Estimation device, restoration device, and estimation method

Abstract

The present invention provides an estimation device for estimating an expansion coefficient used when sound field restoration from optical measurement data is performed in a case where a sound source is present inside a sound field restoration region. The estimation device estimates a sound field expansion coefficient based on circular harmonic function expansion by using a measurement value measured by a sound field measurement system by means of light and information representing a laser light path.

Description

Estimation device, restoration device, and estimation method

[0001] The present invention relates to sound field measurement using light.

[0002] Optical sound field measurement is used as a method for measuring and visualizing sound fields without contact. When trying to obtain the sound pressure distribution on a certain plane from the line integral values ​​measured by optical measurement, a process called sound field restoration or sound field reconstruction is required to estimate the value of each point from the projection data.

[0003] In conventional sound field restoration methods, the sound field to be measured is expressed as a plane wave expansion based on the wave equation, and the coefficients of the plane wave expansion are calculated from the measurement data using the least squares method or the like, thereby restoring the sound field (see non-patent document 1).

[0004] Samuel A. Verburg and Efren Fernandez-Grande, "Acousto-Optical Volumetric Sensing of Acoustic Fields", Phys. Rev. Applied 16, 044033, 2021.

[0005] Conventional technology uses plane wave expansion, which allows for accurate sound field restoration when no sound source is present within the area where sound field restoration is being performed, but it is not possible to perform accurate sound field restoration when a sound source is present within the area.

[0006] The present invention aims to provide a restoration device that can restore a sound field from optical measurement data more accurately than conventional devices when a sound source is located within a sound field restoration area, and an estimation device and estimation method that estimate expansion coefficients used when performing sound field restoration.

[0007] In order to solve the above problem, according to one aspect of the present invention, an estimation device estimates expansion coefficients of a sound field based on a circular harmonic expansion using measurements taken by an optical sound field measurement system and information representing a laser optical path.

[0008] According to the present invention, when a sound source is present inside a sound field restoration area, it is possible to perform sound field restoration from optical measurement data with higher accuracy than conventional methods.

[0009] FIG. 1 is a diagram showing an overview of measurement of optical measurement data. FIG. 2 is a diagram showing an example of a measurement system for performing sound field measurement. FIG. 3 is a functional block diagram of a restoration system according to a first embodiment. FIG. 4 is a diagram showing an example of a processing flow of the restoration system according to the first embodiment. FIG. 5 is a diagram showing restoration results. FIG. 6 is a diagram showing an example configuration of a computer to which the present method is applied.

[0010] An embodiment of the present invention will be described below. In the drawings used in the following description, components having the same function and steps performing the same processing are denoted by the same reference numerals, and duplicate explanations will be omitted. In the following description, symbols such as "~" used in the text should normally be written directly above the character immediately preceding it, but due to limitations in text notation, they are written immediately after the character in question. In formulas, these symbols are written in their original positions. Furthermore, unless otherwise specified, processing performed on each element of a vector or matrix is ​​assumed to apply to all elements of that vector or matrix.

[0011] <Key Points of the First Embodiment> In this embodiment, circular harmonic expansion of the sound field is used for two-dimensional sound field reconstruction from optical measurement data.

[0012] By using circular harmonic functions, it is possible to restore a sound field with high accuracy when the sound source is located inside the restoration target region.

[0013] Such conditions arise when measuring the sound radiated from a speaker, for example, and are highly practical.

[0014] Fig. 1 shows an outline of optical measurement data. A sound source 10 is placed inside the measurement area, and laser line integral values ​​s are measured from various directions and distances surrounding the sound source 10. m The measured line integral values ​​s mFrom this, an estimated value a~ of the expansion coefficient a of the sound field based on circular harmonic function expansion is obtained, and the sound field is restored using the estimated value a~. If the total number of laser optical paths is M, then m = 1, 2, ..., M. M is any integer equal to or greater than 1. The larger M is, the higher the accuracy of the sound field restoration, but the measurement cost and calculation cost also increase. Therefore, M is appropriately set taking into consideration the required accuracy, measurement cost, and calculation cost. Since the measurement region includes the start point to the end point of the laser optical path, for example, by setting the laser optical path so as to evenly surround the sound source 10, the sound field can be restored with even accuracy. However, if it is desired to increase the accuracy of the sound field restoration at a specific position or direction, it is possible to set many laser optical paths that pass through that position or direction. First, the line integral value s m This section briefly explains the sound field measurement system that measures the above.

[0015] <Sound field measurement system> Figure 2 shows an example of a measurement system for measuring a sound field. The sound field measurement system includes a laser 14, a mirror 16, a moving body 18, a rotation stage 20, and a speaker 22. Here, a laser Doppler velocimeter (LDV) is used as the sound field measurement system, but other optical sound field measurement systems may also be used.

[0016] The speaker 22 to be measured is placed on a rotation stage 20 on a moving body 18 that moves along one axis, and measurements are repeatedly performed while changing the position and angle of the speaker 22 relative to the laser light emitted by the laser 14, measuring the line integral value of the sound field along the laser light path at multiple positions and angles as shown in Figure 1. Note that the two circles made up of dashed lines in Figure 1 indicate that when measurements are performed with the speaker 22 in Figure 2 placed on the rotation stage 20 on the moving body 18, the speaker 22 rotates 360° and lies within the area from the smaller circle to the larger circle. 1, the inner circle indicates the boundary of the measurement area (the outside of the circle is the measurement area) when the rotating body 20 is rotated 360° by moving the speaker 22 closer to the laser light path (in FIG. 2, the moving body 18 is moved to the leftmost position), and the outer circle indicates the boundary of the measurement area (the outside of the circle is the measurement area) when the rotating body 20 is rotated 360° by moving the speaker 22 away from the laser light path (in FIG. 2, the moving body 18 is moved to the rightmost position). Note that the restoration area can be set to any area regardless of the measurement area.

[0017] At this time, the same sound is reproduced from the speaker 22 and measurements are repeated, with the timing of sound reproduction and recording synchronized. From the line integral value data measured in this way, expansion coefficients of the sound field based on circular harmonic function expansion are derived, and the sound field is restored using the expansion coefficients.

[0018] First, the circular harmonic expansion of the sound field will be explained.

[0019] <Circular Harmonic Expansion of Sound Field> According to Reference 1, any two-dimensional sound field in which sound sources exist only inside the region of interest can be expressed by circular harmonic expansion as follows: Here, r and φ are the radius and angle of the polar coordinates, ω is the angular frequency of the sound, n is the expansion order, a n is the expansion coefficient of the sound field based on the circular harmonic function expansion, H n (2) is the second kind Hankel function, k is the wave number, and j is the imaginary unit. If λ is the wavelength and c is the speed of sound, then λ = 2πc / ω, k = 2π / λ, and k = ω / c.

[0020] According to equation (1), the expansion coefficient a of the sound field based on the circular harmonic function expansion of the sound field isn If we know the expansion coefficients a, we can reconstruct any two-dimensional sound field in which the sound source exists only inside the region. n Estimate.

[0021] (Reference 1) Y. Ren and Y. Haneda, "2D Local Exterior Sound Field Reproduction Using an Addition Theorem Based on Circular Harmonic Expansion", 2021 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), New Paltz, NY, USA, 2021, pp. 271-275. <Derivation of sound field expansion coefficients based on circular harmonic function expansion from optical measurement data> In optical acoustic measurements, the line integral value s of the sound pressure along the laser beam path is m Here, if the sound pressure distribution is expressed using the above circular harmonic function expansion, the measured value s m teeth However, circular harmonic functions are truncated to the Nth order. Here, L m represents the laser path corresponding to the m-th measurement value, and ∫ dL m is the laser light path L m This represents the line integral value along the line. where s and a are vectors representing the measurement data and expansion coefficients, and s = [s1, s2, ..., s m ,…,s M ] T ,a=[a -N ,a -N+1 ,…,s n ,…,s N ] T , H is a matrix with M rows and 2N+1 columns, The element h(n,m) of the matrix H is In equation (3), s is the measurement data, and H is the measurement condition (M laser light paths L) as can be seen from equations (4-1) and (4-2). m), it is possible to estimate the expansion coefficient a. For example, the following equation can be used to estimate the expansion coefficient a using the regularized least squares method: a~=[a~ -N ,a~ -N+1 ,…,s~ n ,…,s~ N ] T Calculate. In addition, ε in equation (5) represents a constraint in the regularized least squares method.

[0022] <Sound field restoration from expansion coefficients of sound field based on circular harmonic function expansion> Using the estimated values ​​a~ of the expansion coefficients of the sound field based on circular harmonic function expansion obtained by Equation (5), the sound field at an arbitrary position can be restored. where p~=[p~1,p~2,…,p~ i ,…,p~ L ] T is the restored sound pressure at point L, G is a matrix with L rows and 2N+1 columns, The element g(n,i) of the matrix G is the coordinate of the i-th restoration point (r i ,φ i ) corresponds to the basis of the nth order circular harmonic functions in The i-th restoration point coordinate (r i ,φ i ) is the nth order circular harmonic function and the i-th restoration point coordinate (r i ,φ i The restored sound pressure p~ at the point can be expressed as follows by circular harmonic expansion: A restoration system that realizes the above processing will now be described.

[0023] <Restoration System According to First Embodiment> FIG. 3 shows an example of the configuration of a restoration system according to the first embodiment, and FIG. 4 shows the processing flow thereof.

[0024] The reconstruction system includes an estimator 100 and a reconstruction unit 200 .

[0025] The restoration system takes the measurement value s measured by the above-mentioned sound field measurement system as input, estimates the expansion coefficients of the sound field based on circular harmonic function expansion, performs sound field restoration using the estimated value a~, and outputs the restoration result.

[0026] The restoration system is a special device configured by loading a special program into a publicly known or dedicated computer having, for example, a central processing unit (CPU), a main memory (RAM), etc. The restoration system executes each process under the control of the central processing unit. Data input to the restoration system and data obtained from each process are stored, for example, in the main memory, and the data stored in the main memory is read by the central processing unit as needed and used for other processes. At least a portion of each processing unit in the restoration system may be configured with hardware such as an integrated circuit. Each storage unit in the restoration system may be configured, for example, with a main memory such as a RAM (Random Access Memory) or middleware such as a relational database or a key-value store. However, each storage unit does not necessarily have to be provided internally in the restoration system; it may be configured with an auxiliary storage device configured with a hard disk, optical disk, or semiconductor memory element such as flash memory, and be configured external to the restoration system.

[0027] Each part will be explained below.

[0028] <Estimation Unit 100> The estimation unit 100 estimates the measured values ​​s=[s1, s2, ..., s m ,…,s M ] T and the laser path L=[L1,L2,…,L m ,…,L M ] is input, and using these values, the expansion coefficient a of the sound field based on circular harmonic function expansion is estimated (S100), and the estimated value a~ is output.

[0029] As mentioned above, Since H is determined by the measurement conditions (laser optical path L), the expansion coefficient a can be estimated from the measured value s and the laser optical path L. m The information representing the laser beam path L m Line integral value along (element h(n,m) of matrix H) As a method for estimating the expansion coefficient a, various conventional techniques can be used. For example, the estimated value a~ = [a~ -N ,a~ -N+1 ,…,s~ n ,…,s~ N ] T Calculate. The expansion coefficient a may be estimated by a method using a pseudo-inverse matrix based on sparse optimization or singular value decomposition. <Restoration unit 200> The restoration unit 200 receives the estimated values ​​a~ of the expansion coefficients of the sound field based on the circular harmonic function expansion and the restoration point coordinates as input, performs sound field restoration using the circular harmonic function expansion (S200), and outputs the restoration result. For example, the restoration unit 200 calculates the ith restoration point coordinates (r i ,φ i ) is calculated using equation (8). The restoration unit 200 performs this process for all L restoration points, and obtains the restored sound pressure p~=[p~1, p~2, ..., p~ i ,…,p~ L ] is obtained and output as the restoration result.

[0030] The above processing is assumed to be performed for one angular frequency ω. In the case of data containing two or more frequencies, the processing is performed for Q angular frequencies ω1, ω2, ..., ω q ,…,ω Q For each angular frequency ω q Then, the estimation process S100 and the restoration process S200 are performed independently, and Q restored sound pressures p~(1), p~(2), ..., p~(q), ..., p~(Q) (where p~(q) = [p~ q,1 ,p~ q,2 ,…,p~ q,i ,…,p~ q,L ]), or a superposition of Q restored sound pressures p~(1), p~(2), ..., p~(q), ..., p~(Q) may be output.

[0031] <Effects> With the above configuration, when a sound source is present inside the sound field restoration area, it is possible to restore the sound field from optical measurement data with higher accuracy than before.

[0032] <Restoration Results> Figure 5 shows examples of a sound field measured by microphones at multiple points and a sound field restored by optical measurement and circular harmonic functions according to the present invention. An example of the placement of the microphones 30 is shown in Figure 2. As explained in the above <Sound Field Measurement System>, measurements are repeatedly taken while changing the position and angle of the speaker 22 relative to the microphone 30.

[0033] The sound source is a loudspeaker placed near the origin of the coordinate system in Figure 5, and its boundary is indicated by the inner circle. From the figure, it can be seen that the sound field radiated outward from the sound source is correctly restored when the sound source is located inside the restoration area.

[0034] <Modification> The estimation unit 100 and the restoration unit 200 may be configured as an estimation device and a restoration device, respectively, which are separate devices.

[0035] <Other Modifications> The present invention is not limited to the above-described embodiments and modifications. For example, the various processes described above may not only be executed in chronological order as described, but may also be executed in parallel or individually depending on the processing capacity of the device that executes the processes or as needed. Other modifications are possible as long as they do not deviate from the spirit of the present invention.

[0036] <Program and Recording Medium> The various processes described above can be implemented by loading a program that executes each step of the above method into the recording unit 2020 of the computer 2000 shown in FIG. 6 and operating the control unit 2010, input unit 2030, output unit 2040, display unit 2050, etc.

[0037] The program describing the processing contents can be recorded on a computer-readable recording medium, which may be, for example, a magnetic recording device, an optical disk, a magneto-optical recording medium, a semiconductor memory, or any other suitable recording medium.

[0038] The program may be distributed by, for example, selling, transferring, lending, etc. portable recording media such as DVDs and CD-ROMs on which the program is recorded. Furthermore, the program may be stored in a storage device of a server computer, and then transferred from the server computer to other computers via a network, thereby distributing the program.

[0039] A computer that executes such a program may first temporarily store the program recorded on a portable recording medium or transferred from a server computer in its own storage device. Then, when executing a process, the computer reads the program stored on its own recording medium and executes the process in accordance with the read program. Alternatively, the computer may read the program directly from a portable recording medium and execute the process in accordance with the program. Furthermore, the computer may execute the process in accordance with each program transferred from the server computer. Alternatively, the server computer may not transfer the program to the computer, but may instead execute the process through a so-called ASP (Application Service Provider) service, which realizes the processing function by issuing an execution instruction and obtaining the results. In this embodiment, the program includes information used for processing by a computer that is equivalent to a program (e.g., data that is not a direct instruction to the computer but has properties that define computer processing).

[0040] Furthermore, in this embodiment, the device is configured by executing a predetermined program on a computer, but at least a part of the processing contents may be realized by hardware.

Claims

1. An estimation device that estimates the expansion coefficients of a sound field based on a circular harmonic function expansion using measurements taken with an optical sound field measurement system and information representing a laser optical path.

2. An estimation device according to claim 1, wherein a vector representing the expansion coefficients is estimated using a matrix whose elements are line integral values ​​along one or more laser optical paths, and a vector whose elements are the measured values.

3. A restoration device that uses the estimated values ​​of expansion coefficients estimated by the estimation device of claim 1, and performs sound field restoration using circular harmonic function expansion from the estimated values ​​and restoration point coordinates.

4. An estimation method for estimating expansion coefficients of a sound field based on a circular harmonic function expansion using measurements taken with an optical sound field measurement system and information representing a laser optical path.

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