truncation number is determined by the thresholding / cutoff number determination unit. The base, singular value matrix and input-side base are truncated according to the number of truncations to form an output-side base, singular value matrix and input-side base in the inverse matrix after truncation, The basis on the output side in the inverse matrix of the transfer function matrix generated by the inverse matrix singular value calculation unit, when stored in the storage unit and determined not to be aborted by the threshold processing / termination number determination unit, singular values The matrix and the input-side basis are stored in the storage unit as the output-side basis, singular value matrix and input-side basis of the truncated inverse matrix. When the censoring number and the number of censorings are determined by the thresholding / censoring number determining unit, a set of control points not included in the transfer function matrix and included in the predetermined number of control points is used as an additional control point The transfer function of the additional control point determined by the additional control point determination unit is read out from the additional control point determination unit to be determined and the transfer function table stored in the storage unit, and the additional control point and presentation of the predetermined number Based on a second transfer function matrix formation unit that forms a transfer function matrix between the points, and an output-side basis, a singular value matrix, and an input-side basis in the inverted inverse matrix stored in the storage unit And an inverse matrix formation unit that forms an inverse matrix, and when the number of censors is determined by the threshold processing / termination number determination unit, the additional control point determination unit determines the additional control points, and Processing to form a transfer function matrix between the additional control point and the predetermined number of presentation points in the transfer function matrix formation unit, and the second transfer function matrix formation unit being formed in the singular value decomposition unit A process for generating an output-side basis, a singular value matrix and an input-side basis in the transfer function matrix, the outputside basis, singular value matrix and input in the inverse matrix of the transfer function matrix in the inverse matrix singular value calculation unit Processing for generating a base on the side and truncation processing according to the number of truncations in the truncation unit to form an output-side basis, singular value matrix and input-side basis in the inverse matrix after truncation When the process of storing in the storage unit is repeated and it is determined not to abort by the threshold processing / termination number determination unit, the inverse matrix forming unit transmits Reading the output-side basis, singular value matrix and input-side basis in the inverse matrix after packing, and combining the output-side basis, singular value matrix and input-side basis respectively to form an overall inverse matrix, It is characterized by 07-05-2019 10 [0029] Furthermore, the inverse system design program according to claim 7 causes a computer to execute the inverse system design method according to any one of claims 1 to 5. [0030] As described above, according to the present invention, it is possible to design an inverse system capable of presenting a signal with an accuracy according to the priority with respect to control points in the control target system. [0031] It is the schematic which shows the hardware constitutions of the reverse system design apparatus by embodiment of this invention. It is a conceptual diagram explaining a controlled system. It is a figure which shows the program etc. which were stored in the memory ¦ storage device. It is a figure explaining a transfer function table. It is a figure explaining a threshold value table. It is a figure explaining the data after truncation. It is a block diagram showing functional composition of a control part in a reverse system design device by an embodiment of the present invention. It is a flowchart which shows the inverse matrix formation process of a control part. It is a figure explaining the process (step S804) of a threshold value process / discontinuation 07-05-2019 11 number determination part. It is a figure explaining the truncation process (step S806) of the inverse matrix by a truncation part. It is a figure explaining the example of inverse matrix formation processing. It is a figure explaining the example of inverse matrix formation processing. It is a conceptual diagram explaining a reverse system. It is a conceptual diagram explaining a reverse system. It is a conceptual diagram explaining the multi-input multi-output inverse system. In an acoustic system, it is a conceptual diagram explaining a controlled system and a reverse system at the time of using a listening sound field as a controlled system. [0032] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In general, when calculating the inverse matrix of the transfer function matrix of the control target system, if the transfer function matrix is square (the number of input signals and the number of output signals are the same in the control target system), or non-square In either case (in the case of a superior decision system in which the number of output signals is larger than the number of input signals in the controlled system) or in the case of an underdetermined system in which the number of input signals is larger than the number of output signals) Processing is required to improve the quality. For example, in the case of an acoustic system, an inverse system is designed using signals in the frequency domain, the inverse system in the frequency domain is converted to the time domain, and the design result in the inverse system in the time domain is often implemented as a filter. [0033] In the present invention, a truncated singular value decomposition method is used as a method for enhancing the stability of the inverse system. The truncated singular value decomposition performs singular value decomposition on the transfer function matrix when calculating the inverse matrix of the transfer function matrix of the control target system, and uses the input / output side base and the singular value matrix to calculate the inverse matrix. Find input / output basis and singular value matrix in singular value decomposition. Then, among the singular values of the derived transfer function matrix, the singular value of the inverse matrix corresponding to the small singular value is replaced with 0 to terminate the singular value. Thereby, the amplitude of the inverse matrix can be suppressed and stabilized. 07-05-2019 12 [0034] Further, the present invention presupposes a controlled system having a wide control range (a large number of control points), ie, an overdetermined system in which the number of output signals is larger than the number of input signals in the controlled system. Control range by recursively increasing the output signal (control point) of the control target system so that the transfer function matrix is transformed from a square matrix to a matrix of overdetermined system (a matrix whose number of rows is larger than the number of columns). It is characterized by spreading. [0035] In the example of the acoustic system shown in FIG. 16, a desired acoustic signal is presented to the control points in a wide control range by recursively increasing the number of listening positions as control points. In this case, instead of giving a solution that minimizes the square of the error by the least squares method, priority is given to the control points to be increased, and a high precision control signal is presented at the control points with high priority. The control points are increased to present the acoustic signal at a lower accuracy to some degree at lower rank control points. [0036] As described above, in the present invention, an inverse system is designed by recursively adding control points with different approximation accuracy to the control target system and calculating an inverse matrix in which the control range is expanded. Hereinafter, an acoustic system will be described as an example. [0037] [Hardware Configuration] First, the hardware configuration of the inverse system design apparatus according to the embodiment of the present invention will be described. FIG. 1 is a schematic view showing a hardware configuration of an inverse system design apparatus 07-05-2019 13 according to an embodiment of the present invention. The reverse system design apparatus 1 includes a CPU 51, a storage unit 52 including ROM and RAM for storing programs and tables, etc., a storage device (hard disk drive) 53 for storing application programs, tables and data, and the like. An operation / input unit 54 for inputting and controlling predetermined data according to the operation of a keyboard and a mouse by the operator of the system design apparatus 1, and a display for outputting screen information for prompting the operator to perform data input operation and the like on a display An output interface unit 55 and a communication unit 56 for transmitting and receiving programs and data via a network such as the Internet are provided. These components are mutually connected via a system bus 57. [0038] The storage device 53 includes an operating system (OS) program for providing the basic functions of the inverse system design apparatus 1, so that the transfer function matrix of the control target system is transformed from the square matrix to the matrix of the overdetermined system. , An inverse system design program for designing an inverse system by recursively increasing control points of a control target system and calculating an inverse matrix with a wide control range, and various tables and data used in the inverse system design program Etc are stored. [0039] The reverse system design program is read out from the storage device 53 to the RAM of the storage unit 52 and executed by the CPU 51 when the reverse system design device 1 performs a process. The various tables and data are generated by the inverse system design program, are written from the RAM of the storage unit 52 to the storage device 53 by the CPU 51, and are read from the storage device 53 to the RAM of the storage unit 52 as necessary. [0040] Here, the OS program is executed by the CPU 51, and manages the storage unit 52, the storage unit 53, the operation / input unit 54, the display output interface unit 55, and the communication unit 56 as basic functions of the inverse system design device 1. . Then, with the OS program being executed by the CPU 51, the above-mentioned inverse system design program 07-05-2019 14 is executed. [0041] The control unit 50 is constituted by the CPU 51 and the storage unit 52, and the CPU 51 reads out the inverse system design program stored in the storage device 53 into the storage unit 52 and executes the program to control the entire inverse system design device 1 collectively. FIG. 1 shows a state in which the inverse system design program is read from the storage device 53 to the storage unit 52. As described above, in the inverse system design apparatus 1, the control unit 50 performs various processes in accordance with the inverse system design program with the hardware configuration shown in FIG. [0042] (Control Target System) FIG. 2 is a conceptual diagram for explaining a control target system. This control target system is the listening sound field of the sound system, and the speakers 30-1 to 30-M which are M secondary sound sources, and N microphones 40-at each control point which is a predetermined listening position. 1 to 40-N are arranged. Here, M and N are positive integers and M <N. [0043] FIG. 3 is a diagram showing a program and the like stored in the storage device 53 shown in FIG. The storage device 53 stores an inverse system design program, a transfer function table, a threshold value table, data after truncation, and the like. The reverse system design program is read from the storage device 53 to the RAM of the storage unit 52 and executed by the CPU 51. The transfer function table, the threshold value table, and the data after truncation are generated by the CPU 51 executing the inverse system design program, written to the RAM of the storage unit 52, and written to the storage device 53 from the RAM of the storage unit 52. In addition, the transfer function table, the threshold value table, and the data after truncation are read from the storage device 53 to the RAM of the storage unit 52 as necessary. [0044] 07-05-2019 15 The inverse system design program, the transfer function table, and the threshold value table may be downloaded from an external server to the storage device 53 via the network such as the Internet and the communication unit 56. Further, even if the transfer function table, the threshold value table and the truncated data generated by the inverse system design program and stored in the storage device 53 are uploaded to an external server via the communication unit 56 and a network such as the Internet. Good. [0045] Transfer Function Table FIG. 4 is a diagram for explaining a transfer function table. This transfer function table is formed of transfer function groups between the speakers 30-1 to 30-M, which are M secondary sound sources, every control point 1 to N. The transfer function group of control point 1 is (g 11, g 12,..., G 1M), and the transfer function group of control point 2 is (g 21, g 22,..., G 2M) Similarly, the transfer function group of the control point N is (g N1, g N2,..., G NM). Here, g 11 represents a transfer function between the microphone 40-1 as the control point 1 and the speaker 30-1 as the secondary sound source in FIG. 2, and g 12 represents the microphone 40 as the control point 1. 7 shows a transfer function between the signal −1 and the secondary sound source speaker 30-2. That is, g ij represents a transfer function between the microphone 40-i which is the control point i and the speaker 30-j which is the secondary sound source. [0046] The transfer function table shown in FIG. 4 is generated by the table generation unit 10 described later, and stored in the storage unit 52 and the storage device 53. The transfer function table is read from the storage unit 52 by the transfer function matrix formation unit 11 described later and used to form a transfer function matrix, and read from the storage unit 52 by the additional control point determination unit 17. Used to determine the control point to be added. The transfer functions g 11, g 12,..., G NM are measured in advance in the control target system shown in FIG. 2 and are operationally input to the inverse system design device 1 by the operator. [0047] 07-05-2019 16 (Threshold Table) FIG. 5 is a diagram for explaining a threshold table. The threshold value table is configured of control points and threshold values for each of a single control point and a plurality of control points at control points 1 to N. One or more control points correspond to an initial control point set by a transfer function matrix formation unit 11 described later and an additional control point determined by the additional control point determination unit 17. The control score indicates the number of control points, and the threshold is a threshold for truncation processing, and indicates a reference value to be compared with the singular value for generating a truncated matrix. [0048] The threshold value table shown in FIG. 5 is generated by the table generation unit 10 described later, and stored in the storage unit 52 and the storage device 53. The threshold value table is read from the storage unit 52 by the threshold value processing / termination number determination unit 15 described later, and is used to determine the number of terminations of the singular value. Each data which comprises a threshold value table is operation-inputted to the reverse system design apparatus 1 by the operator. [0049] (Data after truncation) FIG. 6 is a diagram for explaining the data after truncation. The data after truncation is the basis on the output side of the inverse matrix G # 0 <-1>,..., G # K <-1> of the transfer function matrix G # 0,. V # 0,..., V # K, singular value matrices ## 0 <−1>,..., ## K <−1> and input side bases U # 0 <H>,. It is U # K <H>. Details will be described later. [0050] The post-cutout data shown in FIG. 6 is formed by the cut-out unit 16 described later, and stored in the storage unit 52 and the storage device 53. Also, the data after truncation is read from the storage unit 52 by the inverse matrix formation unit 18 described later, and used to form the entire inverse matrix G <−1>. [0051] 07-05-2019 17 [Functional Configuration] FIG. 7 is a block diagram showing a functional configuration of control unit 50 in reverse system design apparatus 1 shown in FIG. 1, and control unit 50 shown in FIG. 1 executes reverse system design program processing. It shows the functional configuration at the time. The control unit 50 includes a table generation unit 10, a transfer function matrix formation unit 11, an inverse matrix singular value calculation unit 12, a singular value decomposition unit 13, an inverse matrix calculation unit 14, a thresholding / cutoff number determination unit 15, and a truncation unit 16. , An additional control point determination unit 17, an inverse matrix formation unit 18, and a storage unit 52. [0052] The table generation unit 10 inputs respective transfer functions between the microphones 40-1 to 40-N and the speakers 30-1 to 30-M, which are measured in advance, in accordance with the operation input of the operator. Then, the table generation unit 10 has a transfer function shown in FIG. 4 configured by a transfer function group between the control points 1 to N and the speakers 30-1 to 30-M which are M secondary sound sources. A table is generated, and the generated transfer function table is stored in the storage unit 52. [0053] Further, the table generation unit 10 inputs the number of control points and the threshold for each of the single control point and the plurality of control points in the control points 1 to N according to the operation input of the operator, and generates the threshold table shown in FIG. The generated threshold value table is stored in the storage unit 52. Here, a single control point and a plurality of control points in the control points 1 to N are prioritized, and a threshold value corresponding to the priority is input. For example, referring to FIG. 5, when the priority of control point 9 is higher than the priority of control point 11, a threshold smaller than control point 11 is input to control point 9. [0054] The transfer function matrix formation unit 11 has a square transfer function matrix G k = G of N 0 × N 0 corresponding to the initial number of control points N 0 equal to the number of speakers 30-1 to 30-M as secondary sound sources. Form 0. Further, the transfer function matrix 07-05-2019 18 formation unit 11 receives additional control point information from the additional control point determination unit 17 described later, reads the transfer function group of the additional control point from the transfer function table of the storage unit 52, and transfers the additional control point. Form a function matrix G k. Then, the transfer function matrix formation unit 11 outputs the formed transfer function matrix G k to the singular value decomposition unit 13. Here, k indicates the number of repetitions of the process described later. [0055] The singular value decomposition unit 13 receives the transfer function matrix G k from the transfer function matrix formation unit 11 and performs singular value decomposition on the transfer function matrix G k according to the following equation to output the basis U k on the output side and the singular value Generate a matrix k k and an input-side basis V k <H>. Then, the singular value decomposition unit 13 outputs the generated singular value matrix Σ k to the threshold value processing / cutoff number determination unit 15, and at the same time, the transfer function matrix G k = U k k k V k <H> It is output to the inverse matrix singular value calculation unit 12. In addition, since the method of singular value decomposition is known, the detailed description is omitted here. Here, u is an output vector, σ is a singular value, v is an input vector, N k is the number of control points, and H of the superscript indicates complex conjugate transposition. Also, N k ≦ M. [0056] In the equation (1), the elements constituting the singular value matrix k k consist of singular values and values of 0, and the singular values are N k rows and N k columns from the position of the first row and the first column. Are arranged diagonally toward the position of (the row and column numbers are the same position), and σ 11> σ 22>...> Σ N k N k. In addition, elements other than singular values are 0. [0057] The inverse matrix singular value calculation unit 12 receives the transfer function matrix G k = U k k k V k <H> from the singular value decomposition unit 13 and, as shown in the equation (1) and the equation (2) described later , Base V k at the output side of the inverse matrix, singular elements using respective elements constituting the output U k of the transfer function matrix G k, the singular value matrix k k and the input base V k <H> A value matrix k k <−1> and an input-side basis U k <H> are generated and output to the inverse matrix calculation unit 14. 07-05-2019 19 [0058] The inverse matrix calculation unit 14 receives the basis V k on the output side of the inverse matrix, the singular value matrix Σ k <-1> and the basis U k <H> on the input side from the inverse matrix singular value calculation unit 12, and Calculate the inverse matrix G k <−1> = V k k k <−1> U k <H> by the equation, and set the basis V k on the output side of the input inverse matrix, the singular value matrix Σ k <−1> and The inverse matrix G k <−1> = V k k k <−1> U k <H> is output to the truncation unit 16 together with the basis U k <H> on the input side. [0059] In the equation (2), elements constituting the singular value matrix Σ k <−1> consist of singular values and values of 0, and the singular values are N k rows from the position of the first row and the first column, and It is arranged diagonally toward the position of the N kth column (the position where the row and column numbers are the same), and the reciprocal 1 / σ of the singular value σ 11> σ 22>...> Σ N k N k in the equation (1) It becomes 11 <1 / σ 22 <... <1 / σ N k N k. [0060] The threshold processing / termination number determination unit 15 receives the singular value matrix Σ k of the transfer function matrix G k from the singular value decomposition unit 13, and forms the transfer function matrix G k from the threshold table of the storage unit 52. The threshold values T k corresponding to the set of control points are read out, and singular values σ 11, σ 22,..., Σ Nk Nk constituting the singular value matrix k k and the threshold value T k are listed in ascending order of singular value (σ 11 , Σ 22,..., Σ Nk N k), and in the order, first identify the singular value σ nn determined to be smaller than the threshold T k, and determine the truncation number as N k −n + 1 Do. Then, the threshold processing / termination number determination unit 15 outputs the termination number (N k −n + 1) to the truncation unit 16 and the additional control point determination unit 17. The threshold processing / termination number determination unit 15 can not identify the singular value σ nn smaller than the threshold T k, and determines no termination (do not terminate) if there is no termination, and information without termination is obtained. It is output 07-05-2019 20 to the truncation unit 16 and the inverse matrix formation unit 18. The censoring number (N k −n + 1) is an integer of 1 or more. [0061] The threshold processing / termination number determination unit 15 specifies the singular value σ nn by comparing the result of division using the largest singular value with the threshold T k, and determines the number of terminations to be N k −n + 1. (Hereinafter referred to as comparison processing based on the division result of the largest singular value). Specifically, the thresholding / cutoff number determination unit 15 identifies the largest singular value among the singular values σ 11, σ 22,..., Σ Nk Nk constituting the singular value matrix k k, and identifies the largest. The singular values of are divided by singular values σ 11, σ 22,..., Σ NkNk respectively. Then, the threshold processing / termination number determination unit 15 compares each of the division results with the threshold T k in the order of the largest singular value (in order of σ 11, σ 22,..., Σ Nk Nk), and Among them, the singular value σ nn determined to be larger than the threshold T k at first is identified, and the number of censors is determined to be N k −n + 1. [0062] The truncation unit 16 receives the number of truncations (N k −n + 1) or information without truncation from the threshold processing / termination number determination unit 15, and the inverse matrix calculation unit 14 inputs inverse matrix G k <−1> = V k k k < 1. Input the base V k on the output side of the inverse matrix, the singular value matrix Σ k <-1>, and the base U k <H> on the input side of the inverse matrix. [0063] When the truncation unit 16 receives the censoring number (N k −n + 1), the value in the singular value matrix に 対 し k with respect to the inverse matrix G k <−1> = V k k k <−1> U k <H> The singular values of the inverse matrix k k <−1> corresponding to small singular values of are removed by truncation number (N k −n + 1) by the truncation number (termination), and the corresponding output side of the inverse matrix G k <−1> Each matrix is truncated by truncating the elements of the basis V k and the basis U k <H> on the input side. [0064] 07-05-2019 21 The truncation unit 16 calculates a new singular value number (the number of singular values after truncation) N # k = n−1 after truncation as shown in the following formula: inverse matrix G # k <−1> after truncation The base V # k on the output side, the singular value matrix ## k <−1>, and the base U # k <H> on the input side are formed, and these are stored in the storage unit 52 as truncated data. [0065] When the truncation unit 16 receives the no-termination information from the threshold value processing / termination number determination unit 15, the truncation unit 16 outputs the inverse matrix G # k <-1> input from the inverse matrix calculation unit 14 without performing the above-mentioned truncation process. The base V # k on the side, the singular value matrix ## k <−1>, and the base U # k <H> on the input side are stored in the storage unit 52 as data after truncation. In this case, K = k. k indicates the number of iterations as described above, and K indicates the final number of iterations. A specific example will be described later. [0066] The additional control point determination unit 17 receives the number of truncations (N k −n + 1) from the thresholding / termination number determination unit 15 and is a target when the transfer function matrix formation unit 11 forms the transfer function matrix G k. It determines based on the transfer function table stored in the memory ¦ storage part 52 by making the control point for no censoring number (Nk-n + 1) into an additional control point. For example, among the control points 1 to N of the transfer function table, the control points have a truncation number (N k −n + 1) that is not a target when the transfer function matrix forming unit 11 forms the transfer function matrix G k. Then, control points with small numbers or control points set in advance are determined as additional control points. The additional control point determination unit 17 outputs information (such as the number of the additional control 07-05-2019 22 point) on the determined additional control point to the transfer function matrix formation unit 11. [0067] Here, the matrix truncated according to the censoring number (N k −n + 1) will be ranked down. Using the same number of control points as the number of truncations (N k −n + 1) determined by the threshold processing / termination number determination unit 15 as an additional control point is used to increase the control points as a control remaining capacity. It is for. [0068] When the inverse matrix formation unit 18 receives the information on no truncation from the thresholding / termination number determination unit 15, the inverse matrix formation unit 18 determines from the storage unit 52 the truncated inverse matrix G # 0 <-1> to G # K <-1> after truncation. Read out the basis V # 0 to V # K on the output side, the singular value matrix ## 0 <1> to ## K <-1> and the basis U # 0 <H> to U # K <H> on the input side . Then, as shown in the following equation (4), the inverse matrix forming unit 18 sets the output-side bases V # 0 to V in the inverted matrix G # 0 <−1> to G # K <−1> after truncation. # K, singular value matrices ## 0 <-1> to ## K <-1> and input-side bases U # 0 <H> to U # K <H> are respectively synthesized, and an inverse matrix G <-1 Form> and output. [0069] Specifically, the inverse matrix forming unit 18 calculates an inverse matrix for a matrix of complex conjugate transposition in which the bases V # 0 to V # K on the output side after truncation are arranged in order, and this is output side after synthesis Generate as the basis of [V <H>] <-1>. In addition, the inverse matrix forming unit 18 sets the singular value matrices ## 0 <−1> to ## K <−1> after truncation, from the position of the first row and the first column to the K th row and the K th column. A singular value matrix 向 け <-1> after synthesis is generated by arranging diagonally to the position and arranging 0 in other elements. In addition, the inverse matrix forming unit 18 determines the bases U # 0 <H> to U # K <H> on the input side after truncation from the positions of the first row and the first column to the positions of the Kth row and the Kth column. By arranging them diagonally to the head and arranging 0 in the other elements, a base U <H> on the input side after synthesis is generated. Then, the inverse 07-05-2019 23 matrix forming unit 18 sets the output-side basis [V <H>] <− 1> after combining, the singular value matrix Σ <−1> after combining, and the basis U <H> of the input-side after combining To form an inverse matrix G <-1> = [V <H>] <-1> Σ <-1> U <H> according to the equation (4). [0070] The inverse matrix G <-1> formed in this manner is, for example, a filter for generating an acoustic signal to be output to the speakers 30-1 to 30-M which are secondary sound sources of the acoustic system shown in FIG. Used for the factor of That is, the control device receives the inverse matrix G <-1> formed by the inverse system design device 1, generates a filter using the inverse matrix G <-1>, and uses the generated filter to obtain the speaker 30- Generate an acoustic signal for output to 1 to 30-M. Then, the loudspeakers 30-1 to 30-M receive the acoustic signal generated by the control device and output the acoustic signal to the microphone 40-1 and the like. As a result, it is possible to present an acoustic signal with an accuracy according to the threshold value of the threshold value table in which the priority is reflected, with respect to the control point such as the microphone 40-1. [0071] [Process (Inverse Matrix Forming Process)] Next, the process (inverse matrix forming process) of the control unit 50 shown in FIG. 7 will be described. As described above, the control unit 50 calculates an inverse matrix while recursively increasing control points in order to widen the control range of the control target system by executing the inverse system design program. [0072] FIG. 8 is a flowchart showing the inverse matrix forming process of the control unit 50 shown in FIG. Hereinafter, the inverse matrix forming process of FIG. 8 will be described by taking the case where the listening sound field of the acoustic system shown in FIG. 2 is a control target system as an example. In FIG. 2, the number of speakers 30-1 to 30 -M as secondary sound sources is M, and the number of microphones 40-1 to 40 -N as control points is N. Further, in the inverse matrix formation processing, the number of control points in repeating the formation of the transfer function matrix G k, singular value decomposition, threshold processing, truncation number determination processing, and the like is set to N 0 to N K. 07-05-2019 24 [0073] The sound propagation from the speakers 30-1 to 30-M, which are secondary sound sources, to the microphones 40-1 to 40-N, which are control points, has characteristics described by a transfer function, and inverse matrix formation processing , And discrete frequency bins of the transfer function. In addition, it is assumed that the transfer function table and the threshold value table generated by the table generation unit 10 are stored in the storage unit 52. [0074] Let N 0 be the initial value of control points, and N 0 = M. That is, in the 0th process (initial process) where k = 0, the speakers 30-1 to 30-M as secondary sound sources and the microphones 40-1 to 40- as control points of the same number M as this. The processing is performed on the assumption of a control target system configured by M and the like. [0075] In FIG. 8, first, the control unit 50 sets the number of iterations k = 0 (step S801), and performs the 0th process (initial process). The transfer function matrix formation unit 11 sets the control point 1 from the transfer function table (see FIG. 4) of the storage unit 52 for the control points 1 to M of the number of initial values N 0 = M set in advance as initial processing. Transfer functions of ˜M are read out to form a square transfer function matrix G 0 of N 0 × N 0 (M × M) (step S802). Thus, a square transfer function matrix G 0 having transfer functions g 11 to g N 0 M (g MM) between the control points 1 to N 0 (M) and the secondary sound sources 1 to M is formed. [0076] The singular value decomposition unit 13 performs singular value decomposition on the transfer function matrix G k, and generates the basis U k on the output side, the singular value matrix Σ k and the basis V k <H> on the input side, as in the equation (1). (Step S803). [0077] 07-05-2019 25 The threshold processing / termination number determination unit 15 performs threshold processing on the singular value matrix Σ k of the transfer function matrix G k subjected to singular value decomposition by the singular value decomposition unit 13 to determine the number of truncations (N k −n + 1) or no termination. (Step S804). Specifically, from the threshold value table of the storage unit 52, the threshold processing / termination number determination unit 15 sets a threshold T k corresponding to a set of control points (control points N k) when forming the transfer function matrix G k. Reading out, singular values σ 11, σ 22,..., Σ Nk Nk (singular values arranged in descending order) constituting the singular value matrix k k are sequentially compared with the threshold T k, and smaller than the threshold T k The first singular value σ nn determined to be determined is determined, and the number of censors is determined to be N k −n + 1. The singular values are σ 11> σ 22>...> Σ N k N k as described above. The threshold processing / termination number determination unit 15 determines no termination if singular values σ 11, σ 22,..., Σ Nk Nk smaller than the threshold T k do not exist. [0078] The threshold processing / termination number determination unit 15 may perform comparison processing based on the division result of the maximum singular value described above. Specifically, the thresholding / cutoff number determination unit 15 determines the largest singular value of the singular values σ 11, σ 22,..., Σ NkNk constituting the singular value matrix k k as the singular value σ 11, .., .sigma. NkNk and divide each of the division results and the threshold T.sub.k in the order of large singular value (in the order of .sigma..sub.11, .sigma..sub.22,..., .sigma.NkNk), The first singular value σ nn determined to be larger than T k may be identified, and the number of censors may be determined to be N k −n + 1. [0079] FIG. 9 is a diagram for explaining the process (step S804) of the threshold process / termination number determination unit 15. The singular value σ nn specified by sequentially comparing the singular values σ 11, σ 22,..., Σ Nk Nk and the threshold T k is given by the singular value σ n1 n−1> T k> σ nn It is related. Further, the truncation number (N k −n + 1) is a singular value σ nn, which is smaller than the threshold T k among the singular values σ 11, σ 22,..., Σ Nk Nk included in the singular value matrix k k. , Σ N k N k. 07-05-2019 26 [0080] As shown in the parenthesis in FIG. 9, when the thresholding / termination number determination unit 15 performs comparison processing based on the division result of the maximum singular value described above, the division results σ 11 / σ 11, σ 11 / σ 22 , ..., σ 11 / σ N k N k and the threshold value T k are identified in order, and the singular value σ nn is (σ 11 / σ n-1 n-1) <T k <(σ 11 / There is a relation of σ nn). Further, the censoring number (N k −n + 1) is the singular value σ nn, of the singular values σ 11, σ 22,..., Σ Nk Nk contained in the singular value matrix k k, the division result is larger than the threshold T k. ..., the number of σ NkNk. [0081] In step S 804 in FIG. 8, the threshold value table includes control points 1,..., N 0 of initial value N 0 = M in number for the 0th process (initial process) where k = 0. It is assumed that a threshold T 0 corresponding to M) is stored. In this case, in the zeroth process (initial process) where k = 0, the threshold process / termination number determination unit 15 sets a preset threshold T instead of reading the threshold T 0 from the threshold table of the storage unit 52. 0 may be used. [0082] Further, the threshold processing / termination number determination unit 15 can not specify the singular value σ nn smaller than the threshold T k in step S804, and can not determine the number of truncations (N k −n + 1), no termination decide. [0083] When the threshold processing / termination number determination unit 15 performs the comparison processing based on the division result of the maximum singular value described above, in the case of no termination, specifying the singular value σ nn whose division result is larger than the threshold T k. Is determined when [0084] Referring back to FIG. 8, the inverse matrix singular value calculation unit 12 generates the 07-05-2019 27 inverse matrix G from the basis U k on the output side generated by the singular value decomposition unit 13, the singular value matrix k k and the basis V k <H> on the input side. The base V k on the output side of <−1>, the singular value matrix k k <−1> and the base U k <H> on the input side are generated, and the inverse matrix calculation unit 14 generates The inverse matrix G k <−1> is calculated (step S 805). [0085] When the truncation number (N k −n + 1) is determined in step S804, the truncation unit 16 determines the inverse matrix G k <−1> = V k k k <−1> U k <1 obtained in step S805. For H>, truncate it to an element according to the truncation number (N k −n + 1), and form the inverse matrix G # k <−1> = V # k ## k <−1> U # k <H> after truncating In the case where it is determined in step S804 that no termination has been made, the termination process is not performed (step S806). A specific example will be described later. Then, the truncation unit 16 stores the inverse matrix G # k <−1> = V # k ## k <−1> U # k <H> after truncation in the storage unit 52. [0086] FIG. 10 is a diagram for explaining the truncation process (step S806) of the inverse matrix G k <−1> = V k k k <−1> U k <H> by the truncation unit 16. FIG. 10 corresponds to the equations (2) and (3), and the basis V k on the output side is truncated by removing the element of the truncation number (N k −n + 1), and the basis on the output side after truncation V # k is formed. The elements in this case are v 1,..., V n-1 and N # k = n-1. In addition, the singular value matrix Σ k <−1> is truncated by removing the elements of the truncation number (N k −n + 1), and the truncated singular value matrix Σ # k <−1> is formed. The singular values in this case are 1 / σ 11,..., 1 / σ n-1 n-1 and N # k = n-1. Also, the basis U k <H> on the input side is truncated by removing the element of the truncation number (N k −n + 1), and the basis U # k <H> on the input side after truncation is formed. The elements in this case are u 1,..., U n-1 and N # k = n-1. 07-05-2019 28 [0087] Thus, the truncation process of the truncation unit 16 forms a truncated inverse matrix G # k <1> = V # k ## k <-1> U # k <H> based on the threshold value T k. The number of singular values is reduced from N k to N # k = n-1. [0088] Here, the number of singular values N # k in the matrix after truncation is larger when the threshold T k is smaller than when the threshold T k is large. On the other hand, the threshold T k is set to a smaller value when the priority of the control point is higher than when the priority is lower. Therefore, the control point with high priority has a larger number N # k of singular values than the control point with low priority. The approximation accuracy at the control point can be enhanced by using an inverse matrix G <-1> in which a matrix having a large number of singular values is synthesized. On the other hand, for control points with lower priorities, the number of singular values N # k decreases. By using the inverse matrix G <-1> having a small number of singular values, it is possible to generate an acoustic signal in which steep amplification is suppressed, and stabilization of the control target system can be achieved. This combination can realize stable control as a whole. [0089] When the threshold processing / termination number determination unit 15 performs the comparison processing based on the division result of the maximum singular value described above, the number N # k of singular values in the matrix after truncation is smaller than the case where the threshold T k is small. The larger one is more. On the other hand, the threshold T k is set to a larger value when the priority of the control point is higher than when the priority is lower. [0090] That is, by changing the threshold value T k for each recursive process which is the k-th process, the accuracy of the acoustic signal to be presented to the control point is changed for each set of control points, and stabilization is achieved. it can. 07-05-2019 29 [0091] For example, in the control target system shown in FIG. 2, at the control point near the center of the room, the priority is increased and a small threshold T k is set, and at control points in other places, the priority is lowered. When a large threshold T k is set, a matrix with a large number of singular values is formed for control points near the center of the room, so the acoustic signal is kept as is as possible, that is, an accurate acoustic signal is presented. be able to. In addition, since a matrix with a small number of singular values is formed for other control points, it is possible to present an acoustic signal of moderate accuracy. Filters designed in this way are generally stable. [0092] When the threshold processing / cutoff number determination unit 15 performs comparison processing based on the division result of the maximum singular value described above, for example, in the control target system shown in FIG. The higher the priority, the larger threshold T k is set, and at the other control points, the lower the priority, lower threshold T k. Also in this case, an accurate acoustic signal can be presented for a control point near the center of the room, and an audible signal of moderate accuracy can be presented for other control points. [0093] As a result, by using the inverse matrix G <-1> formed by the inverse matrix forming process, an acoustic signal in which steep amplification is suppressed can be generated, and stabilization of the control target system can be achieved. Further, since the cessation singular value decomposition is performed according to the threshold T k, an acoustic signal with accuracy according to the threshold T k reflecting the priority can be generated, and a control system desired by the operator can be constructed. Can. [0094] 07-05-2019 30 Returning to FIG. 8, the control unit 50 determines whether or not the aborting process has been performed in step S806 (step S807). Specifically, when the control unit 50 determines that the number of aborts (N k −n + 1) is determined in step S804 in step S807, and the abort process is performed in step S806 (step S807: Y), It transfers to step S808. On the other hand, when control unit 50 determines in step S807 that the number of aborts (N k −n + 1) is not determined in step S804, that no abort is determined, and it is determined that the abort process is not performed in step S806 (step S 807: N), and the process proceeds to step S 811. [0095] The additional control point determination unit 17 transitions from step S 807 (when truncation processing is performed), and the number of truncations not being a target when the transfer function matrix formation unit 11 forms the transfer function matrix G k (N The number of control points equal to k-n + 1) is determined as an additional control point based on the transfer function table stored in the storage unit 52 (step S808). For example, when the control points 1 to 8 are targets for forming the transfer function matrix G k, they are stored in the transfer function table of the storage unit 52 in ascending order of control point numbers, as shown in FIG. Therefore, the additional control point determination unit 17 determines the control point 9 to the control point 9+ (N k −n + 1) −1 as the additional control point based on the transfer function table. [0096] After step S808, the control unit 50 sets N k -n + 1 as a new N k and increments k to set a new k (step S809). Then, the transfer function matrix formation unit 11 reads the transfer function group of the additional control point from the transfer function table of the storage unit 52 for the additional control point added in step S808 as processing of the number of iterations k, Form a matrix G k (step S810). As a result, a transfer function matrix G k having elements of transfer functions between the additional control points and the secondary sound sources 1 to M is formed. Then, the process proceeds to step S803. Thus, the number of iterations k is incremented in step S809, a new N k is set, and the k-th process is sequentially performed until it is determined in step S807 that the abort process has not been executed. [0097] 07-05-2019 31 The inverse matrix formation unit 18 proceeds from step S 807 (when truncation processing is not performed), and the truncated inverse matrix G # 0 <−1 stored in the storage unit 52 as post-truncation data in step S 806. > ˜G # K <−1> on output side basis V # 0 to V # K, singular value matrices ## 0 <−1> to Σ # K <−1> and input side basis U # 0 <H > Read ˜ U # K <H> and combine these matrices as shown in equation (4) above to combine the inverse matrix G # 0 <-1> ˜ G # K <-1> , Form the entire inverse matrix G <-1> (step S811). That is, K is the maximum value of the number of iterations k and indicates the number of times processing was actually performed. [0098] [Specific Example] Next, the inverse matrix forming process of the control unit 50 shown in FIG. 8 will be described by taking a specific example. 11 and 12 are diagrams for explaining specific examples of the inverse matrix formation process. Taking the case where the listening sound field of the acoustic system shown in FIG. 2 is the control target system as an example, in the control target system, the speakers 30-1 to 30-8, which are eight secondary sound sources, and each control point It is assumed that fifteen microphones 40-1 to 40-15 are disposed in the. つま り、Ｍ＝８、Ｎ＝１５とする。 [0099] In addition, it is assumed that the transfer function table and the threshold value table generated by the table generation unit 10 are stored in the storage unit 52. The transfer function table is formed of transfer function groups between the speakers 30-1 to 30-8, which are eight secondary sound sources, every control point 1 to 15. The threshold value table is configured of control points and threshold values for each set of control points. In this example, since the initial number N 0 of control points is 8 and the number N of control points is 15, control points 8 and threshold T 0 for control points 1 to 8 are set in the threshold table. For the other control points 9 and the like, thresholds corresponding to the number of control points to be added are respectively set. [0100] For example, the control points 1 to 8 are arranged near the center of the listening sound field of 07-05-2019 32 the control target system, the control points 9 to 15 are arranged in other places, and the control points 1 to 8 have high priority and control The priority of points 9 to 15 is assumed to be in the order of numbers. In this case, the threshold value of the threshold value table is set smaller for control points 1 to 8 and larger for the control points 9 to 15 as the number is larger. This is because when the threshold value is set to a small value, the number of truncations of singular values decreases, and by using the inverse matrix formed by this, it is possible to generate an accurate acoustic signal. In addition, when the threshold value is set to a large value, the number of truncations of the singular value increases, and by using the inverse matrix formed by this, an acoustic signal of moderate accuracy can be generated and designed. This is because the entire filter can be stabilized. [0101] When the threshold processing / cutoff number determination unit 15 performs the comparison processing based on the division result of the maximum singular value described above, the threshold of the threshold table is set to a large value for the control points 1 to 8 and the control is performed. A smaller value is set for points 9 to 15 as the number is larger. [0102] Let N 0 = 8 be the initial value of the control score. That is, in the 0th process (initial process) in which the number of repetitions k is 0, the speakers 30-1 to 30-8, which are secondary sound sources, and the microphones 40-1 to 40, which are the same number of control points. The process is performed on the assumption that the control target system is configured of −8. [0103] As shown in FIG. 11, in the 0th process of k = 0, the transfer function matrix G 0 formed by the transfer function matrix forming unit 11 is a square matrix with eight rows and eight columns (8 × 8). It becomes. Then, the basis U 0 on the output side generated by the singular value decomposition of the singular value decomposition unit 13, the singular value matrix さ れ る 0 and the basis V 0 <H> on the input side are respectively 8 × 8 matrices. 07-05-2019 33 [0104] Here, it is assumed that the number of censors determined by the threshold value processing / number of censors determination unit 15 is two. The basis V # 0 on the output side, the singular value matrix ## 0 <-1>, and the basis U # 0 <H> on the input side in the inverted matrix G # 0 <1> formed by the truncation unit 16 are , 8 × 6 matrix, 6 × 6 matrix and 6 × 8 matrix respectively. [0105] Next, in the first process of k = 1, the additional control points 9 formed by the transfer function matrix forming unit 11 with the two control points 9 and 10 corresponding to the truncation number 2 as the additional control points, The ten transfer function matrices G 1 are 2 × 8 matrices. The basis U 1 on the output side generated by the singular value decomposition of the singular value decomposition unit 13, the singular value matrix Σ 1 and the basis V 1 <H> on the input side are 2 × 2 matrices and 2 × 8, respectively. It will be a matrix and an 8 × 8 matrix. [0106] Here, it is assumed that the number of censors determined by the threshold processing / number of censors determination unit 15 is one. The base V # 1 on the output side, the singular value matrix ## 1 <−1> and the base U # 1 <H> on the input side in the truncated inverse matrix G # 1 <−1> formed by the truncation unit 16 are , 8 × 1 matrix, 1 × 1 matrix and 1 × 2 matrix respectively. [0107] In addition, when the threshold processing / termination number determination unit 15 determines that no termination is performed at k = 1, the truncation unit 16 does not perform the termination process. The truncation unit 16 truncates the output-side basis V 1, the singular value matrix 1 1 <−1> and the input-side basis U 1 <H> in the inverse matrix G 1 <−1>, and the inverse matrix G # 1 < It is stored in the storage unit 52 as an output-side basis V # 1, a singular value matrix ## 1 <−1> and an input-side basis U # 1 <H> at −1>. In this case, the basis V # 1 07-05-2019 34 on the output side, the singular value matrix-# 1 <−1> and the basis U # 1 <H> on the input side in the inverted matrix G # 1 <−1> after truncation are each 8 × Two matrices, two by two matrices, and two by two matrices. [0108] Next, in the second process of k = 2, the transfer function of the additional control point 11 formed by the transfer function matrix forming unit 11 with the control point 11 of one point corresponding to the cutoff number as the additional control point. The matrix G 2 is a 1 × 8 matrix. The basis U 2 on the output side, the singular value matrix 2 2 and the basis V 2 <H> on the input side generated by the singular value decomposition of the singular value decomposition unit 13 are 1 × 1 matrices and 1 × 8, respectively. It will be a matrix and an 8 × 8 matrix. [0109] Here, it is assumed that the threshold processing / termination number determination unit 15 determines that no termination is made. No truncation process is performed in the truncation unit 16, and the truncation unit 16 outputs the basis V 2 on the output side in the inverse matrix G 2 <−1>, the singular value matrix Σ 2 <−1>, and the basis U 2 <H> on the input side. Is stored in the storage unit 52 as the output-side basis V # 2, singular value matrix ## 2 <−1> and input-side basis U # 2 <H> in the inverse matrix G # 2 <−1> after truncation. Ru. In this case, the base V # 2 on the output side and the singular value matrix-# 2 <-1> and the base U # 2 <H> on the input side in the inverted matrix G # 2 <−1> after truncation are each 8 × It becomes a matrix of 1, a matrix of 1 × 1 and a matrix of 1 × 1. [0110] Then, as shown in FIG. 12, the entire inverse matrix G <-1> formed by the inverse matrix forming unit 18 is a truncated inverse matrix G # 0 <-1>, G # 1 <-1>, A matrix [V which is a composite of the output-side basis V # 0 (8 × 6 matrix), V # 1 (8 × 1 matrix), V # 2 (8 × 1 matrix) at G # 2 <−1> <H>] <-1>, singular value matrix ## 0 <-1> (6 × 6 matrix), ## 1 <-1> (1 × 1 matrix), ## 2 <-1> A matrix <<-1> obtained by combining (1 × 1 matrix) and a basis U # 0 <H> (6 × 8 matrix) on the input side, U # 1 <H> (1 × 2 matrix), A matrix of U # 2 <H> (1 × 1 matrix) is multiplied by a matrix U <H> to form an 8 × 11 matrix. [0111] 07-05-2019 35 As a result, the control points of the control target system are recursively increased by two points and one point starting from eight points, so that the total can be increased to 11 points, and the control range can be expanded. Also, since the initial eight control points have high priority and a small threshold value, it is possible to present accurate acoustic signals to these control points, and the three control points that are recursively increased are Since the priority is low and the threshold is high, it is possible to present an acoustic signal of moderate accuracy to these control points, and to stabilize the entire designed filter. [0112] It should be noted that, when the threshold processing / termination number determination unit 15 performs comparison processing based on the division result of the maximum singular value described above, since the initial eight control points have high priority and a large threshold, these controls Since it is possible to present highly accurate acoustic signals to the points, and the three control points that are recursively increased have low priorities and small threshold values, acoustic signals of moderate accuracy are given to these control points. It is possible to present and stabilize the entire filter to be designed. [0113] Therefore, for example, when the control points 1 to 8 are disposed near the center of the listening sound field of the control target system and the control points 9 to 15 are disposed at other places, the reverse formed in this manner A control device that generates a filter or the like using matrix G <-1> and presents an acoustic signal can present an acoustic signal with high accuracy near the center of the listening sound field, and elsewhere On the other hand, an acoustic signal of moderate accuracy can be presented, and stabilization of the entire designed filter can be achieved. [0114] As described above, according to the inverse system design apparatus 1 according to the embodiment of the present invention, when forming the inverse matrix G <-1> of the transfer function matrix G in the control target system, the desired approximation accuracy (to the control point For each set of control points corresponding to the priority of the accuracy of the signal to 07-05-2019 36 be presented, the basis V # k on the output side in the inverse matrix G # k <-1> after truncation for the inverse matrix G k <-1>, singular The value matrix ## k <-1> and the basis U # k <H> on the input side are calculated. Then, the basis V # k on the output side, the singular value matrix ## k <-1> and the basis U # k <H> on the input side in the inverse matrix G # k <-1> after truncation for each set of control points Are synthesized to form the entire inverse matrix G <-1>. As a procedure, calculation is started from an initial set of control points, and a set of control points is added recursively. In the calculation for each set of control points, the inverse matrix G # k <−1> for obtaining a desired approximation accuracy is formed by changing the threshold to which the priority of the approximation accuracy is reflected. Then, after the recursive processing is completed, the entire inverse matrix G <-1> is formed. [0115] Specifically, the transfer function matrix formation unit 11 forms a square transfer function matrix G k = G 0 of N 0 × N 0 corresponding to the initial control score N 0, and adds the control score N k The transfer function matrix G k for the control points is formed, and the singular value decomposition unit 13 performs singular value decomposition on the transfer function matrix G k to output the basis U k on the output side, the singular value matrix Σ k and the basis on the input side. Vk <H> is generated, and the inverse matrix singular value calculation unit 12 outputs the basis V k on the output side in the inverse matrix G k <-1> of the transfer function matrix G k, the singular value matrix Σ k <-1> The basis U k <H> on the input side is generated. Then, the threshold processing / cutoff number determination unit 15 sequentially compares the singular values σ 11, σ 22,..., Σ NkNk constituting the singular value matrix k k with the threshold T k corresponding to the control point, When singular values σ nn smaller than the threshold T k are specified (if comparison processing is performed based on the division result of the largest singular values, singular values σ 11, σ 22,... The largest singular value of σ Nk Nk is divided by each of singular values σ 11, σ 22,..., σ Nk Nk, and each of the division results is compared with threshold T k in order, and the singular is larger than threshold T k The value σ nn is specified), the censoring number (N k −n + 1) is determined, and when the singular value σ nn can not be specified, no censoring is determined. Then, the truncation unit 16 removes (discontinues) the elements corresponding to the truncation number (N k −n + 1) with respect to the inverse matrix G k <−1> = V k k k <−1> U k <H>. Truncate with to form the output-side basis V # k, singular value matrix Σ # k <-1> and input-side basis U # k <H> in the inverse matrix G # k <-1> after truncation I did it. Then, the additional control point determination unit 17 07-05-2019 37 determines, as additional control points, control points for which the number of truncations (N k −n + 1) which is not a target when forming the transfer function matrix G k is determined. [0116] In this manner, the truncation unit 16 forms each matrix after truncation for each set of control points corresponding to the desired order of approximation accuracy. Then, when it is determined by the threshold processing / termination number determination unit 15 that no truncation is performed, the inverse matrix formation unit 18 generates a truncation inverse matrix G # k <−1 formed for each set of control points by the truncation unit 16. Each matrix in> was combined to form an inverse matrix G <-1>. [0117] As a result, in the control target system assuming an overdetermined system in which the number of output signals is larger than the number of input signals, the control range can be expanded by calculating the inverse matrix while recursively increasing the control points. . In addition, it is possible to design an inverse system capable of presenting a signal with an accuracy according to the priority for each set of control points arranged in the control target system. [0118] Furthermore, the embodiment of the present invention capable of expanding the control range can be applied to various systems other than the acoustic system, and a more robust system can be constructed. In the sound system shown in the embodiment of the present invention, in a sound field reproduction system (for example, a transaural reproduction system) using an inverse system, good listening can be performed in a wider range. In addition, in an acoustic system that performs room dereverberation, reverberation can be suppressed in a wider range. [0119] The present invention has been described above by the embodiment. However, the present 07-05-2019 38 invention is not limited to the embodiment, and can be variously modified without departing from the technical concept thereof. In the above embodiment, when the thresholding / termination number determination unit 15 determines the number of truncations (N k −n + 1), the singular values σ 11 and σ 22 constituting the singular value matrix Σ k of the transfer function matrix G k ,..., Σ Nk N k and threshold value T k are compared, but this is only an example, and any process may be used as long as it is a process of determining the number of truncation (N k −n + 1). [0120] For example, the threshold value processing / cutoff number determination unit 15 sets singular values 1 / σ 11, 1 / σ 22,..., 1 constituting singular value matrices k k <−1> of the inverse matrix G k <−1>. Singular value 1 larger than threshold T k by comparing / σ N k N k and threshold T k in ascending order of singular values (in order of 1 / σ 11, 1 / σ 22,..., 1 / σ Nk Nk) It is also possible to specify / σ nn and determine the number of censors to be N k −n + 1. In this case, when the priority of the additional control point is high, a larger value is set as the threshold of the threshold table than when the priority is low, and when the priority of the additional control point is low, the priority is high. A small value is set compared to the case. [0121] In the above embodiment, as shown in the control target system of FIG. 2, the N microphones 401 to 40-N are arranged at all control points. The microphones 40-1 to 40-N may not necessarily be disposed, and the control points may be treated as mere listening positions. [0122] Moreover, although the acoustic system was mentioned as the example and demonstrated in the said embodiment, an acoustic system is an example, and this invention is applied also to control systems other than an acoustic system. For example, the present invention is also applicable to a control system that performs temperature control or humidity control of a plurality of control points. [0123] 07-05-2019 39 Reference Signs List 1 inverse system design apparatus 10 table generation unit 11 transfer function matrix formation unit 12 inverse matrix singular value calculation unit 13 singular value decomposition unit 14 inverse matrix calculation unit 15 threshold processing / termination number determination unit 16 truncation unit 17 additional control point determination unit 18 Inverse matrix forming unit 30, 104 speaker 40, 105 microphone 50 control unit 51 CPU 52 storage unit 53 storage device 54 operation / input unit 55 display output interface unit 56 communication unit 57 system bus 100-103 system 07-05-2019 40

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