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 JP2000152372 [0001] BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a directional microphone composed of a plurality of microphones and a sound source tracking device using the same. [0002] 2. Description of the Related Art Conventionally, an array microphone has been proposed as a directional microphone obtained by forming directivity. FIG. 20 shows the basic configuration of the array microphones disclosed in conventionally proposed Japanese Patent Application LaidOpen Nos. 3-113998 and 7-131886. In FIG. 20, reference numerals 101, 102, and 103 denote a first microphone unit, a second microphone unit, and an Nth microphone unit, respectively. Reference numeral 104 denotes a microphone array configured by arranging the first microphone unit 101 to the Nth microphone unit 103 on the same line segment. 105 is a directivity forming device, and 106 is an output terminal. Here, the first microphone unit 101 to the Nth microphone unit 103 receive the incoming sound wave and output it to the directivity forming device 105, respectively. In this directivity forming apparatus 105, directivity is formed using the relationship between the phase shift of the output signal of each microphone unit and the incident angle of the plane wave that appears when the plane wave arrives at the microphone array 104. [0003] 03-05-2019 1 The basic configuration of directivity forming apparatus 105 includes delay calculation results by delay devices 111 to 113 as many as the microphone units shown in FIG. 21 corresponding to each microphone unit 101 to 103 of microphone array 104, and the delay devices 111 to 113. The configuration is based on one adder 114 for adding. The first input terminal 108 receives a signal from the first microphone unit 101 shown in FIG. 20, the second input terminal 109 receives a signal from the second microphone unit 102 shown in FIG. 20, and the Nth input terminal 110 The signal from the N-th microphone unit 103 shown in FIG. 20 is received. Furthermore, the first delay device 111 is a device that gives time delay to the signal from the first input terminal 108, and the second delay device 112 is a device that gives time delay to the signal from the second input terminal 109. The delay device 113 is a device for giving a time delay to the signal from the Nth input terminal 110. The adder 114 superposes all the delay calculation results in the respective delay devices from the first delay device 111 to the N-th delay device 113, and outputs the addition calculation result of the adder 114 at the output terminal 115. [0004] To explain the directivity forming principle of the directivity forming device 105, in FIG. 22, a straight line including the microphone array 104 is taken as an x-axis, and the y-axis and z-axis are considered to be orthogonal to each other. Let y, z) be introduced into the relationship between the microphone array and the introduced rectangular space coordinates as shown in FIG. When the angle formed by the propagation direction of the plane wave arriving at the microphone array 104 and the microphone array 104 is θ, the frequency of the plane wave arriving at the microphone array 104 is single frequency f, and the amplitude is unit amplitude, the plane wave is If coming from a direction other than the direction perpendicular to the microphone array axis, the wavefront of the plane wave reaches the microphone units 101 to 103 constituting the microphone array 104 at different times, so the outputs of the microphone units 101 to 103 are different. The phase difference appears. Therefore, when the output on the microphone array is subjected to Fourier transform with respect to time, a spatial waveform as represented by the following equation (1) is obtained. [0005] p (x) = exp (ikx cos θ) (1) where k is the wave number of a plane wave and is defined by k≡2πf / c, where π and c are the ratio of the circle and the speed of sound, respectively. Also, i is an 03-05-2019 2 imaginary unit and is defined by i≡ (−1) 1/2. Also, x means the coordinates of the microphone unit. A time delay is given to the output of each microphone unit so as to correct this phase difference, and the obtained result of the delay calculation is Fourier-transformed with respect to time to be q (x). q (x) is expressed by the following equation (2). [0006] q (x) = exp (ikx cos θ) exp (−ikx cos θ0) (2) where θ0 is the direction in which directivity is desired. When the arrival direction .theta. Of the sound wave coincides with the direction .theta.0 of directivity, the results obtained by giving delay times to the respective microphone units 101 to 103 represented by the equation (2) all have the same phase. The delay calculation results q (x) of each of the microphone units 101 to 103 represented by the equation (2) are all superimposed and an average value is calculated. The average value of the delay calculation results is A (θ). A (θ) is expressed by the following equation (3) [Equation 1]. [0007] Where L is the length of the microphone array, and integration means integration along the microphone array. Here, when assuming an infinite-length microphone array composed of an infinite number of microphone units 101 to 103, the delay sum A (θ) is expressed as the delta function δ (θ-θ0) of Deiraq from Equation (3). Is represented. As a result, it is possible to strongly output only plane waves coming from the direction of θ 0 by the delay sum of equation (3). [0008] Although the delta function is expressed for an infinite number of microphone units and an infinite length microphone array, the actual microphone array 104 is of a finite length, and the number of microphone units is also finite. Therefore, it can not be expressed by the ideal delta function. That is, the directivity formed by the conventional directivity forming apparatus causes a calculation error by using the equation (3) of delay sum calculation for the microphone array of infinite length also in the microphone array of finite length Therefore, it can not be expressed by the ideal delta function. The calculation error of the conventional directivity formation principle as described above becomes larger as the frequency of the incoming sound wave lowers, and as a result, the directivity of the array microphone for the sound wave of lower frequency becomes 03-05-2019 3 weaker. Incidentally, the directivity of the array microphone disclosed in Japanese Patent LaidOpen No. 7-131886 is shown in FIG. [0009] In view of the above problems, the present invention provides a directional microphone having excellent directivity regardless of the frequency without decreasing directivity as the frequency of the sound wave decreases, and a sound source tracking device using the same. To aim. [0010] SUMMARY OF THE INVENTION The present invention for achieving the above object has the following invention specific matters. The first invention is to obtain directivity by processing each output of a plurality of microphone units regularly arranged in an arbitrary plane with a finite spatial coordinate based on the regularity in the plane. It features. [0011] According to a second aspect of the present invention, in the first aspect, the plurality of microphone units regularly arranged in an arbitrary plane is a plurality of microphone units arranged in a circle. [0012] According to a third aspect of the present invention, in the first aspect, the plurality of microphone units regularly arranged in an arbitrary plane do not overlap a plurality of microphone rings in which the plurality of microphone units are arranged in a circle. It is characterized in that the centers are made to coincide and distributed on a spherical surface. [0013] According to a fourth aspect of the present invention, in the first aspect, the plurality of microphone units regularly arranged in an arbitrary plane has a plurality of microphone rings each including a plurality of microphone units arranged in a circle. In such a way that the microphone units are in a straight line parallel to the cylinder axis on the cylindrical surface formed by the microphone units so that the respective microphone rings do not overlap and the 03-05-2019 4 centers of the respective microphone rings are on the same straight line. A multilayer microphone ring is configured to be arranged to constitute a multilayer microphone ring, and a delay time is added to an output of a microphone unit constituting a microphone array of the multilayer microphone ring, and the output is obtained. [0014] According to a fifth invention, in the first invention, the data of the microphone unit over the area outside the finite area is predicted based on the outputs of the plurality of microphone units arranged in the finite area, and the prediction is performed It is characterized in that the data and the measured data are added and used as an output. [0015] According to a sixth aspect of the present invention, in the fifth aspect, the finite area is a circular arc including an arc outside of the finite area. [0016] According to a seventh invention, in the fifth invention, the finite area is formed by arranging the microphone array which is a microphone unit row on a circular arc and including the area outside the finite area and arranging the microphone array on the circumference It is characterized by having done. [0017] According to an eighth aspect of the present invention, in the fifth aspect, the finite area is a rotating arc surface, and the area outside the finite area is also spherical. [0018] The ninth invention is the invention according to any one of the first to eighth inventions, wherein each output data of the microphone unit by the plane wave assumed to come only from the reference direction and each output data of the microphone unit actually measured It is characterized by comparing with and. [0019] According to a tenth aspect of the present invention, in any one of the first to eighth aspects, as the above processing, a function having orthogonality in the above-mentioned finite space coordinates as a change in phase difference occurring in each output of the above microphone 03-05-2019 5 unit It is characterized in that it is expanded into columns. [0020] An eleventh invention is in any of the first to tenth inventions, characterized in that the direction of arrival of the sound wave is searched by changing the direction of the directivity obtained. [0021] A twelfth aspect of the present invention is a space in which the output data of the microphone unit is arranged as the value obtained by expanding each output data of the microphone unit by the plane wave assumed to arrive only from the reference direction into a space orthogonal to the space The comparison with the value expanded to the orthogonal function is performed in the time domain by the convolution operation to obtain the time waveform of the sound wave, and the directivity is obtained. [0022] The thirteenth invention is an apparatus for mode expanding each output data of the microphone unit along the circumferential direction of the microphone unit, a convolution for convoluting an output of the apparatus for each mode, and an arrival of the sound wave. It is characterized by having a multiplier which takes in the direction. [0023] A fourteenth invention is in the twelfth and thirteenth invention, characterized in that the microphone units are arranged in any one of a circumferential shape and a spherical surface. [0024] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT An embodiment of the present invention will be described below with reference to FIGS. FIG. 1 is an example of the present invention, and FIGS. 2 and 3 also show the principle of the present invention. In the figure, a microphone ring 4 composed of a plurality of microphone units 1, 2, 3 arranged 03-05-2019 6 in a circle, a Fourier transform unit 5 for performing Fourier transform on the output from each microphone unit with respect to time, and each microphone unit The Fourier expansion device 6 spatially Fourier-expands the result of the output with respect to time along the circumferential direction of the microphone ring 4 and the addition device 7 performing superposition while giving weights to the Fourier-expanded result And a directivity forming device 9. [0025] In the present invention, the outputs of a plurality of microphone units disposed on a closed curve are arithmetically processed using curvilinear coordinates along the closed curve on which the microphone units are disposed to obtain directivity. When a circle is a closed curve, polar coordinates as shown in FIG. 2 having the center of the microphone ring 4 formed by the plurality of microphone units arranged in a circle as the origin are used as the curved coordinates. Then, space coordinates necessary to express all directions of space in polar coordinates are finite intervals of circumferential coordinates 0 (rad) to 2π (rad). It is a feature of the present invention that the space coordinates required to fully express this direction are finite. In FIG. 2, 10 is the circumferential coordinate θ, and all directions can be expressed in a finite section of 0 rad to 2π rad for this θ. [0026] In the configuration shown in FIG. 1, the first to Nth microphone units 1 to 3 receive the incoming sound wave and output it to the directivity forming device 9. In this directivity forming device 9, directivity is formed using a change in spatial phase shift of the output of each microphone unit due to a change in the sound wave arrival angle, and a sound wave coming from a limited range of direction is strongly output Do. 03-05-2019 7 [0027] In this case, as the directivity formation principle, when the plane wave arrives only from the direction defined as the reference direction, the data measured by the microphone is used as the reference data, and the measurement data actually obtained by the microphone is the reference data Form directivity by comparing with. Also, in forming directivity, each of the measurement data and the reference data is expanded into a function sequence having orthogonality with respect to space, and the higher order terms are considered. Incidentally, in the conventional directivity formation, after averaging the outputs of each microphone unit, the average value is taken and the average value is evaluated. Only the next section is considered. [0028] The directivity formation principle will be described with reference to FIGS. 1 and 2 and FIG. For example, when the direction of circumferential coordinate θ = 0 is defined as a reference direction, and it is assumed that a plane wave arrives only from that direction, the output of each microphone unit 1, 2, 3 constituting microphone ring 4 is What has been Fourier-transformed with respect to time by the conversion device 5 is defined as reference direction data F (θ). Then, the measurement data obtained by subjecting the output of each of the microphone units 1, 2, 3 to the plane wave coming from the direction of the circumferential coordinate θ = Ψ to Fourier transform with respect to time by the Fourier transform device 5 is F (θ-Ψ It is expressed as). In FIG. 3A, assuming that a plane wave arrives from θ = Ψ, one of the devices forming the directivity forming device is the output of each of the microphone units 1, 2, 3 forming the microphone ring 4 In the Fourier transform device 5 which is the Fourier transform with respect 03-05-2019 8 to time, the horizontal axis is schematically shown as the positions of the microphone units 1, 2, 3. That is, the frequency component of the sound wave is taken out and the sound pressure change to the microphone units 1, 2, 3 is shown. [0029] FIG. 3 (b) shows measurement data F (θ obtained by subjecting the output of each microphone unit 1, 2, 3 to Fourier transform with respect to time by the Fourier transform device 5 when a plane wave arrives from the direction of θ = Ψ. As a result of Fourier expansion of −Ψ) along the circumferential direction θ of the microphone ring 4 by the spatial Fourier expansion device 6, the horizontal axis is schematically shown as each mode number of the Fourier expansion. Here, the ratio of the Fourier coefficients obtained by Fourier expanding the reference direction data F (θ) and the measurement data F (θ-Ψ) along the circumferential direction of the microphone ring 4 by the next space Fourier expanding device 6 is It is expressed as a function of a sine waveform. In FIG. 3B, the positional deviation on the component is taken out on the microphone ring. [0030] In the following equations (41) and (42) [equation 2], when the plane wave arrives from the direction of θ = Ψ, the output of each microphone unit 1, 2, 3 is Fourier transformed with respect to time by the Fourier transform device 5 The measurement data F (θ−Ψ) obtained by the above are expressed by the Fourier transform unit 6 by the Fourier transform of the microphone ring 4 along the circumferential direction θ. However, the coefficient ε m is ε 0 = 1, ε m = 2 (m> 0). [0031] Further, in the following equations (51) and (52) [Equation 3], when plane waves arrive from the direction of θ = 0, the output of each microphone unit 1, 2, 3 is The reference directional data F (θ) obtained by performing a Fourier transform on time according to F.sub.i represents Fourier coefficients obtained by performing a Fourier expansion on the circumferential direction .theta. 03-05-2019 9 [0032] By comparing the equations (41) and (42) with the equations (51) and (52), the ratio of the Fourier coefficients of the measurement data and the reference direction data can be expressed as a function of a sine waveform. Assuming that the Fourier coefficient ratio between the reference direction data and the measurement data is αm and βm, Equations (61) and (62) of [Equation 4] indicate αm and βm, and the Fourier coefficient ratio in FIG. The α m is schematically shown. [0033] Next, the ratio of the Fourier coefficients of the reference direction data and the measured data obtained by the spatial Fourier spreader 6 is output to the adder 7 shown in FIG. 1, and in FIG. 3 (d), the reference direction data is added by the adder 7. The result of calculation of a Fourier series in which the ratio of the Fourier coefficient of the measurement data is regarded as the Fourier coefficient again is schematically shown. The following equation (7) represents a Fourier series having Fourier coefficient ratios α m and β m of reference direction data and measurement data as Fourier coefficients. [0034] Since the Fourier coefficient ratios α m and β m of the reference direction data and the measurement data are expressed as a function of a sine waveform as in the above equations (61) and (62), the calculation result of equation (7) The function δ (·) is expressed as A (θ) = δ (θ−Ψ), and the directivity forming principle of the present invention provides a sharp directivity with a delta function. The directivity obtained by the directivity formation principle of the present invention described above does not depend on the radius of the microphone ring 4 and the frequency of the sound wave. Therefore, according to the directivity formation principle of the present invention, it is possible to secure strong directivity at a low frequency as compared with the conventional array microphone. 03-05-2019 10 [0035] Next, the results of numerical experiments are shown. In numerical experiments, assuming that a plane wave arrives from a certain direction in the microphone ring where the number of microphone units is 16 and the microphone ring radius is 250 [mm], the direction in which the plane wave arrives is the circumferential coordinate θ The output of the example shown in FIG. 1 is obtained when the direction of directivity is changed from θ = −π [rad] to θ = π [rad], and the intensity of directivity is calculated from this output. I asked. At this time, the space Fourier expansion in directivity formation considers up to the 15th mode. [0036] In addition, in order to compare the directivity in the example of FIG. 1 with the directivity of the conventional array microphone, the microphone array length is equal to the maximum microphone unit distance of the microphone ring of this example used for numerical experiments, and 500 [mm] The numerical experiment of the directivity of the array microphone which made the number of microphone units equal to the number of microphone units of this example used for numerical experiment 16 was conducted. However, in the numerical experiment of the directivity of the array microphone, assuming that a plane wave has arrived from the axial direction of the microphone array, the origin of the arrival angle θ of the plane wave arrival direction is taken as the origin of the directivity The output of the array microphone when changing from −π [rad] to θ = π [rad] was determined, and the strength of directivity was determined from the output of the array microphone. Moreover, the frequency of a sound wave considers each case of 250 [Hz] and 500 [Hz]. [0037] FIG. 4 shows a comparison of the directivity of this example based on numerical experiments and the conventional array microphone, and as the frequency of the sound wave decreases, the directivity of the conventional array microphone becomes weaker, whereas this example Directivity shows strong directivity regardless of frequency. Also, the directivity of this example is stronger as the number of modes in expanding the measurement data of the microphone ring in the circumferential direction mode by the space Fourier expansion apparatus is larger. Furthermore, since the directivity of this example does not depend on the radius of the microphone ring, the size of the device can be reduced as compared with the conventional array microphone. 03-05-2019 11 [0038] In this example, other than using as a directional microphone that collects sound waves coming from a limited narrow direction well, when sound waves come from a plurality of directions, sound waves of any size come from any direction It is also possible to use it as a sound source tracking device that outputs whether it is coming. When sound waves come from a plurality of directions, the output of this example is obtained as a superposition of delta functions corresponding to the sound waves from the respective directions. FIG. 5 shows a sound field where plane waves with sound pressure levels of 100 [dB] and 90 [dB] arrive from the direction of circumferential coordinate θ = 0 [rad] and circumferential coordinate θ = π / 2 [rad], respectively. The result of having examined the measurement result which used this example at the time of assumption by numerical experiment is shown. However, FIG. 5 shows the result when the number of microphone units constituting the microphone ring used in the numerical experiment is 32, and the microphone ring radius is 250 [mm]. [0039] 6, 7 and 8 show a second example of the embodiment of the present invention. FIG. 6 shows the configuration, and FIG. 7 shows a block of the directivity forming apparatus. In these figures, 11 is a 0.1th microphone unit, 12 is a 0.2 microphone unit, 13 is 0.. N microphone unit, 14 is an M.M. 1 microphone unit, 15 is the first M. One microphone unit, 16 is a double microphone ring, 17 is a spherical directivity forming device, 18 is an output terminal, and in the spherical directivity forming device, 19 is an M-. 20 is a 0.1 input terminal, 21 is a 0.2 input terminal, 22 is an M.I. One input terminal, 23 is a Fourier transform device, 24 is a sphere function expansion device, and 25 is an addition device. [0040] Here, a plurality of microphone rings 16 each composed of a plurality of microphone units 11, 12, 13, 14, 15 arranged in a circle, so that the respective microphone rings do not overlap each other Of the microphones are distributed on one spherical surface, and outputs from the microphone units 11, 12, 13, 14 and 15 constituting each microphone ring Fourier transform device 23 for performing Fourier transform on time each time, Fourier transform of the output of each microphone unit constituting each microphone ring for time on the sphere formed by a plurality of microphone rings, and the result of square sphere function expansion on the spherical surface Device 24, Square Region formed of directional forming apparatus 17 in adder 03-05-2019 12 25 for superimposing while giving weight to expanded results. [0041] In this example, the outputs of the plurality of microphone units 11, 12, 13, 14, 15 disposed on the closed curved surface which is a sphere are three-dimensional polar coordinate space along the closed curved surface on which the plurality of microphone units are disposed. The calculation process is performed using the curved surface coordinates in the above, and in this example, the data obtained when it is assumed that the plane wave arrives only from the direction defined as the reference direction is used as the reference data, and the measurement is actually obtained The directivity is to be formed by comparison with the data, and in comparison of the reference data and the measurement data in the directivity formation of this example, each of the reference data and the measurement data is arranged with a plurality of microphone units. This is an improvement based on the same idea of FIG. 1 in that it is developed into a function sequence having orthogonality on a closed surface, and in FIG. [0042] In this example, a plurality of microphone rings constituted by a plurality of microphone units 11, 12, 13, 14, 15 arranged in a circle, respectively, so that the respective microphone rings do not overlap with each other The output of all the microphone units distributed on one spherical surface is arranged by arranging the centers of the two to coincide with each other, and a plurality of microphone rings each made up of a plurality of microphone units arranged in a circular shape, Arranging processing using polar coordinates whose origin is the center of the multiple microphone ring 16 in which all the microphone units are distributed on the spherical surface by arranging the microphone rings so that the microphone rings do not overlap and the centers of the respective microphone rings coincide. It is characterized by By using polar coordinates, space coordinates required to represent all directions in a threedimensional space are limited to longitude coordinates 0 [rad] to 2π [rad] and latitude coordinates 0 [rad] to π [rad] It becomes a section. In FIG. 8, reference numeral 26 denotes a latitude direction coordinate θ, and reference numeral 27 denotes a longitude direction coordinate φ. [0043] 03-05-2019 13 In operation, the M.M. 1 microphone unit 14 to M.M. All microphone units up to one microphone unit 15 receive the incoming sound wave and output it to the spherical directivity forming device 17 respectively. The spherical directivity forming device 17 forms directivity using a change in spatial phase shift of the output of each microphone unit due to a change in the sound wave arrival angle, and strongly strengthens the sound wave coming from a limited range of directions. Output. To explain the directivity forming principle of the spherical directivity forming device 17, the directivity of this example uses data measured by multiple microphones as a reference data when a plane wave arrives only from the direction defined as the reference direction. Used, it is obtained by comparing the data actually measured in the double microphone ring with the reference data. [0044] For example, the direction of the latitude direction coordinate θ = π / 2 [rad] and the direction of the longitude direction coordinate φ = 0 [rad] are defined as the reference direction, and it is assumed that a plane wave arrives from only that direction. The output of each of the microphone units constituting 16 is received at the input terminals 19 to 22 corresponding to each microphone unit, and the signals received at the input terminals 19 to 22 are Fouriered with respect to time by the Fourier transform device 23 corresponding to each input terminal Data obtained by conversion is defined as reference direction data F (θ, φ). Then, when receiving a plane wave coming from the direction of latitude direction coordinate θ = π / 2 + Ψ and longitude direction coordinate φ = η by each microphone unit constituting the double microphone ring, each microphone unit constituting the double microphone ring The measurement data obtained by subjecting the output at the input terminals 19 to 22 corresponding to each microphone unit to Fourier transform the signals received at the input terminals with respect to time by the Fourier transform device 23 corresponding to each input terminal is F (θ It is expressed as −Ψ, φ−η). [0045] Expansion obtained by expanding the function of the reference direction data F (θ, φ) and the measurement data F (θ-Ψ, φ-)) on the sphere formed by the double microphone ring by the function sphere expanding device 24 The ratio of coefficients is represented by a square sphere function. The following equations (81) and (82) shown in [Equation 6] are microphones constituting a double microphone ring of a plane wave in which a plane wave arrives from the 03-05-2019 14 direction of latitude direction coordinates θ = π / 2 + Ψ and longitude direction coordinates φ = η When receiving by the unit, the output of each microphone unit constituting the multiple microphone ring is received by the input terminals 19 to 22 corresponding to each microphone unit, and the signal received at this input terminal is corresponded to each input terminal Measurement data F (θ−Ψ, φ−η) obtained by performing Fourier transform on time by the Fourier transform device 23 is subjected to square sphere function expansion on a spherical surface formed by multiple microphones by the square sphere function expansion device 24 Represents the resulting expansion factor. However, the coefficient ε m is ε 0 = 1, ε m = 2 (m> 0). [0046] In the equations (81) and (82), P nm (·) is a Legendre 陪 function. The following equations (91) and (92) shown in [Equation 7] correspond the outputs of the respective microphone units constituting the multi-microphone ring to the respective microphone units when it is assumed that the plane wave has arrived only from the reference direction The reference directional data F (θ, φ) obtained by performing Fourier transform of the signals received at the input terminals 19 to 22 and received at the input terminals with respect to time by the Fourier transform device 23 corresponding to each input terminal are double microphones It represents the expansion coefficient obtained by expanding the spherical function on the sphere formed by the ring. [0047] From the comparison of the equations (81) and (82) and the equations (91) and (92), the ratio of the expansion coefficient of the measurement data and the reference direction data is represented by a square sphere function. The expansion coefficient ratio between the reference direction data and the measurement data is ξmn and ζmn. The following equations (101) and (102) of [Equation 8] show expansion coefficient ratios ξmn and ζmn of the measurement data and the reference direction data. [0048] The expansion coefficient ratio of the reference direction data and the measurement data obtained by the square sphere function expansion device 24 is output to the addition device 25 and the expansion coefficient ratio of the reference direction data and measurement data is 03-05-2019 15 regarded as the expansion coefficient again in the addition device 25. Calculates the spherical function series. The following equation (11) of [Equation 9] represents a square sphere function series which is an expansion coefficient of expansion coefficient ratio ξmn, ζmn of reference direction data and measurement data. [0049] Since the expansion coefficient ratio ξmn, ζmn of the reference direction data of [Equation 8] and the measurement data is expressed by a square sphere function, the calculation result of the equation (11) of [Equation 9] is the delta function δ (· ) Is expressed as A (.theta.,. Phi.) =. Delta. (. Theta .-. Zeta.). Delta. (. Phi .-. Eta.), And according to the directivity formation principle of this example, a sharp directivity with a delta function is obtained. According to the directivity formation principle of the present example described above, the directivity does not depend on the radius of the spherical surface formed by the double microphone ring and the frequency of the sound wave. Therefore, according to the directivity formation principle of this example, it is possible to secure stronger directivity at a low frequency as compared with the conventional array microphone. Moreover, analysis of three-dimensional space becomes possible by the directivity formation principle of this example. [0050] In this example, in addition to using as a directional microphone that collects sound waves coming from a limited narrow direction well, sound waves come from a plurality of directions by continuously changing the direction of directivity. It is also possible to use as a sound source search device that outputs from which direction and how large the sound wave is coming from. When sound waves come from a plurality of directions, the outputs of the ring microphones are obtained as a superposition of delta functions corresponding to the sound waves from the respective directions. [0051] 9 to 11 show still another example. In FIG. 9, 28 is a 1.1st microphone unit, 29 is a 1.2nd microphone unit, and 30 is a 1st microphone unit. The N microphone unit, 31 is the 2.1st microphone unit, 32 is the 2.2 microphone unit, 33 is the 2nd. The N microphone unit 34 is an M.M. 1 microphone unit, 35 is the M.I. 2 microphone units, 36 is the M.I. N microphone unit, 37 03-05-2019 16 is a first microphone ring, 38 is a second microphone ring, 39 is an Mth microphone ring, 40 is a first microphone array, 41 is a second microphone array, 42 is an N microphone array, 43 is a multilayer microphone Ring 44, first microphone array directivity forming device 45, second microphone array directivity forming device 46, Nth microphone array directivity forming device 47, cylindrical circumferential directivity forming device 48, output terminal is there. [0052] Here, as shown in FIG. 9, a plurality of microphone rings 37, 38 each having the same radius, the number of microphone units (28, 29, 30), (31, 32, 33), (34, 35, 36), and the microphone unit spacing being equal. , 39, with their centers aligned on the same straight line, and at this time the microphone units are arranged to form a plurality of straight lines 40, 41, 42 parallel to each other on the cylindrical surface formed by the microphone units The ring 43 and each of the plurality of microphone arrays 40, 41, 42 formed on the cylindrical surface of such a multilayer microphone ring 43 are regarded as a conventional microphone array and are conventional in a plane including respective microphone array axes Directivity forming devices 44, 45 and 46 for forming directivity and their directivity Composed of directional forming apparatus 47 for forming a cylindrical circumferential direction of the directivity of the output of the forming device. [0053] FIG. 10 shows the configuration of directivity forming devices 44, 45 and 46 for forming directivity in a plane including the microphone array axis with respect to microphone arrays 40, 41 and 42 configured on multilayer microphone ring 43. This is similar to FIG. 21 in the prior art description. 49 is an input terminal for receiving the output of the microphone array, 50 is a delay device, 51 is a summing device, and 52 is an output terminal. FIG. 11 shows the configuration of a directivity forming device 47 that forms directivity in the circumferential direction of the cylinder, and is similar to the device 9 of FIG. 1 in Example 1 described above. 54 is an input terminal for receiving the output of the directivity forming device in the plane including the microphone array axis, 55 is a Fourier transform device for performing Fourier transform of the signal with respect to time, 56 is a Fourier expansion device for performing Fourier expansion for space An adder 58 is an output terminal. [0054] 03-05-2019 17 In this example, directivity is formed in a three-dimensional space by using the principle of the ring microphone shown in Example 1 described above and the principle of the conventional array microphone. The arrangement of the microphones in this example is ring-shaped in a plane orthogonal to the cylinder axis, and linear in the direction parallel to the cylinder axis. In this example, first, focusing on a linear arrangement parallel to the cylinder axis as the arrangement of the microphone units, the output of each microphone unit constituting each of the microphone arrays 40, 41 and 42 formed on the cylindrical surface is The directivity in the plane including the microphone array axis is formed by performing the operation of giving the delay time in the same manner as the array microphone of the above, and the outputs of the plurality of array microphones obtained are shown in Example 1 above. The directivity in the circumferential direction of the cylinder is formed by performing an operation according to the principle. [0055] This example corresponds to one in which each microphone unit constituting the same microphone ring 37, 38, 39 as the above-mentioned example is replaced with a microphone array constituted by a plurality of microphone units. Therefore, as in Example 1, this example exhibits strong directivity independent of the frequency of the sound wave in the circumferential direction of the cylinder. In addition to the use as a directional microphone that collects sound waves coming from a limited narrow direction well, as in the first example, this example also changes the direction of directivity continuously by changing the direction of directivity from a plurality of directions. It is also possible to use it as a sound source search device that outputs from which direction and how large the sound wave is coming from when. [0056] FIG. 12 shows still another example, in which a method of predicting a virtual point is added. FIG. 12 shows the case where four microphone units are linearly arranged. In FIG. 12, 59 is a microphone unit, 60 is a delay device, 61 is a prediction device for calculating prediction data, 62 is an addition device, 63 is an output terminal, and 64 is a directivity forming device. FIG. 13 shows the configuration of the prediction device 61. Reference numeral 65 is an input terminal for receiving the output of each microphone unit given a delay time, 66 is a resistor for weighting each signal, 67 is a summing device for combining two channel signals, and 68 is an output terminal. In this example, based on the outputs of the plurality of microphone units 59, the signal at a virtual point outside the area where the microphone units are arranged is 03-05-2019 18 predicted, and the delay time is calculated to the data predicted from the measured data and the measured data. The directivity is formed by adding all of the given results. [0057] In this example, based on the outputs of the plurality of microphone units 59, a signal outside the area where the microphone units 59 are arranged is predicted, and a delay time is given to measured data and data predicted from the measured data. It is to form directivity by adding all the results, and is characterized in that it is possible to form sharp directivity in order to virtually expand the signal reception area. As an example of this embodiment, a finite section on a straight line is considered as an area in which a plurality of microphone units 59 are arranged. The position coordinate of each microphone unit 59 is represented by xn, and the delay time of each microphone unit output is represented by y (xn, t). FIG. 14 schematically shows the position of the microphone unit and the output thereof. In FIG. 14, a circle means a measurement result obtained by giving a delay time to the output of the microphone unit at that position, and a solid line virtually assumes that an infinite number of microphone units are arranged in an infinite interval on a straight line In the case of a virtual result is meant. In FIG. 14, if virtual data of a solid line is predicted from actual measurement data of circles, the arrangement section of the microphone unit can be virtually expanded, and directivity can be improved. As a method of calculating prediction data, a method of weighting by a resistor 66 shown in FIG. 13 and a method of superposition by an adder 67 are used. The recurrence equation for calculating predicted data is shown in equation (12) of [Equation 10]. [0058] The initial value of recurrence equation (12) is Bn = y (xn, t), and x is the coordinates of a virtual point whose data is to be predicted. Based on equation (12), the resistance value of each of the resistors in FIG. 13 is determined. The prediction unit 61 of FIG. 14 predicts data at virtual points in accordance with the recurrence formula of the formula. The number of prediction devices 61 is the same as the number of virtual points to be predicted. The directivity is formed by adding all of the measured data obtained by giving the delay time to the output of each microphone unit and the predicted data predicted based on the measured data by the adding device. FIG. 15 shows the result of comparison of directivity of this example and the conventional method by numerical simulation. The solid line is the directivity of this example, and the dotted line is the directivity of the conventional method. As the conditions of the numerical simulation, the number of microphone units is 10, the microphone units are arranged in a finite section on a straight line, the section length is 1 m, and the directivity direction is the microphone unit column axis 03-05-2019 19 direction . Moreover, the frequency of the sound wave was assumed to be 200 [Hz]. From FIG. 15, it can be confirmed that the directivity of this device is sharp. [0059] FIG. 16 shows another example, 69 is a microphone unit, 70 is a Fourier transform device, 71 is a spatial Fourier expansion device, 72 is an addition device, 73 is an output terminal, 74 is a Fourier transform device and a spatial Fourier expansion device It is a circumferential direction data analysis device constituted by In this example, an arc-shaped microphone unit array composed of a plurality of microphone units 69 arranged on an arc, a Fourier transform device 70 for performing a Fourier transform on the output from each microphone unit with respect to time, and each microphone unit A Fourier transform unit 71 spatially Fourier-expands the result of the output with respect to time along the circumferential direction of the microphone ring, and an adder 72 which performs addition while giving weights to the Fourier-expanded result. [0060] In this example, based on the outputs of the plurality of microphone units 69 arranged on the arc of a part of a circle of a radius, a part on which the microphone unit is not arranged on the circle including the arc arranged , And Fourier-expanding the data along a circle on a circle including an arc in which the microphone unit is arranged, to form directivity from changes in Fourier coefficients. [0061] Let M be the number of microphone units arranged on an arc, and consider polar coordinates whose origin is the center of a circle including the arc where the microphone units are arranged as space coordinates, and position coordinates of each microphone unit be θm (1 <m Let <M), and let the output of each microphone unit be Pm (1 <m <M). Suppose that the data obtained when the microphone units are arranged over the entire circumference of a circle is represented as a function F (θ) with respect to the angle θ. Since F (θ) is a function of period 2π, it becomes as shown in equation (13) of [Equation 11]. [0062] 03-05-2019 20 Here, the Fourier coefficients an can be obtained by solving the equation (14) of the equation (12) using the measured data. [0063] Thus, data F (θ) around the entire circumference of the circle can be predicted by calculating an in the equation (14) based on the actual measurement data. On the other hand, let bn be the Fourier coefficient of the data over the entire circumference of the circle predicted from the data on the arc obtained when sound waves arrive from the direction defined as the reference direction, and sound waves coming from an actual unknown direction Assuming that the Fourier coefficient of the data over the entire circumference of the circle predicted from the measured data is an, the arrival direction of the sound wave follows the principle of the previous example 1 and outputs A (θ) of the following equation (15) of [Equation 13] You can know more. [0064] In FIG. 16, the prediction according to the equation (14) is performed in the spatial Fourier expansion device 71, and the addition device 72 outputs the sound wave arrival direction of the equation (15). As described above, in the present example, from the output of the microphone unit 69 disposed only on the arc that is a portion of a circle, data of a portion on which the microphone unit is not disposed on the circle including the arc where the microphone unit is disposed By predicting, it is possible to obtain the same effect as when the microphone unit is disposed all around. [0065] 17 shows still another embodiment, and in FIG. 17, 69 is a microphone unit, 64 is a directivity forming device, 74 is a circumferential data analysis device, 70 is a Fourier transform device, 71 is a spatial Fourier expansion device, 72 is an adder, and 73 is an output terminal. In this example, a plurality of microphone unit rows arranged on the arc orthogonal to a plane including a certain arc and parallel to each other, and a plane including each microphone unit row for each microphone unit row A microphone on a cylindrical surface including a directional shaping 03-05-2019 21 device 64 for forming directivity within, a Fourier transform device 70 for Fourier transforming an output of each microphone unit row with respect to time, and an arc surface on which the microphone unit row is arranged A circumferential data analyzer 74 configured of a spatial Fourier expander 71 that predicts data outside the region in which unit columns are arranged by Fourier expansion for space, and measured data and data predicted from the measured data are weighted It is comprised by the addition apparatus 72 which adds while adding. [0066] In this example, the microphone units 69 are arranged on a plurality of straight lines which intersect the arc and are parallel to one another so as to be orthogonal to a plane including the arc. The area in which the microphone units 69 are arranged on each straight line is a finite section. In this example, the area in which the microphone units are arranged is a finite area with respect to the microphone unit array axis direction, but it is possible to virtually expand the arrangement area of the microphone units according to Example 4 above, Thereby, it is possible to improve the directivity in the direction of the cylinder axis. That is, in the directivity forming device 64 of FIG. 17, the prediction device predicts data outside the region where the microphone units are arranged in the microphone unit row axis direction according to the equation (15). Then, from the actual measurement data and the data predicted from the actual measurement data, the delay sum is calculated for each microphone unit row, and directivity in a plane including the microphone unit row is formed. [0067] After forming directivity in a plane including each microphone unit array for each microphone unit array, directivity is formed in a plane orthogonal to each microphone unit array. It is possible to predict data over the entire circumference of the circle including the arc from the data on the arc according to the above example 5 in the circumferential data analysis device 74, and the sound wave comes from the direction defined as the reference direction The directivity is formed by comparing the result of the Fourier expansion along the circumference of the data on the circumference of the circle and the result of the Fourier expansion of the data measured when the sound wave is actually coming from an unknown direction. Do. In other words, the result of forming directivity in the plane including each microphone unit row for each microphone unit row is regarded as Pm in the equation (14) of the previous example 5, and a plane orthogonal to each microphone unit row The data over the entire circumference of the circle including the arc is predicted from the data on the arc formed by the intersections of the microphone unit rows. Then, the data predicted from the actual measurement data and the actual 03-05-2019 22 measurement data are regarded as the data F (θ−Ψ) of the first example, and in the plane orthogonal to each microphone unit row according to the equation (7) of the first example. Form directivity. [0068] 18 and 19 show other examples. In FIG. 18, 75 is a microphone unit, 76 is a spherical directivity forming device, 77 is an output terminal, and FIG. 19 is a spherical directivity forming device of FIG. Reference numeral 78 denotes an input terminal, 79 denotes a spherical prediction device, 80 denotes an input terminal, 81 denotes a Fourier transform device, 82 denotes a measured data output device, 83 denotes a sphere function expansion device, and 84 denotes an addition device. [0069] In this example, a plurality of microphone rings obtained by disposing the microphone units on circles different in radius from one another is such that planes including the respective microphone rings are parallel to each other on a rotation arc surface obtained by rotating the arc. Place in In this example, based on the data obtained from each microphone unit arranged on the rotation arc surface, the data over the entire spherical surface including the rotation arc surface is predicted, and the predicted data is expanded by the function having orthogonality. Form directivity. [0070] In this example, a plurality of microphone rings obtained by disposing the microphone units on circles different in radius from each other is formed so that planes including the respective microphone rings are parallel to each other on a rotation arc surface obtained by rotating the arc. Place in In the present invention, based on data obtained from each microphone unit disposed on a rotating arc surface, data over the entire spherical surface including the rotating arc surface is predicted, and the predicted data is expanded with a function having orthogonality Form directivity. For example, it is assumed that the number of microphone units constituting each of the plurality of microphone rings arranged on the arc surface is the same, and the microphone units constituting each microphone ring are equally spaced. At this time, the arrangement of the 03-05-2019 23 microphone units on the circular arc surface can be viewed as a plurality of circular microphone unit rows and a plurality of arcuate microphone unit rows arranged on arcs orthogonal to the respective circles. . Focusing on the view of a plurality of arc-shaped microphone unit arrays arranged on an arc, data on the entire circumference of a circle including the arc can be obtained from data on the arc according to Example 5 above. If the same operation is performed for all of the plurality of arc-shaped microphone unit rows, as a result, data over the entire spherical surface including the rotation arc surface can be predicted from actual measurement data on the rotation arc surface. [0071] In FIG. 19, the data analysis device 74, which is one of the devices constituting the spherical prediction device 79, prepares the same number as the number of arc microphone unit rows on the rotation arc surface, and Correspond to one to one. An input terminal of each data analysis device receives an output from a microphone unit constituting an arc-shaped microphone unit row corresponding to each data analysis device. The data analysis device 74 predicts data at a point outside the area where the microphone units are arranged on a circle including the arc, from the outputs of the microphone units constituting each arc microphone unit row. Using the data over the entire predicted sphere, directivity can be formed using the 83 square function expander and adder 84 of FIG. 19 in accordance with Example 3 above. According to this example, it is possible to form the same directivity as that in the case where the microphone unit is disposed over the entire spherical surface from the output of the microphone unit disposed in a slight area on the spherical surface. [0072] By the way, in the above description, in order to prevent the deterioration of the directivity characteristic depending on the frequency of the sound wave, particularly the directivity characteristic in the low frequency region, the processing in the frequency region independent of the frequency is performed. However, although processing in this frequency domain is related to its accuracy, it has been processed by fast Fourier transform, and it has been found that it takes measurement and processing time. For this purpose, the present inventors performed processing in the time domain without processing in the frequency domain so that processing can be performed in real time and the output can be heard. [0073] 03-05-2019 24 Prior to the description of the apparatus, an algorithm of theoretical configuration and processing in the time domain will be described. The situation according to FIG. 24 which is the same as FIG. 1 in which a plurality of microphone units (sensors) are disposed on the circumference will now be described. In the arrangement shown in FIG. 24, M microphone units are arranged at equal intervals on the circumference of radius a, and polar coordinates (r, θ) are assumed with the center of the circle of this microphone unit as the origin. A plane wave arrives at the circumferentially arranged microphone units, and propagation direction vectors of each plane exist only in the microphone unit arrangement plane, and a sound field superimposed by the plane waves is considered. In the processing, the time interval of digital sampling is Δt. [0074] In such a situation, directivity is given to the output A of the microphone unit on the circumference, and the signal B consisting of only sound waves in the direction of arrival is extracted from the signal obtained by superimposing plane waves on top of each other. In this case, the output on the circumference of each microphone is A (nΔt, 2πμ / M), the direction giving directivity is Ψ, and the signal B (nΔt ¦ Ψ) of only the sound wave by giving directivity is In the determination, n is time and nΔt represents time, μ is space coordinates of circumferentially arranged microphones, μ is 1, 2, 3 ... M, and therefore 2πμ / M is a space angle Indicates Further, with regard to the microphones arranged in a circumferential shape, the spatial phase is taken into consideration, and the following equation is given. Now, before the conclusion, the operation method for obtaining the above A to B will be described in order. [0075] For example, in one-dimensional space, it is assumed that the sound wave f (t, x) can be written as a solution of the wave equation of the following formula [Equation 15]. [0076] In this equation, the rectangular coordinate x can be written as r cos θ in polar coordinate display, and the output when a plane wave in the propagation direction θ 0 (arrival direction θ 0 -π) of the sound wave is received on the radius r = a A (t, θ) is the following equation [Equation 16] in which θ 0 and a are added to [Equation 16]. [0077] 03-05-2019 25 That is, A (t, θ) is obtained by setting x to a and θ to (θ-θ 0). Furthermore, in actual measurement, when considering that it is a discrete expression with respect to time and space and that there is an upper limit to the frequency that can be analyzed, the output A nm is as follows. [0078] Here, in the plane wave signal Anm, the first subscript subscript of the display Anm, where n is the data number in the time or frequency domain, the second subscript subscript, Where m indicates the mode number on the space or circumference, and in the above equation [Equation 16] [Equation 17], for example, # shown in A # indicates that it is in the frequency domain, and * Shown in A * indicates that it is a mode on the circumference. [0079] Furthermore, in the above-mentioned equation [Equation 17], spatial phase is taken into consideration, and the output on the circumference when the plane wave is received is modedeveloped on the circumference. As a result, the following equation is obtained. [0080] In the theoretical development in the above equation [Equation 15] [Equation 16] [Equation 17] [Equation 18], an example in which the propagation direction of the sound wave is θ 0 has been described. Sound wave Fnm is shown by following Formula [Equation 19]. In this equation [Equation 19], θ 0 is taken as the reference direction, and θ 0 = 0. [0081] 03-05-2019 26 Comparing A nm * of the above-mentioned equation [Eq. 18] with F nm * of the equation [Eq. 19], the spatial phase of the following equation [Eq. 20] is given to F nm *. [0082] The relationship between the equation [Equation 19] and the equation [Equation 18] is similar to, for example, the case where a given data f (m) is subjected to Fourier transform to give an arbitrary phase difference θ 0. That is, it is given by the following equation [Equation 2], and the power of -2πiθ 0 μ / M of bμe according to θ 0 is given to the basic data f (m). [0083] Incidentally, the same applies to the case where an arbitrary phase difference θ 0 is given to the inverse Fourier transform of the basic data f (m), and θ 0 is related to the basic data aμ as in the following equation [Equation 22]. The power of 2πiθ 0 μ / M is given. [0084] In this way, the equation [Eq. 19] is obtained from the equation [Eq. 19] in the same manner as the equation [Eq. 21] [Eq. [Equation 18] is obtained, that is, A nm * is obtained from F nm *, and this holds true. [0085] When Anm * and Fnm * of the equation [18] and the equation [19] are Fourier transformed, the following equation [23] is obtained. [0086] The equation of Alm * and Flm * by this Fourier transform [Equation 23] is the location of the Fourier transform with respect to time to the equation of Kronecker's delta (δ of kronecker) when the frequency resolution of the Fourier transform is sufficiently high. It can be approximated to 0.1, and it becomes like a following formula [Equation 24]. [0087] 03-05-2019 27 Here, with respect to (subscript 1 μ in G) in the equation [24], the theoretical development in the present invention does not become an essential problem, and so analysis is not made, but the microphone units on the circumference In the case of an ideal model in which is an infinite number, Flm * is displayed by a Bessel function. [0088] Thus, the following equation [Equation 25] is derived from the above equation [Equation 24]. [0089] As a result of the above, sound waves in the propagation direction θ 0 up to now are obtained, and Fourier transform and inverse Fourier transform are performed on data in the reference direction to obtain sound waves B in the direction of arrival. In other words, in the following equation [26], a plane wave is superimposed on a direction せ る giving directivity by the microphone output on the circumference to obtain B, and the Fourier transform in time is temporarily replaced by inverse transform to space. We are replacing and folding. [0090] This equation [Equation 26] is the conclusion of the present invention. That is, taking the spatial position into consideration with the microphone output An μ on the circumference, Anm * (Expression (26-1)) is obtained from Expression [18]. On the other hand, the spatial Fourier transform is performed on the equation [Eq. 19] (Eq. (262)) of the signal F nm * from the reference direction to perform Flm * # (Eq. (26-3)) and the inverse transform is performed * (Equation (26-4)) is obtained. Here, a directional sound wave is obtained based on Ajm * Kn-jm * in the convoluted part of the equation (26-5). 03-05-2019 28 [0091] Here, the proof of equation (26-5) is performed. Let the convolution part of equation (26-5) be I in equation (27). [0092] By applying the Fourier transform to this equation [Equation 27], the following equation [Equation 28] is obtained. [0093] In this equation [δ], δkl is the Kronecker's delta. Further, K lm # * is an inverse transformation of F as shown by [Equation 25], and substituting Eq. [Equation 25] into Eq. [28] yields Eq. [0094] As a result, the equation (26-5) of [Equation 26] becomes the following equation [Equation 30]. [0095] This equation [Equation 30] outputs the time waveform A (nΔt ¦ θ 0) of the sound wave when the wave is taken in the direction of arrival of the sound wave, and very weak noise when the wave is taken outside the direction of arrival of the sound wave. We show that we form directivity that only outputs. Then, the sharpness of the directivity is given by the following equation [Equation 31]. 03-05-2019 29 [0096] As a result, it is possible to obtain the sharpness of the directivity in the parameter Ψ direction by the equations (26-1) and (26-5) of [Equation 26]. Therefore, the structure for obtaining directivity in the embodiment of the present invention can be represented by FIG. 25. The input 1, 2,... M of each microphone is passed through the A / D converter 100, and the delay unit 111 is obtained. Anm * of Equation (26-1) is determined by Fourier expansion along the circumferential direction of the microphone ring by the device 112 through Eq. (26), and input to the convolution 113 for each mode 1, 2,. The right side of 5) is determined, and the left side (Ψ direction beam input) of equation (26-5) is input by multiplier 114 and the whole is added to obtain the output B n by D / A converter 115. is there. As a result, equation (26-5) is obtained. [0097] Next, as a specific example, consider the case where the microphone unit arrangement is arranged on the spherical surface as in FIG. 6 as shown in FIG. 26A, and sound source estimation independent of the sound wave frequency based on the output from each microphone unit Describe the method. In this case, first, a model is considered in which an infinite number of microphone units are uniformly arranged on a spherical surface. FIG. 26 (b) shows the space mark used in the analysis, and the direction vector is an angle 表示 between the polar coordinate display γθ and the z axis. Assuming that the sound field can be described by superposition of plane waves, the microphone output on the spherical surface at this time becomes the following equation 32 by Fourier integration. [0098] Focusing only on plane waves arriving from a specific direction from this output, the following equation is obtained. [0099] The spherical function expansion of the following equation is performed on this data. 03-05-2019 30 [0100] Among the coefficients α mn (measurement data) of this sphere function expansion, the expansion coefficients in the case where the arrival direction of the sound wave is Ψ 0 = 0, θ 0 = 0 and the sound wave size A (Ψ 0 θ 0) = 1 are When mn, α0, mn = in (2n + 1) jn (ka), (m = 0) or 0, (m> 0). [0101] On the other hand, βmn is determined as the following equation [35] as reference data. [0102] When this equation [Equation 35] is replaced by the equations α0 and mn, the reference data β mn becomes the following equation [Equation 36]. [0103] Then, assuming that the ratio between the measurement data α mn and the reference data β m n is γ m n, the following equation 37 is obtained. [0104] Assuming that the final sound source search result is F (θΨ), this result can be obtained by the series operation of a square sphere function by the following equation [Equation 38]. [0105] In practice, substituting the equation [Equation 37], the result can indicate the sound source direction by the delta function of the delay as follows. F (.theta..zeta.) = A (.theta.0 .noteq.0) .delta. (.Theta .-. Theta.0, .zeta .-. Noteq.0) Thus, in the case of a sphere as well as in the circular arrangement, the output result does not depend on the radius of the sphere or the wavelength of the sound wave. [0106] 03-05-2019 31 As described above, according to the present invention, the following effects can be obtained. Each output of a plurality of microphone units regularly arranged in an arbitrary plane is processed using finite space coordinates based on the regularity in the plane to obtain directivity, and the frequency dependence of the sound wave is obtained. You can get strong directivity. [0107] Further, the output of the microphone unit predicts the data of the microphone unit over the area outside the finite area based on the outputs of the plurality of microphone units arranged in the finite area, and the predicted data and the measured data By adding and outputting, it is possible to obtain the same effect as described above by the simplified configuration. [0108] Furthermore, by comparing each output data of the microphone unit by the plane wave assumed to arrive only from the reference direction with each output data of the microphone unit actually measured, the above processing can be performed as the above processing. By expanding the change of the phase difference generated at each output of the microphone unit into a function sequence having orthogonality in the above-mentioned finite space coordinates, a certainty and sharp directivity can be obtained. [0109] The direction of arrival of the sound wave can be detected by changing the direction of directivity obtained. [0110] In addition, the output data of the microphone unit by the plane wave assumed to come only from the reference direction is expanded into the orthogonal function in the space where the microphone unit is arranged, and the output data of the microphone unit is orthogonal in the space where the microphone unit is arranged The comparison with the value developed in is performed in the time domain by the convolution operation to obtain the time waveform of the sound wave, and by obtaining the directivity, the measurement time can be shortened and the measurement in real time becomes possible. You can listen to the measurement results with your ear. 03-05-2019 32

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