JP6154777B2 - High-speed convolution approximation device, high-speed convolution approximation method, program - Google Patents

Description

  The present invention relates to a high-speed convolution approximation apparatus, a high-speed convolution approximation method, and a program that execute a convolution operation between a digital signal and an FIR (finite impulse response) filter at approximately high speed.

  High-speed convolution technology that performs a convolution operation between a digital signal and a finite-length impulse response filter (FIR filter) at high speed is useful for efficiently realizing signal processing that requires a large-scale convolution operation. is there. As an example of signal processing that requires a large-scale convolution operation, there is a case where an indoor transfer characteristic is given to an acoustic signal. The convolution operation can be realized based on, for example, the overlap-save method disclosed in Non-Patent Document 1.

  Hereinafter, the high-speed convolution approximation device 9 of Non-Patent Document 1 will be described with reference to FIG. FIG. 1 is a block diagram showing the configuration of the high-speed convolution approximation device 9 of Non-Patent Document 1. As shown in FIG. 1, a high-speed convolution approximation device 9 of Non-Patent Document 1 includes an impulse response frequency characteristic holding unit 101, an input signal frequency characteristic holding unit 102, a combined signal frequency characteristic generating unit 103, and a combined signal array. An inverse conversion unit 104 and a windowing superimposing unit 105 are included.

  The impulse response frequency characteristic holding unit 101 is a (fast) discrete Fourier transform into an array obtained by combining zero arrays so that the overall length becomes 2L in the second half of the array h of filter impulse responses of finite length L or less. 2L coefficients obtained by applying (FFT or DFT) are held (step S101, hereinafter, “step” is omitted as appropriate). The input signal frequency characteristic holding unit 102 holds 2L coefficients obtained by performing discrete frequency conversion on the array accumulated retroactively to the past 2L points of the input signal x (S102). Next, the synthesized signal frequency characteristic generation unit 103 performs discrete Fourier transform of an array obtained by combining the zero array so that the overall length becomes 2L in the second half of the array h of filter impulse responses having a finite length L or less. And 2L coefficients corresponding to discrete frequency conversion of the array of input signals x accumulated retroactively in the past 2L points, and multiplied by 2L for each discrete frequency. A conversion coefficient is generated (S103). The composite signal array inverse transform unit 104 performs inverse discrete frequency transform on the composite signal frequency transform coefficient generated by the composite signal frequency characteristic generation unit 103 by, for example, inverse (fast) discrete Fourier transform (IFFT, IDFT) (S104). ). The windowing superimposing unit 105 multiplies the 2L-point composite signal array obtained from the composite signal array inverse transform unit 104 by a window function of 2L points that multiplies the first half L point by zero and the second half L point by 1 to obtain the second half L A composite signal of points is obtained and combined with the latter half L of the array of composite signals obtained in the same manner for the input signal of the past L points (S105). By executing step S105, an output signal y is obtained.

  Here, the L point of the array of 2L synthesized signals is cut out like the windowing superimposing unit 105 in FIG. 1 (Non-Patent Document 1), combined with the signal of one step past (L sample past), and output. When obtaining a signal, when non-linear signal processing such as noise suppression is performed on the array of the synthesized signal frequency characteristics, discontinuity occurs at the joint of the output signal for each L sample, and if the signal is an audio signal, abnormal noise Cause the occurrence of

  For this reason, in Patent Document 1, processing steps are executed at L / 2 sample intervals instead of L sample intervals. Hereinafter, with reference to FIG. 2, the high-speed convolution approximation apparatus 8 of Patent Document 1 will be described. FIG. 2 is a block diagram showing the configuration of the high-speed convolution approximation device 8 of Patent Document 1. As shown in FIG. 2, the high-speed convolution approximation device 8 of Patent Document 1 has an impulse response frequency characteristic holding unit 101 and an input signal frequency characteristic holding unit 102 as the same configuration requirements as the high-speed convolution approximation device 9 of FIG. And a synthesized signal frequency characteristic generation unit 103. The high-speed convolution approximation device 8 of Patent Document 1 includes, as configuration requirements not included in the high-speed convolution approximation device 9 of FIG. 1, an odd component imaginary part extraction unit 107, an addition unit 110, a signal processing unit 106, a signal A processing array inverse transform unit 108 and a Hanning windowing overlap unit 109 are included.

  The impulse response frequency characteristic holding unit 101, the input signal frequency characteristic holding unit 102, and the combined signal frequency characteristic generation unit 103 perform the same operations (S101 to S103) as described above.

  The odd-numbered component imaginary part extraction unit 107 corresponds to the odd-numbered discrete frequency in the array of the synthesized signal frequency conversion coefficients, with the lowest discrete frequency in the array of the synthesized signal frequency conversion coefficients as the first coefficient of the even-numbered array. A predetermined array is extracted as an odd-numbered component imaginary number array such that the imaginary part of the result obtained by performing the inverse discrete frequency conversion on the array including the coefficients to be equal to the result obtained by performing the inverse discrete frequency conversion on the predetermined array (S107). The adding unit 110 adds an odd-numbered component imaginary number array and an array of even-numbered components element by element (S110). The signal processing unit 106 performs signal processing on the added array as necessary (S106). The signal processing unit 106 is configured to perform signal processing as necessary, and can be omitted as appropriate. In FIG. 2, the signal processing unit 106 is indicated by a dotted line to indicate that it can be omitted as appropriate. The signal processing array inverse transform unit 108 performs inverse discrete frequency transform on the added array or an array obtained by performing predetermined signal processing on the added array to obtain a time domain signal array (S108). The Hanning window overlap superimposing unit 109 applies a Hanning window having a shape as shown in FIG. 8 to the acquired signal arrangement in the time domain, and superimposes the signal arrangement in the past by one step (L / 2 samples) (S109). .

  1 converts the 2L point frequency domain array into a 2L point time domain array, whereas the signal processing array inverse transform unit 108 shown in FIG. The frequency domain array of points is converted to an L point time domain array. In addition, in order to alleviate the discontinuity at both ends due to signal processing, the high-speed convolution approximation device 8 of Patent Document 1 is configured to include a Hanning windowing overlap unit 109. As described above, the Hanning window overlap superimposing unit 109 multiplies the Hanning window having the shape shown in FIG. 8 by the signal converted into the L-point time domain, and smoothly performs one step (L / 2 samples) in the past. Superimposes the signal and outputs the signal.

  The high-speed convolution approximation device 8 of FIG. 2 converts the 2L point array of the synthesized signal frequency characteristic into an L point array in order to match the signal processing array inverse transform unit 108 that transforms the L point array. For the purpose, an odd component imaginary part extraction unit 107 is included.

JP 2005-63137 A

J. J. Shynk, "Frequency-domain and multirate adaptive filtering", Signal Processing Magazine, IEEE, Volume: 9, Issue: 1, pp.14-37 (Date of Publication: Jan. 1992)

  However, in the configuration shown in FIG. 2, due to the discontinuity at both ends of the signal array, signal processing is performed on the array with low frequency resolution, which may cause a decrease in signal processing performance. Accordingly, an object of the present invention is to provide a high-speed convolution approximation device that can increase the frequency resolution of a signal used for signal processing.

  The high-speed convolution approximation device of the present invention includes a composite signal frequency characteristic generation unit, an odd component imaginary part extraction unit, an even component windowing correction unit, an addition unit, a signal processing array inverse conversion unit, and a square root Hanning windowing. And a superimposing unit.

  The synthesized signal frequency characteristic generator generates 2L corresponding to the discrete Fourier transform of the array obtained by combining the zero array so that the length becomes 2L as a whole in the second half of the array h of filter impulse responses having a finite length L or less. 2L coefficients corresponding to the discrete frequency transform of the array of the input signal x accumulated retroactively in the past 2L points are multiplied for each discrete frequency to generate 2L synthesized signal frequency transform coefficients. To do. The odd-numbered component imaginary part extraction unit corresponds to the odd-numbered discrete frequency in the array of the synthesized signal frequency conversion coefficients, with the lowest discrete frequency in the array of the synthesized signal frequency conversion coefficients as the first coefficient of the even-numbered array. A predetermined array is extracted as an odd-numbered component imaginary number array so that the imaginary part of the result of inverse discrete frequency conversion of the array of coefficients is equal to the result of inverse discrete frequency conversion of the predetermined array. The even component windowing correction unit applies a square root Hanning window consisting of a sine function with a half cycle L in the time domain to an array consisting of coefficients corresponding to even-numbered discrete frequencies in the array consisting of synthesized signal frequency conversion coefficients. A frequency domain process equivalent to the case is executed to obtain an even component windowed correction array. The adder adds the odd component imaginary number array and the even component windowed correction array. The signal processing array inverse conversion unit performs inverse discrete frequency conversion on the added array or an array obtained by performing predetermined signal processing on the added array to obtain a time domain signal array. The square root Hanning window overlap superimposing unit applies a square root Hanning window to the acquired signal arrangement in the time domain and superimposes it on the past signal arrangement.

  According to the high-speed convolution approximation apparatus of the present invention, the frequency resolution of a signal used for signal processing can be increased.

The block diagram which shows the structure of the high-speed convolution approximation apparatus of a nonpatent literature 1. FIG. The block diagram which shows the structure of the high-speed convolution approximation apparatus of patent document 1. FIG. 1 is a block diagram illustrating a configuration of a high-speed convolution approximation device according to a first embodiment. 5 is a flowchart illustrating the operation of the high-speed convolution approximation apparatus according to the first embodiment. The figure explaining the operation | movement which decomposes | disassembles the arrangement | sequence of a synthetic | combination signal frequency characteristic into even number and odd number, converts it into a time domain, and acquires the coupling | bonding arrangement | sequence of the output influenced by cyclic convolution, and the output by linear convolution. The figure explaining the operation | movement which approximates the output by a linear convolution by the even-numbered signal sequence and the odd-numbered signal sequence with a sine window. The figure explaining the operation | movement which approximates the output by linear convolution with a sine window. The figure which illustrates a Hanning window function. The figure which illustrates a square root Hanning window function.

  Assuming that Y (0),..., Y (2L-1) is an array of synthesized frequency characteristics composed of 2L elements generated by the synthesized signal frequency characteristics generating unit 103 in FIG. , When the array of this characteristic is transformed into the time domain, the output yc (0), ..., yc (L-1) affected by the L cyclic convolutions and the output yl by the L linear convolutions A combined sequence of (0), ..., yl (L-1) is obtained. Here, the desired signal is only the output yl (0), ..., yl (L-1) by linear convolution, and the output yc (0), ..., yc affected by cyclic convolution (L-1) is not necessary for obtaining the output signal y.

The output yl (k), k = 0, ..., L-1 by linear convolution is the odd-numbered component of the composite frequency characteristic array Y (0), ..., Y (2L-1). The signal array a (k), k = 0, ..., L-1 and Y (0), ..., Y (2L-1) even numbers obtained by inverse discrete frequency conversion as zero Is a sum of signal array b (k), k = 0, ..., L-1 obtained by inverse discrete frequency transform with zero component
yl (k) = a (k) + b (k) (Formula 1)
It can be expressed as.

In order to obtain an arrangement of components resulting from linear convolution in the frequency domain according to Equation 1, it is first necessary to obtain a series of L points obtained by frequency-transforming each of the aforementioned a (k) and b (k). As shown in FIG. 6, the arrangement of components in the frequency domain of a (k) is directly arranged as an even-numbered L-point arrangement Y (0), Y (2) ..., Y (2L-2). Can be obtained. On the other hand, the arrangement of components in the frequency domain of b (k) cannot be obtained directly from the arrangement of odd-numbered L points Y (1), Y (3) ..., Y (2L-1). In the configuration of FIG. 2, the odd-component imaginary part extraction unit 107 obtains a frequency domain array of b (k) with a square root Hanning window sw (k) called sw (k) b (k) in the time domain. . That is, in the configuration of FIG.
yl '(k) = a (k) + sw (k) b (k) (Formula 2)
Is approximated in the frequency domain. If Equation 2 is further rewritten,
yl '(k) = a (k) + sw (k) b (k)
= [a (k) + b (k)] + [sw (k) -1] b (k)
= yl (k) + [sw (k) -1] b (k) ... (Formula 3)
It becomes. That is, the estimated value yl ′ (k) is expressed as the sum of yl (k) and its approximation error (sw (k) −1) b (k). Therefore, in the configuration of FIG. 2, the array of linear convolution outputs yl (k) in the time domain is approximately calculated in the frequency domain.

  Normally, when nonlinear signal processing such as noise suppression is performed in the frequency domain, first, an array of L points is extracted from the time signal to be processed, and discontinuities at both ends thereof are eliminated, as shown in FIG. The frequency conversion is executed after the signal is multiplied by the square root Hanning window. Then, after the signal processing, the signal is returned to the time signal array by inverse frequency conversion, and then multiplied by the square root Hanning window, and the signal is superimposed while canceling the discontinuity due to the output distortion of the signal processing. By multiplying the square root Hanning window twice before and after the processing, the whole is multiplied by the Hanning window having the property of complete reconstruction, and when no signal processing is performed, The input signal and the output signal completely match.

  However, in the configuration shown in FIG. 2, the signal input to the signal processing unit 106 is equivalent to a frequency domain signal array obtained by cutting out the array of L points from the output signal of the linear convolution even though it is an approximation. To do. In other words, the signal processing is performed on the signal array obtained by multiplying the output signal of the linear convolution by the L-point square window and converting the frequency. The frequency conversion result of the signal array cut out by the rectangular window generally has a low frequency resolution due to the discontinuity at both ends of the signal array. For this reason, signal processing is performed on an array having a low frequency resolution, causing a reduction in signal processing performance.

  As described above, an object of the present invention is to improve the frequency resolution of the signal given to the signal processing unit 106 in the configuration of FIG. 2 and improve the performance.

  Hereinafter, embodiments of the present invention will be described in detail. In addition, the same number is attached | subjected to the structure part which has the same function, and duplication description is abbreviate | omitted.

  Hereinafter, the high-speed convolution approximation apparatus 1 according to the first embodiment of the present invention will be described with reference to FIGS. FIG. 3 is a block diagram illustrating a configuration of the high-speed convolution approximation apparatus 1 according to the present embodiment. FIG. 4 is a flowchart showing the operation of the high-speed convolution approximation apparatus 1 of the present embodiment. As shown in FIG. 3, the high-speed convolution approximation device 1 of this embodiment is the same as the high-speed convolution approximation device 8 of FIG. 2, and an impulse response frequency characteristic holding unit 101, an input signal frequency characteristic holding unit 102, and a synthesis A signal frequency characteristic generation unit 103, an odd component imaginary part extraction unit 107, a signal processing unit 106, and a signal processing array inverse conversion unit 108 are included. Further, the high-speed convolution approximation device 1 of the present embodiment includes an even component windowing correction unit 111 that is not included in the high-speed convolution approximation device 8 of FIG. Further, the high-speed convolution approximation device 1 of this embodiment includes a square root Hanning windowing superimposing unit 112 instead of the Hanning windowing superimposing unit 109 of the high-speed convolution approximation device 8 of FIG. Instead of the addition unit 110 of the approximation device 8, the addition unit 113 is included.

  The impulse response frequency characteristic holding unit 101, the input signal frequency characteristic holding unit 102, the combined signal frequency characteristic generation unit 103, and the odd component imaginary part extraction unit 107 of the high-speed convolution approximation apparatus 1 of the present embodiment are the same as the above-described steps S101 and S102. , S103, and S107 are executed in the same manner as described above. Next, the even component windowing correction unit 111 sets a square root Hanning window consisting of a sine function having a half cycle of L to an array consisting of coefficients corresponding to even-numbered discrete frequencies in the array consisting of synthesized signal frequency conversion coefficients. A frequency domain process equivalent to that applied in the domain is executed to obtain an even component windowed correction array (S111). The adder 113 adds the odd component imaginary number array and the even component window correction array (S113). Hereinafter, the signal processing unit 106 and the signal processing array inverse transformation unit 108 of the high-speed convolution approximation apparatus 1 according to the present embodiment execute the above-described steps S106 (if necessary) and S108. The square root Hanning window overlap superimposing unit 112 performs a square root Hanning window on the acquired signal arrangement in the time domain and superimposes it on the past signal arrangement (S112).

  The high-speed convolution approximation device 8 of FIG. 2 approximates the frequency conversion array when the linear convolution output yl (k) is cut out by applying a rectangular window as shown in FIG. As shown in FIG. 7, the example high-speed convolution approximation device 1 has a configuration that approximates the frequency array of sw (k) yl (k) cut out by applying a square root Hanning window.

  As for the array of odd-numbered elements Y (1), Y (3),..., Y (2L-1), as in FIG. In addition, a value corresponding to frequency conversion of sw (k) b (k) to which the square root Hanning window is applied is obtained. On the other hand, for even-numbered element arrays Y (0), Y (2), ..., Y (2L-2), even-numbered component windowing correction that applies a square root Hanning window approximately in the frequency domain By newly introducing the unit 111, a value corresponding to the frequency conversion of sw ′ (k) a (k) to which the approximation sw ′ (k) of the square root Hanning window is applied is obtained. The adder 13 adds the arrays output from the even component windowing correction unit 111 and the odd component imaginary part extraction unit 107, so that the output sw (k) yl (k) of the linear convolution subjected to the square root Hanning window. The approximate value of the frequency conversion can be obtained, and a signal array with improved frequency resolution can be input to the signal processing unit 106.

  The time domain signal array obtained by the signal processing array inverse transform unit 108 is subjected to a square root Hanning window in order to match the input of a signal that has been subjected to the square root Hanning window before the signal processing in advance. The signal is input to the square root Hanning windowing superimposing unit 112 which is superimposed on the signal arrangement of the step, and an output signal y is obtained.

<Even-numbered component window correction unit 111>
Hereinafter, a specific method of realizing the even component window correction unit 111 will be described. For example, the even component windowing correction unit 111 temporarily converts the even-numbered element array Y (0), Y (2),..., Y (2L-2) into a time signal by inverse discrete frequency conversion of the L point. Then, after applying the square root Hanning window sw (k), the signal converted into the frequency domain by discrete frequency conversion can be obtained again as a desired signal array. However, if this procedure is followed, an increase in the amount of calculation is inevitable. For this reason, it is considered that the even-numbered component window correction unit 111 is configured to directly perform equivalent processing in the frequency domain. Strictly equivalent processing is performed by the even component windowing correction unit 111. The signal array formed by performing discrete frequency conversion on the square root Hanning window sw (k) and the array Y (0) including coefficients corresponding to the even-numbered discrete frequencies. , Y (2), ..., Y (2L-2) may be executed. However, in this case as well, the amount of computation required for cyclic convolution is still large. Therefore, in this embodiment, the even component window correction unit 111 uses only K elements in descending order of the elements of the signal array formed by performing discrete frequency conversion on the square root Hanning window sw (k). Then, cyclic convolution with an array of coefficients corresponding to even-numbered discrete frequencies is executed (S111). It is preferable that K is an integer satisfying K <L, and K is about 1/10 of L. As described above, the high-speed convolution approximation apparatus 1 according to the present embodiment is configured so that the even component windowing correction unit 111 performs cyclic convolution only on K elements, thereby suppressing an increase in the amount of calculation. A high approximation of can be realized.

<Input Signal Frequency Characteristic Holding Unit 102>
A specific method for realizing the input signal frequency characteristic holding unit 102 will be described below. For example, the input signal frequency characteristic holding unit 102 may directly perform discrete frequency conversion on the 2L-point time domain reference signal array.

  Further, the input signal frequency characteristic holding unit 102 divides the 2L-point time domain reference signal array into two parts, the first half L point and the second half L point, and is configured as the sum of the respective elements of the two points. The discrete frequency transform is performed to obtain an even-numbered frequency domain array, and the difference between each element divided into the first half L point and the second half L point is shifted 0.5 points of the discrete frequency. After multiplying the modulation window as described above, an odd-numbered frequency domain array may be obtained by performing discrete frequency conversion at point L.

  The high-speed convolution approximation apparatus 1 according to the present embodiment performs linear convolution approximately at high speed in the frequency domain, and is closely coupled to a non-linear signal processing unit in the frequency domain following the latter stage, and further includes a signal in the rear stage. The processing unit 106 can be given a signal with high frequency resolution. As a result, the frequency resolution of the signal applied to the signal processing unit 106 can be increased, and the overall performance can be improved.

<Points of invention>
The high-speed convolution approximation apparatus of the present invention, when realizing linear convolution in the frequency domain, does not use an approximation target as a frequency signal array of linear convolution output cut out by a rectangular window, but by a square root Hanning window. By adopting a frequency domain signal array of the extracted linear convolution output, a configuration that maintains the performance of the signal processing unit high is realized following the subsequent stage.

  In order to approximate the frequency domain signal array of the linear convolution output clipped by the square root Hanning window, the time signal array applying the square root Hanning window to the odd-numbered array of the synthesized signal frequency characteristics without performing inverse frequency transform An odd component imaginary part extraction unit 107 that obtains a frequency transform array and a processing that is approximately equivalent to performing a square root Hanning window in the time domain without performing inverse frequency transform on the even array of the synthesized signal frequency characteristics. By adding the output of the odd-numbered component imaginary part extraction unit 107 and the output of the even-numbered component windowing correction unit 111, the frequency resolution is improved by the square root Hanning window as a whole. It was possible to generate a frequency conversion array.

  The various processes described above are not only executed in time series according to the description, but may also be executed in parallel or individually as required by the processing capability of the apparatus that executes the processes. Needless to say, other modifications are possible without departing from the spirit of the present invention.

  Further, when the above-described configuration is realized by a computer, processing contents of functions that each device should have are described by a program. The processing functions are realized on the computer by executing the program on the computer.

  The program describing the processing contents can be recorded on a computer-readable recording medium. As the computer-readable recording medium, for example, any recording medium such as a magnetic recording device, an optical disk, a magneto-optical recording medium, and a semiconductor memory may be used.

  The program is distributed by selling, transferring, or lending a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of the server computer and transferring the program from the server computer to another computer via a network.

  A computer that executes such a program first stores, for example, a program recorded on a portable recording medium or a program transferred from a server computer in its own storage device. When executing the process, the computer reads a program stored in its own recording medium and executes a process according to the read program. As another execution form of the program, the computer may directly read the program from a portable recording medium and execute processing according to the program, and the program is transferred from the server computer to the computer. Each time, the processing according to the received program may be executed sequentially. Also, the program is not transferred from the server computer to the computer, and the above-described processing is executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by the execution instruction and result acquisition. It is good. Note that the program in this embodiment includes information that is used for processing by an electronic computer and that conforms to the program (data that is not a direct command to the computer but has a property that defines the processing of the computer).

  In this embodiment, the present apparatus is configured by executing a predetermined program on a computer. However, at least a part of these processing contents may be realized by hardware.

Claims (8)

2L coefficients corresponding to the discrete Fourier transform of the array obtained by combining the zero array so that the length is 2L as a whole in the second half of the array h of filter impulse responses of finite length L or less, and the past 2L points A combined signal frequency characteristic generation unit that generates 2L combined signal frequency conversion coefficients by multiplying each discrete frequency by 2L coefficients corresponding to the discrete frequency conversion of the array of input signals x accumulated retroactively to ,
The lowest discrete frequency in the array of synthesized signal frequency conversion coefficients is set as the first coefficient of the even-numbered array, and the array of coefficients corresponding to odd-numbered discrete frequencies in the array of synthesized signal frequency conversion coefficients is reversed. An odd component imaginary part extraction unit that extracts the predetermined array as an odd component imaginary array such that the imaginary part of the result of discrete frequency conversion and the result of inverse discrete frequency conversion of the predetermined array are equal;
A frequency domain equivalent to the case where a square root Hanning window consisting of a sine function whose half cycle is L is applied in the time domain to an array consisting of coefficients corresponding to even-numbered discrete frequencies in the array consisting of the composite signal frequency transform coefficients. An even component window correction unit that executes processing to obtain an even component window correction array;
An adder that adds the odd component imaginary number array and the even component window correction array;
A signal processing array inverse transform unit that obtains a time-domain signal array by performing inverse discrete frequency conversion on the added array or an array obtained by performing predetermined signal processing on the added array;
Applying the square root Hanning window to the acquired signal arrangement in the time domain, and superimposing a square root Hanning window overlaid unit on a past signal arrangement;
High-speed convolution approximation device. The high-speed convolution approximation device according to claim 1,
The even component window correction unit is
A high-speed convolution approximation apparatus that performs cyclic convolution of a signal array obtained by performing discrete frequency conversion on the square root Hanning window and an array including coefficients corresponding to the even-numbered discrete frequencies. The high-speed convolution approximation device according to claim 1,
Let K be an integer satisfying K <L,
The even component window correction unit is
Cyclic convolution with an array of coefficients corresponding to the even-numbered discrete frequencies using only K elements in descending order of the elements of the signal array formed by performing discrete frequency conversion on the square root Hanning window. A high-speed convolution approximation device. The fast convolution approximation device according to claim 3,
A high-speed convolution approximation device in which K is 1/10 of L. 2L coefficients corresponding to the discrete Fourier transform of the array obtained by combining the zero array so that the length is 2L as a whole in the second half of the array h of filter impulse responses of finite length L or less, and the past 2L points A composite signal frequency characteristic generation step of generating 2L composite signal frequency conversion coefficients by multiplying each discrete frequency by 2L coefficients corresponding to the discrete frequency conversion of the array of input signals x accumulated retroactively to ,
The lowest discrete frequency in the array of synthesized signal frequency conversion coefficients is set as the first coefficient of the even-numbered array, and the array of coefficients corresponding to odd-numbered discrete frequencies in the array of synthesized signal frequency conversion coefficients is reversed. An odd component imaginary part extraction step for extracting the predetermined array as an odd component imaginary number array such that the imaginary part of the result of the discrete frequency conversion is equal to the result of inverse discrete frequency conversion of the predetermined array;
A frequency domain equivalent to the case where a square root Hanning window consisting of a sine function whose half cycle is L is applied in the time domain to an array consisting of coefficients corresponding to even-numbered discrete frequencies in the array consisting of the composite signal frequency transform coefficients. An even component windowing correction step for performing processing to obtain an even component windowing correction array;
An addition step of adding the odd component imaginary number array and the even component window correction array;
A signal processing array inverse transform step for obtaining a time domain signal array by performing an inverse discrete frequency transform on the added array or an array obtained by performing predetermined signal processing on the added array;
Applying the square root Hanning window to the acquired signal arrangement in the time domain and superimposing the square root Hanning window over the past signal arrangement; and
Fast convolution approximation method including The fast convolution approximation method according to claim 5,
The even component windowing correction step comprises:
A high-speed convolution approximation method for performing cyclic convolution between a signal array obtained by performing discrete frequency conversion on the square root Hanning window and an array including coefficients corresponding to the even-numbered discrete frequencies. The fast convolution approximation method according to claim 5,
Let K be an integer satisfying K <L,
The even component windowing correction step comprises:
Cyclic convolution with an array of coefficients corresponding to the even-numbered discrete frequencies using only K elements in descending order of the elements of the signal array formed by performing discrete frequency conversion on the square root Hanning window. A fast convolution approximation method that performs   The program for functioning a computer as a high-speed convolution approximation apparatus in any one of Claim 1 to 4.

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