Head-related transfer function modeling device and program

Abstract

To separate a measured head-related transfer function into a variable, and independently control the distance, azimuth angle, and elevation angle of a sound image.SOLUTION: A head-related transfer function modeling device 1 includes a tensor generation unit 111 that generates a tensor whose mode is two or more variables of distance, azimuth angle, elevation angle, and frequency from each of a plurality of head-related transfer functions measured by changing at least a part of distance, azimuth angle, and elevation angle, and a high-order singular value decomposition unit 112 that performs high-order singular value decomposition on each of the tensors to separate variables into an orthonormal basis matrix of the mode and a core tensor.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a head-related transfer function modeling device and a program. [Background technology]

[0002] In recent years, there has been a growing interest in audio signal reproduction methods that give viewers a high sense of realism. In particular, in content using AR (Augmented Reality) and VR (Virtual Reality) technologies, rendering audio signals in accordance with the movement of video objects and viewers is extremely effective in creating a sense of realism in the content. When considering the reproduction of audio signals for AR / VR content using headphones, rendering may be performed using a head-related transfer function (HRTF), which describes the acoustic characteristics from a virtual sound source (hereinafter referred to as "virtual sound source") to the listening position.

[0003] In recent years, sound field modeling methods based on spatial Fourier series expansion have been attracting attention, and a representative example is a method based on spherical harmonic expansion (see, for example, Non-Patent Document 1). This method is derived by transforming the variables of a three-dimensional wave equation in a Cartesian coordinate system into a polar coordinate system. When a sound source exists inside a sphere of radius r, the sound field outside r is given by the following equation. Here, A nm is the spherical harmonic spectrum. h n (2) is the second kind of spherical Hankel function, which represents the orthonormal basis for the radial component. Y n m are spherical harmonics, which represent an orthonormal basis for the angular directions.

[0004]

number

[0005] As shown in the above formula, the sound field is described in a form in which the radial direction component and the angular direction component are variable-separated in the spherical harmonic expansion, which enables flexible sound field control, such as rotating the virtual sound source in any direction and interpolating the sound pressure at any position. Ambisonics is a well-known and widely used technology that uses this (see, for example, Non-Patent Document 2), and has been adopted and standardized in MPEG-H 3DA, a next-generation audio coding method (see, for example, Non-Patent Document 3). A method has also been proposed for encoding head-related transfer functions measured in three dimensions using Ambisonics (see, for example, Patent Document 1).

[0006] Head-related transfer functions measured in a three-dimensional coordinate system can be considered as multidimensional data with the distance and angle from the origin to the measurement point as variables. Multidimensional data arranged as an array is called a tensor, and with the recent advances in computer computing performance and the scale of networks, the technology to represent and analyze large-scale data as tensors is becoming increasingly important.

[0007] Here, we will explain some of the definitions related to tensor operations. For details, see Non-Patent Document 4. A tensor with N indices is called an N-order tensor (N-tensor), and if an N-order complex tensor is X, X is expressed as follows. For example, TIFF0007663427000002.tif699 is a 3-dimensional tensor. The size of the row index is I 1 , the size of the column-wise index is I 2 , the size of the depth index is I 3 In addition, (i 1 ,i 2 ,...,i N ) component (1≦i n ≦I N )of The notation is TIFF0007663427000003.tif663. The hierarchy represented by each index is called a mode. In the example of a 3rd-order tensor, the row direction is expressed as 1-mode, the column direction as 2-mode, and the depth direction as 3-mode. A tensor defined under the same conditions as tensor X The dot product with TIFF0007663427000004.tif6108 is expressed as follows.

[0008]

number

[0009] Here, * denotes the complex conjugate. Therefore, the Frobenius norm ||X|| of a tensor X is given by

[0010]

number

[0011] Expanding a tensor X into a vector or matrix is ​​called unfolding, and expanding it into a matrix for n-modes (1≦n≦N) is called n-mode matricization. The matrix expanded in this way is called the n-mode expansion matrix, It is written as TIFF0007663427000007.tif779. Tensor X and matrix The product of n-modes of TIFF0007663427000008.tif580 is called n-mode product, and X× n Let us denote it as U. The element is calculated by the following formula:

[0012]

number

[0013] The n-mode product of a tensor X and a matrix U is expressed as the n-mode expansion matrix X of the tensor X as follows: (n) It can also be expressed as the product of and matrix U.

[0014]

number

[0015] One of the data analysis methods using tensors is higher order singular value decomposition (HOSVD) (see, for example, Non-Patent Document 4). Higher order singular value decomposition is a generalization of the singular value decomposition of a matrix, and decomposes the original tensor into a modal product of a core tensor and an orthonormal basis matrix for each mode. The higher order singular value decomposition of a tensor X is expressed by the following equation.

[0016]

number

[0017] Where: TIFF0007663427000012.tif591 is a core tensor of tensor X and satisfies the following equation:

[0018]

number

[0019] TIFF0007663427000014.tif571 is a unitary matrix, which is an orthonormal basis matrix for the n-mode of tensor X. Higher-order singular value decomposition makes it possible to extract and analyze orthonormal basis matrices (i.e., features) for each mode from complex higher-order tensors, and is therefore often used as a data analysis method in the fields of signal processing and statistical processing, such as image classification and data mining. [Prior art documents] [Patent documents]

[0020] [Patent Document 1] Patent No. 6067934 [Non-patent literature]

[0021] [Non-Patent Document 1] Yoichi Haneda, "Wavenumber domain signal processing of sound," IEICE Fundamentals Review, Vol. 11, No. 4, pp. 243-255, 2017. [Non-Patent Document 2] DH Cooper, T. Shiga, Discrete-matrix multichannel stereo. J. Audio Eng. Soc. 20(5), pp.346-360, 1972. [Non-Patent Document 3] ISO / IEC 23008-3 [Non-Patent Document 4] LD Lathauwer, BD Moor, J. Vandewalle, “A multilinear singular value decomposition,” SIAM Journal on Matrix Analysis and Applications, Vol. 21, No. 4, pp. 1253-1278, 2000. Summary of the Invention [Problem to be solved by the invention]

[0022] In modeling a head-related transfer function, it is very important to control the radial component and the angular component independently in order to flexibly express the position of a virtual sound source. However, a head-related transfer function that describes acoustic characteristics as a transfer function does not separate variables into the radial component and the angular component, so that it is not possible to individually control features that depend on only one of the distance and the angle of the coordinates of the virtual sound source.

[0023] On the other hand, the spherical harmonic expansion that uses the spatial Fourier series expansion of the sound field expresses the sound field by separating the variables into radial and angular components as already mentioned, making it possible to control each independently. However, when considering modeling of the head-related transfer function, since the human head has a complex shape, it is necessary to separate the variables based on actual measurement data that includes the effects of reflection and diffraction due to the head shape, rather than describing it as an analytical solution assuming a sphere of radius r.

[0024] In view of the above circumstances, an object of the present invention is to provide a head-related transfer function modeling device and program that can separate variables from an actually measured head-related transfer function and independently control the distance, azimuth, and elevation angle of a sound image. [Means for solving the problem]

[0025] A head-related transfer function modeling device according to one embodiment includes a tensor generation unit that generates a tensor having two or more variables of distance, azimuth angle, elevation angle, and frequency as modes from each of a plurality of head-related transfer functions actually measured while varying at least a portion of the distance, azimuth angle, and elevation angle, and a high-order singular value decomposition unit that performs high-order singular value decomposition on each of the tensors to separate the variables into an orthonormal basis matrix of the mode and a core tensor.

[0026] Furthermore, in one embodiment, the system may further include a common basis matrix acquisition unit that acquires a common basis matrix, an orthonormal basis matrix in which at least a portion of the modes of the orthonormal basis matrix are replaced with the common basis matrix, and a head related transfer function synthesis unit that synthesizes a new head related transfer function using the core tensor.

[0027] Furthermore, in one embodiment, the tensor generation unit may generate a fourth-order tensor with the variables of distance, azimuth angle, elevation angle, and frequency as modes from each of a plurality of head-related transfer functions actually measured while changing the distance, azimuth angle, and elevation angle.

[0028] Furthermore, in one embodiment, the head-related transfer function synthesis unit may synthesize a new head-related transfer function using an orthonormal basis matrix in which only one mode, excluding frequency, of the orthonormal basis matrix is ​​replaced with the common basis matrix, and the core tensor.

[0029] Furthermore, in one embodiment, the common basis matrix acquisition unit may acquire one or an average of a plurality of orthonormal basis matrices that have been variable-separated by the higher-order singular value decomposition unit as the common basis matrix, or may acquire an orthonormal basis matrix obtained by variable-separating a head-related transfer function measured using a dummy head that mimics the average human head shape as the common basis matrix.

[0030] Moreover, a program according to an embodiment causes a computer to function as the head-related transfer function modeling device. Effect of the Invention

[0031] According to the present invention, it is possible to separate variables of an actually measured head-related transfer function and independently control the distance, azimuth angle, and elevation angle of a sound image. [Brief description of the drawings]

[0032] [Figure 1] 1 is a block diagram showing an example of the configuration of a head-related transfer function modeling device according to an embodiment. [Diagram 2] 1 is a block diagram showing an example of the configuration of a variable separation unit in a head-related transfer function modeling device according to an embodiment. FIG. [Diagram 3] 1 is a block diagram showing an example of the configuration of a head-related transfer function synthesis unit in a head-related transfer function modeling device according to an embodiment. FIG. [Figure 4] 10 is a flowchart illustrating an example of the operation of the head-related transfer function modeling device according to an embodiment. [Diagram 5] FIG. 2 is a diagram showing an image of a fourth-order tensor generated by a head-related transfer function modeling device according to an embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0033] Hereinafter, one embodiment will be described in detail with reference to the drawings.

[0034] 1 is a block diagram showing an example of the configuration of a head-related transfer function modeling device according to an embodiment. The head-related transfer function modeling device 1 includes a variable separation unit 11 that separates the head-related transfer functions input from an input data storage unit 20. The head-related transfer function modeling device 1 may further include a head-related transfer function synthesis unit 12 that synthesizes the head-related transfer functions and outputs the synthesized head-related transfer functions to an output data storage unit 30.

[0035] The input data storage unit 20 stores, for each subject, a plurality of head-related transfer functions actually measured by changing at least a part of the distance r of the sound source, the azimuth angle θ, and the elevation angle φ in a polar coordinate system (spherical coordinate system).

[0036] Fig. 2 is a block diagram showing an example of the configuration of the variable separation unit 11. The variable separation unit 11 shown in Fig. 2 includes a tensor generation unit 111, a high-order singular value decomposition unit 112, an orthonormal basis matrix storage unit 113, and a core tensor storage unit 114.

[0037] The tensor generation unit 111 acquires the head-related transfer functions from the input data storage unit 10. Then, the tensor generation unit 111 generates a tensor having two or more variables of distance, azimuth angle, elevation angle, and frequency as modes from each of the multiple head-related transfer functions. When the head-related transfer functions are three-dimensionally measured by changing the distance, azimuth angle, and elevation angle, respectively, the tensor generation unit 111 generates a fourth-order tensor having the distance, azimuth angle, elevation angle, and frequency as modes. The tensor generation unit 111 outputs the generated tensor to the high-order singular value decomposition unit 112.

[0038] The high-order singular value decomposition unit 112 performs high-order singular value decomposition on each of the tensors generated by the tensor generation unit 111, and expands the tensors into an orthonormal basis matrix for each mode and a core tensor, thereby separating the variables. The high-order singular value decomposition unit 112 then stores the derived orthonormal basis matrix in the orthonormal basis matrix storage unit 113, and stores the derived core tensor in the core tensor storage unit 114. This is performed for each subject, and a database for each subject is constructed. By performing high-order singular value decomposition on the tensor, it is possible to separate variables of the measured data into a core tensor and an orthonormal basis matrix for each mode, and to express the measured data in the form of a mode product.

[0039] The orthonormal basis matrix storage unit 113 stores a plurality of orthonormal basis matrices for each subject.

[0040] The core tensor storage unit 114 stores a plurality of core tensors for each subject.

[0041] Fig. 3 is a block diagram showing an example of the configuration of the head-related transfer function synthesis unit 12. The head-related transfer function synthesis unit 12 shown in Fig. 3 includes a common basis matrix acquisition unit 121, a common basis matrix storage unit 122, and a head-related transfer function calculation unit 123.

[0042] The common basis matrix acquisition unit 121 acquires a common basis matrix from the orthonormal basis matrix stored in the orthonormal basis matrix storage unit 113. The common basis matrix acquisition unit 121 outputs the acquired common basis matrix to the common basis matrix storage unit 122.

[0043] The common basis matrix acquisition unit 121 may select one representative orthonormal basis matrix from the orthonormal basis matrix storage unit 113 as the common basis matrix, or may derive the average of a plurality of orthonormal basis matrices stored in the orthonormal basis matrix storage unit 113 as the common basis matrix. In this case, the common basis matrix acquisition unit 121 may derive the common basis matrix from an orthonormal basis matrix related to variables other than frequency. Alternatively, the common basis matrix acquisition unit 121 may use an orthonormal basis matrix obtained by separating variables of head-related transfer functions measured using a dummy head that imitates the average shape of a human head as the common basis matrix.

[0044] When the head-related transfer function calculation unit 123 acquires subject information indicating a subject for which a head-related transfer function is to be synthesized among the subjects of the head-related transfer function, the head-related transfer function calculation unit 123 acquires an orthonormal basis matrix and a core tensor corresponding to the subject from the orthonormal basis matrix storage unit 113 and the core tensor storage unit 114, respectively. The head-related transfer function calculation unit 123 also acquires a common basis matrix derived by the common basis matrix acquisition unit 121 from the common basis matrix storage unit 122. The head-related transfer function calculation unit 123 then synthesizes a new head-related transfer function using an orthonormal basis matrix in which at least a part of the modes of the orthonormal basis matrix is ​​replaced with the common basis matrix, and the core tensor. The head-related transfer function calculation unit 123 stores the synthesized head-related transfer function in the output data storage unit 30.

[0045] It should be noted that the head-related transfer function calculation unit 123 can also synthesize head-related transfer functions by replacing all modes of the orthonormal basis matrix with a common basis matrix, but the accuracy of the synthesized data is degraded compared with the original measured head-related transfer functions. Therefore, when accuracy is important, it is desirable to replace only one mode of the orthonormal basis matrix with a common basis matrix. In particular, it is desirable to replace only one mode of the orthonormal basis matrix excluding the frequency with a common basis matrix. This is because there are individual differences in the spectral shape of the head-related transfer function for the frequency component. In addition, the head-related transfer function calculation unit 123 can also use the orthonormal basis matrix of the subject for all modes without using a common basis matrix.

[0046] (Head-related transfer function modeling) Next, a specific example of modeling of a head-related transfer function will be described with reference to Fig. 4. Fig. 4 is a flowchart showing an example of the operation of the head-related transfer function modeling device 1.

[0047] Here, the head-related transfer function for one ear when the coordinates of the sound source position are (r, θ, φ) is defined as H(r, θ, φ, ω), where ω is a discrete frequency bin. The number of measurement points in the distance direction is K, the number of measurement points in the azimuth direction is L, the number of measurement points in the elevation direction is M, and the total number of frequency bins is N. The component of the nth (n=1, 2, …, N) frequency bin of the head-related transfer function measured at the kth (k=1, 2, …, K) distance, the lth (l=1, 2, …, L) azimuth, and the mth (m=1, 2, …, M) elevation angle is defined as H(r k ,θ l ,φ m ,ω n Here, the description will be given assuming that the distance r, the azimuth angle θ, and the elevation angle φ are each changed.

[0048] In step S101, the tensor generation unit 111 receives a plurality of head-related transfer functions H(r k ,θ l ,φ m ,ω n )

[0049] In step S102, the tensor generation unit 111 generates a fourth-order tensor for each head-related transfer function, in which the radial component is arranged in 1-mode, the azimuth component is arranged in 2-mode, the elevation component is arranged in 3-mode, and the frequency component is arranged in 4-mode. Generates TIFF0007663427000015.tif578.

[0050] Figure 5 shows an image of this fourth-order tensor H. However, the assignment of each mode to a variable is not limited to this, and other assignments may be used as long as the overall procedure is unified, such as 1-mode being the azimuth component, 2-mode being the elevation component, 3-mode being the radial component, and 4-mode being the frequency component.

[0051] In step S103, the high-order singular value decomposition unit 112 applies high-order singular value decomposition to the fourth-order tensor H generated in step S102. The fourth-order tensor H can be expressed as follows.

[0052]

number

[0053] however, TIFF0007663427000017.tif582 represents the core tensor of the fourth-order tensor H, and the operator × i (i ∈ {1,2,3,4}) represents the i-mode product. (i) is a unitary matrix, which is an orthonormal basis matrix for i-mode. That is, U (1) is the radial component, U (2) is the azimuth component, U (3) is the elevation component, U (4) is an orthonormal basis matrix of frequency components. Therefore, by generating the tensor H as described above and performing high-order singular value decomposition, it becomes possible to separate the head-related transfer functions into variables as mode products of the orthonormal basis matrices corresponding to the distance, azimuth angle, elevation angle, and frequency, respectively, and the core tensor (i.e., coefficients).

[0054] In step S104 , the common basis matrix acquisition unit 121 acquires a common basis matrix from the orthonormal basis matrices stored in the orthonormal basis matrix storage unit 113 .

[0055] In step S105, the head-related transfer function calculation unit 123 acquires subject information indicating the subject for whom the head-related transfer function is to be synthesized, and synthesizes a new head-related transfer function using the orthonormal basis matrix and core tensor generated in step S103 and separated into variables from the subject's head-related transfer function (actual measurement data), and the common basis matrix acquired in step S104.

[0056] For example, consider the case where a radial component orthonormal basis matrix derived from the head-related transfer functions measured for a certain subject p is used as a common basis matrix, and a new head-related transfer function is synthesized for another subject q. Let H p ,H q Let the tensor H p ,H q can be expressed as follows, similarly to equation (9):

[0057]

number

[0058] Tensor H p The radial orthonormal basis matrix U p (1) If we use the common basis matrix, the head-related transfer function H' of subject q is q is the common basis matrix U p (1) can be synthesized using the following formula:

[0059]

number

[0060] Similarly, the head-related transfer functions of subject p may be synthesized using a common basis matrix that is an orthogonal basis of the head-related transfer functions of subject q. In addition, another orthogonal basis matrix may be used as a common basis U c (1) For example, the common basis U c (1) Let us consider the orthonormal basis matrix U p (1) and U q (1) Alternatively, as described above, the head-related transfer function may be measured using a dummy head that mimics the average shape of a human head, and the head-related transfer function may be derived from the measured head-related transfer function.

[0061] Here, the reason why a common basis matrix can be used to synthesize a head-related transfer function with little deterioration in accuracy and its effect will be described. The shape of the human head can be approximated to a spheroid, and it is considered that the orthonormal basis matrix does not vary significantly between individuals. In other words, just as the orthonormal basis of the radial component becomes the second kind of spherical Hankel function when describing a sound field outside a sphere of radius r based on a spherical harmonic expansion, it can be assumed that the orthonormal basis of the radial component can be expressed by a common basis when describing a head-related transfer function (i.e., a sound field outside the head) based on a modal product of tensors. The same applies to the azimuth and elevation components. However, as described above, there are individual differences in the spectral shape of the head-related transfer function for frequency components, so it is desirable to use the orthonormal basis matrix of the person himself / herself in order not to deteriorate the reproduction accuracy. Based on this assumption, it is possible to synthesize the head-related transfer function of a subject using any of the orthonormal basis matrices of multiple modes of the head-related transfer function of a certain person. In this case, the remaining orthonormal basis matrices and core tensors are those of the subject himself / herself, so that it is possible to reduce the amount of data to be stored while ensuring the individuality of the head-related transfer function to a certain extent. For example, in the example shown in the above formula (12), U p (1) In order to make U a common basis matrix, the orthonormal basis matrix storage unit 113 stores U p (1) You can delete the rest.

[0062] In step S106, the head-related transfer function calculation unit 123 outputs the synthesized head-related transfer function to the output data storage unit 30.

[0063] So far, we have described an example in which the head-related transfer function measured three-dimensionally by changing the distance, azimuth angle, and elevation angle is input, but the combination of variables is not limited to this. For example, even when the elevation angle is not changed and only the height of the subject's ear canal, that is, the variable of the head-related transfer function measured on the horizontal plane is separated, a third-order tensor with the distance, azimuth angle, and frequency as variables can be generated and expressed as follows.

[0064]

number

[0065] At this time, U (1) is the radial component, U (2) is the azimuth component, U (3) is an orthonormal basis matrix for frequency components. In addition, in the case of head-related transfer functions measured on a horizontal plane at a fixed distance, variables can be separated in a similar manner if the azimuth angle and frequency are used as variables. Note that since a second-order tensor means a matrix, the higher-order singular value decomposition of a tensor is the same as the singular value decomposition of a matrix.

[0066] As described above, the head-related transfer function modeling device 1 can perform high-order singular value decomposition of the tensor using the variable separation unit 11, thereby separating the head-related transfer functions into radial and angular components, thereby making it possible to individually control features that depend on only one of the distance and angle of the coordinates of the virtual sound source.

[0067] In addition, it is also possible to derive orthogonal basis vectors for each row and column component by performing singular value decomposition of the coefficient matrix. Since the matrix constructed from the measured data is decomposed into an orthonormal basis matrix and a coefficient matrix by singular value decomposition, a model that accurately reflects the actual physical phenomenon can be created. However, in this case, only up to two variables of data can be handled, so it is difficult to apply when three or more variables such as distance, azimuth angle, and elevation angle are handled simultaneously. In addition, the following reference documents 1 and 2 disclose a method of performing high-order singular value decomposition of a tensor and interpolating a head-related transfer function. However, the fluctuation of the head-related transfer function in the distance direction is not considered as a variable, and a method of separating the variables of the head-related transfer function including the distance and synthesizing the head-related transfer function using the same is not disclosed. In this respect, according to the present invention, it is possible to independently control the distance, azimuth angle, and elevation angle of a sound image using a head-related transfer function. [Reference 1] G. Grindlay, MAO Vasilescu, “A Multilinear (Tensor) Framework for HRTF Analysis and Synthesis,” 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07, pp. I-161-I-164, 2007. [Reference 2] Q. Huang, L. Li, “Modeling individual HRTF tensor using high-orderpartial least squares,” EURASIP Journal on Advances in Signal Processing, 2014:58, 2014.

[0068] In addition, when modeling and storing the measured data of a plurality of people using the above method, it is necessary to store the core tensor and the orthonormal basis matrix for each individual's data, and there is a concern about an increase in memory capacity. Therefore, the head-related transfer function modeling device 1 may be a device that interpolates any one of the distance, azimuth angle, and elevation angle direction. In other words, a common basis matrix is ​​used for the orthonormal basis matrix of the variable to be interpolated, and the head-related transfer functions may be synthesized using the individual's data for the other coefficients and variables (i.e., the core tensor, the orthonormal basis matrix other than the variable to be interpolated). In this case, by using a common basis matrix for the variable to be interpolated, it is possible to suppress deterioration in the accuracy of the head-related transfer functions after synthesis. In addition, the variable to be interpolated may be deleted after being used to update the common basis matrix, which makes it possible to reduce the amount of data to be stored compared to the data of the original head-related transfer functions, and also makes it possible to reduce the memory used when synthesizing the head-related transfer functions.

[0069] <Program> A computer capable of executing program instructions can be used to function as the head-related transfer function modeling device 1. The computer stores a program describing the processing contents for realizing each function of the head-related transfer function modeling device 1 in a storage unit of the computer, and reads and executes the program by a processor of the computer. A part of the processing contents may be realized by hardware. Here, the computer may be a general-purpose computer, a dedicated computer, a workstation, a PC (Personal Computer), an electronic notepad, or the like. The program instructions may be a program code, a code segment, or the like for executing a required task. The processor may be a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), a DSP (Digital Signal Processor), or the like.

[0070] For example, a program for functioning as the head-related transfer function modeling device 1 causes a computer to execute the steps of generating tensors with two or more variables of distance, azimuth angle, elevation angle, and frequency as modes from each of a plurality of head-related transfer functions actually measured while changing at least a portion of the distance, azimuth angle, and elevation angle, and subjecting each of the tensors to high-order singular value decomposition to variable separation into an orthonormal basis matrix of the mode and a core tensor.

[0071] The program may be recorded on a computer-readable recording medium. By using such a recording medium, the program can be installed on a computer. Here, the recording medium on which the program is recorded may be a non-transient recording medium. The non-transient recording medium is not particularly limited, and may be, for example, a CD-ROM, a DVD-ROM, or the like. The program may also be provided by downloading via a network.

[0072] Although the above-mentioned embodiment has been described as a representative example, it is obvious to those skilled in the art that many modifications and substitutions can be made within the spirit and scope of the present invention. Therefore, the present invention should not be interpreted as being limited by the above-mentioned embodiment, and various modifications or changes can be made without departing from the scope of the claims. For example, it is possible to combine multiple configuration blocks shown in the configuration diagram of the embodiment into one, or to divide one configuration block. It is also possible to combine multiple steps shown in the flow chart of the embodiment into one, or to divide one step. [Explanation of symbols]

[0073] 1 Head-related transfer function modeling device 11 Variable separation section 12 Head-related transfer function synthesis unit 20 Input data storage unit 30 Output data storage unit 111 Tensor Generation Unit 112 High-order singular value decomposition unit 113 Orthonormal basis matrix storage unit 114 Core Tensor Storage 121 Common basis matrix acquisition part 122 Common basis matrix storage 123 Head-related transfer function calculation unit

Claims

1. a tensor generator that generates a tensor having two or more variables of distance, azimuth angle, elevation angle, and frequency as modes from each of a plurality of head-related transfer functions actually measured while changing at least a part of the distance, azimuth angle, and elevation angle; a high-order singular value decomposition unit that performs high-order singular value decomposition on each of the tensors to separate variables into an orthonormal basis matrix of the mode and a core tensor; A head-related transfer function modeling device comprising:

2. A common basis matrix acquisition unit that acquires a common basis matrix; A head-related transfer function synthesis unit that synthesizes a new head-related transfer function using an orthogonal basis matrix in which at least a part of the modes of the orthogonal basis matrix is ​​replaced with the common basis matrix and the core tensor; The head-related transfer function modeling device according to claim 1 , further comprising:

3. The head-related transfer function modeling device of claim 2, wherein the tensor generation unit generates a fourth-order tensor having modes of distance, azimuth angle, elevation angle, and frequency variables from each of a plurality of head-related transfer functions actually measured while changing the distance, azimuth angle, and elevation angle.

4. The head-related transfer function modeling device according to claim 3, wherein the head-related transfer function synthesis unit synthesizes a new head-related transfer function using an orthonormal basis matrix in which only one mode excluding frequency of the orthonormal basis matrix is ​​replaced with the common basis matrix, and the core tensor.

5. The common basis matrix acquisition unit Acquire, as the common basis matrix, one or an average of a plurality of orthonormal basis matrices that have been subjected to variable separation by the high-order singular value decomposition unit; A head-related transfer function modeling device according to any one of claims 2 to 4, which obtains as the common basis matrix an orthonormal basis matrix obtained by separating variables of head-related transfer functions measured using a dummy head that mimics the average human head shape.

6. A program for causing a computer to function as the head-related transfer function modeling device according to any one of claims 1 to 5.

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