JP2011196756A - Method, device, and program for performing waveform analysis - Google Patents

Abstract

PROBLEM TO BE SOLVED: To analyze a sound that changes transiently and abruptly.SOLUTION: In an amplitude pulse-train calculation process 101, an analysis period is set centering on a maximum peak point in an analysis object signal to calculate an amplitude pulse train comprising a plurality of amplitude pulses discretely generated within the analysis period wherein a signal waveform within the analysis period among signal waveforms acquired by weighting/adding impulse responses by respective amplitude pulses acts as a signal waveform within the analysis period in the analysis object signal. In a compositing process 102, a composite signal is generated by adding up the respective impulse responses positioned at generation points of the respective amplitude pulses in the amplitude pulse-train and weighted by the respective amplitude pulses. In an output control process 103, the calculation process 101 and the compositing process 102 are repeated with a residual signal used as a new analysis object signal until the level of the residual signal falls within an allowable range, the residual signal found by subtracting the composite signal from the object signal.

Description

  The present invention relates to a technique for performing waveform analysis of signals such as sound, vibration, and wave.

  Conventional general waveform analysis of sound and voice is to model a time waveform to be analyzed as a set of sine waves. One example is CLSM (Clustered Line-Spectrum Modeling). This CLSM is a method of approximating a signal waveform having this amplitude change by superposition of a plurality of sine waves whose frequencies are close to each other when a musical tone composed of a fundamental tone and a harmonic overtone is slowly attenuated like free vibration of a musical tone. It is. That is, the CLSM expresses an envelope that is a change in the amplitude of a waveform by expressing either the fundamental tone or the harmonic overtone as a sum of a plurality of sine waves that are gathered (close to each other) instead of a sine wave having a single frequency. Means. CLSM can analyze and represent the fundamental and overtones of a signal waveform having a slowly changing envelope. Note that CLSM is disclosed in Non-Patent Document 1, for example.

"Signal Analysis and Acoustics" by Mikio Higashiyama, published by Springer Japan, published by Springer Japan, July 9, 2007, p. 229-233

  The above-mentioned CLSM is effective for obtaining a set of sine waves constituting a stationary part in a musical sound waveform or the like. However, many musical sounds always have a transitional and suddenly changing portion before a steady waveform is generated. The portion showing this abrupt change has a very short time, but is an extremely important portion that determines the characteristics of the musical sound. For example, if a sharp rising portion due to keystrokes cannot be analyzed and reproduced, no matter how much the sine wave component of the fundamental tone and harmonics can be analyzed and reproduced, it does not become a piano sound like a piano sound. The same applies to sounds other than musical sounds. As described above, in order to accurately analyze a sound such as a musical sound, it is necessary to analyze not only a stationary portion but also a transient and rapidly changing portion. There was no effective analysis means to analyze the sound that changes rapidly and suddenly.

  The present invention has been made in view of the circumstances described above, and an object of the present invention is to provide a waveform analysis method capable of analyzing a transient and suddenly changing sound such as a rising portion of a musical sound.

The present invention provides an amplitude pulse train that indicates the generation timing and amplitude of each impulse response for approximating the analysis target signal as an impulse response of each band-pass filter as a linear combination of a plurality of impulse responses that are shifted in time from each other. Is a method of calculating
The process of calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the component that has not been approximated in the analysis target signal as a linear combination of a plurality of impulse responses is repeated, and the amplitude pulse train generated in this repetition A waveform analysis method characterized by calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the analysis target signal as a linear combination of a plurality of impulse responses .

  Conventional waveform analysis has mainly modeled signal waveforms as a collection of sine waves (line spectra) obtained by Fourier transform or the like. However, for waveform analysis of sounds characterized by a sudden rise such as piano sounds and percussion instrument sounds, for example, an analysis method that focuses on temporal changes in the sound signal waveform is required instead of the conventional spectrum-based method. Become. Therefore, in the present invention, an impulse response of a band-pass filter including many spectrums (ideally a continuous spectrum) within a certain band, such as an impulse response of an ideal low-pass filter, is prepared, and signals to be analyzed are compared with each other in time. Considering this as a linear combination of a plurality of shifted impulse responses, an amplitude pulse train indicating the generation timing and amplitude of each impulse response is calculated.

  According to the present invention, the analysis target signal is approximated as a superimposition of impulse responses including many spectra within a certain band, so that the conventional waveform for modeling the analysis target signal as a collection of sine waves (line spectrum) It is possible to analyze and express a transient and sudden change portion of the sound that could not be analyzed by the analysis method.

It is a figure which shows the waveform analysis method by one Embodiment of this invention. It is a flowchart which shows the processing content of the specific example of the waveform analysis method. It is a figure which shows the content of the impulse response matrix in the same embodiment. It is a figure which shows the waveform of the analysis object signal in the 1st analysis example of the waveform analysis method by the embodiment. It is a figure which shows the amplitude pulse train obtained in the amplitude pulse calculation process of the 1st time in the analysis example. It is a figure which shows each waveform of the analysis object signal (dashed line) before performing the amplitude pulse calculation process of the 1st time, and the synthesized signal (solid line) obtained by the 1st synthesis process. It is a figure which shows the waveform of the residual signal E obtained in the output control process of the 1st time. FIG. 8 is a diagram showing an outline of the residual signal E with coarser time accuracy than that of FIG. 7. It is a figure which shows the waveform of the residual signal E after repeating an amplitude pulse train calculation process, a synthetic | combination process, and an output control process 20 times. It is a figure which shows the amplitude pulse train obtained by repeating an amplitude pulse train calculation process, a synthetic | combination process, and an output control process 20 times. Is a diagram showing a waveform obtained synthesized signal by convoluting an amplitude pulse train impulse response sample sequence h ₀ shown in FIG. 10. It is a figure which shows the power spectrum of the synthetic | combination signal synthesize | combined using the amplitude pulse sequence which overlap | superposed each amplitude pulse sequence obtained by the amplitude pulse sequence calculation process of 20 times, a synthesis process, and an output control process. It is a figure which shows the power spectrum of a piano sound signal (C4). It is a figure which shows the power spectrum of the synthetic | combination signal synthesize | combined using the sine wave component obtained by giving CLSM to a piano sound signal. It is a figure which shows the power spectrum of the synthetic | combination signal which added the synthetic | combination signal obtained by CLSM, and the synthetic | combination signal obtained by 20 amplitude pulse train calculation processes, a synthetic | combination process, and an output control process in a time domain. It is a figure which shows the power spectrum of the residual signal E after execution of 20 times of amplitude pulse train calculation processes, a synthesis process, and an output control process. It is a figure which shows the waveform of the analysis object signal in the 2nd analysis example of the waveform analysis by the same embodiment. It is a figure which shows the amplitude pulse train obtained in the amplitude pulse train calculation process of the 1st time in the analysis example. It is a figure which shows each waveform of the analysis object signal (dashed line) before performing the amplitude pulse train calculation process of the 1st time, and the synthetic | combination signal (solid line) obtained by the 1st synthesis process. It is a figure which shows the waveform of the residual signal E obtained in the output control process of the 1st time. FIG. 21 is a diagram showing an outline of the residual signal E with coarser time accuracy than that of FIG. 20. It is a figure which shows the waveform of the residual signal E after repeating an amplitude pulse sequence calculation process, a synthetic | combination process, and an output control process 10 times. It is a figure which shows the amplitude pulse train obtained by repeating an amplitude pulse train calculation process, a synthetic | combination process, and an output control process 10 times. It is a diagram showing a waveform obtained synthesized signal by convoluting an amplitude pulses and the impulse response sample sequence h ₀ shown in FIG. 23. It is a figure which shows the power spectrum of the synthetic | combination signal synthesize | combined using the amplitude pulse train which overlap | superposed each amplitude pulse train obtained by 10 times of amplitude pulse train calculation processes. It is a figure which shows the power spectrum of a drum sound signal. It is a figure which shows the power spectrum of the synthetic | combination signal synthesize | combined using the sine wave component obtained by giving CLSM to a drum sound signal. It is a figure which shows the power spectrum of the synthetic | combination signal which added the synthetic | combination signal obtained by CLSM, and the synthetic | combination signal obtained by the amplitude pulse train calculation process of 10 times, a synthetic | combination process, and an output control process in the time domain. It is a figure which shows the power spectrum of the residual signal E after execution of 10 times of amplitude pulse train calculation processes, a synthesis process, and an output control process. It is a figure which shows the waveform of the analysis object signal in the 3rd analysis example of the waveform analysis by the embodiment. It is a figure which shows the amplitude pulse train obtained by the amplitude pulse train calculation process, the synthesis process, and the output control process in the same analysis example.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
<Basic form>
FIG. 1 is a diagram showing a waveform analysis method according to an embodiment of the present invention. In the Fourier transform, sinusoidal waves of various frequencies over a period from time t = −∞ to + ∞ are used as orthogonal bases, and an analysis target signal is approximated as a set of these orthogonal bases. On the other hand, in the waveform analysis method according to the present embodiment, the impulse response of the band pass filter is prepared for approximating the analysis target signal such as sound, vibration, wave, etc. It is approximated as a linear combination of impulse responses. In the waveform analysis method according to the present embodiment, the process of calculating an amplitude pulse sequence indicating the generation timing and amplitude of each impulse response for approximating the component that has not been approximated in the analysis target signal as a linear combination of a plurality of impulse responses is repeated. Then, by superimposing the amplitude pulse trains generated in this repetition, an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the analysis target signal as a linear combination of a plurality of impulse responses is calculated.

  In this example, sinc (x) = sin (πx) / (πx) = sin (πft) / (πft), which is known as the impulse response of the ideal low-pass filter, is used as the impulse response of the bandpass filter. Here, the Fourier transform of sinc (x) is 1 in the section of | x | ≦ 1/2 and 0 in the other sections. Therefore, the filter that convolves sin (πft) / (πft) with the input signal has a gain (expressed as an integer) in the frequency band of −2f to 2f of 1, and a gain in a band other than the frequency other than this frequency band. This is an ideal low-pass filter in which (true number expression) is zero. In this embodiment, in order to obtain the amplitude pulse train used to approximate the analysis target signal as a linear combination of a plurality of impulse responses, the signal within the analysis period of a predetermined time length centered on the maximum peak point among the entire analysis target signal The operation of calculating the amplitude pulse train for approximating the analysis target signal is limited to the waveform. More specifically, the waveform analysis method according to the present embodiment includes an amplitude pulse train calculation process 101, a synthesis process 102, and an output control process 103 shown in FIG. In a preferred embodiment, the present invention is implemented as a program that causes a computer to execute an amplitude pulse train calculation process 101, a synthesis process 102, and an output control process 103. In another preferred embodiment, the present invention is implemented as a waveform analysis apparatus including means for executing an amplitude pulse train calculation process 101, a synthesis process 102, and an output control process 103.

  In FIG. 1, in the first amplitude pulse train calculation processing 101, the components that have not been approximated in the analysis target signal (in this case, the analysis target signal itself because there is no component that has been approximated yet) are aligned around the center. An amplitude pulse train is calculated using a period of a predetermined time length as an analysis period. That is, an amplitude pulse train composed of a plurality of amplitude pulses generated discretely within the analysis period, and a signal waveform obtained by adding a plurality of impulse responses h weighted by the amplitude of each amplitude pulse at the generation timing of each amplitude pulse. Among them, the amplitude pulse train PS1 is calculated so that the signal waveform in the analysis period approximates the signal waveform in the analysis period in the component that has not been approximated in the analysis target signal.

  Next, in the synthesis processing 102, each impulse response h having a maximum peak point at each amplitude pulse generation point in the amplitude pulse train obtained by the amplitude pulse train calculation processing 101 and weighted by the amplitude of each amplitude pulse is obtained. A composite signal is generated by addition.

  Then, in the output control process 103, it is determined whether or not the component of the analysis target signal that has not been approximated, that is, the level of the residual signal obtained by subtracting the synthesized signal from the analysis target signal falls within the allowable range. When the level of the residual signal does not fall within the allowable range, the output control process 103 causes the second amplitude pulse train calculation process 101 and the synthesis process 102 to be executed with the residual signal as a new analysis target signal. The new analysis target signal in this case is an incomplete component that has not been approximated as a linear combination of a plurality of impulse responses h in the original analysis target signal.

  In the second amplitude pulse train calculation processing 101, the amplitude pulse train PS2 is calculated from the analysis target signal (in this case, the first residual signal) in the same manner as the first time. In the second synthesis process 102, a synthesized signal is generated by using the impulse response h and the amplitude pulse train obtained by the second amplitude pulse train calculation process 101. Then, in the output control process 103, it is determined whether or not the level of the residual signal obtained by subtracting the synthesized signal from the analysis target signal (in this case, the first residual signal) falls within the allowable range. If it does not fall within the range, the third amplitude pulse train calculation process 101 and the synthesis process 102 are executed with the residual signal as a new analysis target signal.

  As described above, in the output control process 103, the amplitude pulse train calculation process 101 and the synthesis process 102 are repeatedly executed using the residual signal as an analysis target signal until the level of the residual signal falls within the allowable range, and obtained by this repetition. The amplitude pulse trains PS1, PS2,... Are overlapped to complete an amplitude pulse train that approximates the entire signal to be analyzed before the analysis is started.

<Specific form>
FIG. 2 is a flowchart showing a specific example of the waveform analysis algorithm in the present embodiment. In this flowchart, each process of steps S11 to S13 constitutes the amplitude pulse train calculation process 101 described above. The process in step S21 corresponds to the above-described combining process 102. Each process of steps S31 and S32 constitutes the output control process 103 described above. In a specific example of this waveform analysis algorithm, an impulse response matrix is used in the amplitude pulse train calculation processing 101. Each process of steps S1 to S3 constitutes a matrix generation process 100 for generating this impulse response matrix.

First, the matrix generation process 100 will be described. In this example, a waveform {sin (πft)} / (πft) representing an impulse response of an ideal low-pass filter is used. A sample string h ₀ (n) obtained by up-sampling the waveform {sin (πft)} / (πft) at f = 1.5 kHz at a sampling frequency of 12 kHz (n = −NMAX to + NMAX; NMAX is a sufficiently large integer) Is calculated (step S1). Here, the reason why the impulse response is sampled at the sampling frequency of 12 kHz is that the analysis target signal is sampled at the sampling frequency of 12 kHz and needs to be adjusted to this. Then, an impulse response matrix is created using the impulse response sample sequence h ₀ (n). More specifically, using the impulse response sample sequence h ₀ (n), as shown in FIG. 3A, adjacent samples are shifted in the same time direction by P samples (P = 5 in this example). N (N = 5 in this example) impulse response sample trains h _j (n− (j−1) P) (j = 1 to N) are created (step S2). Next, as shown in FIGS. 3A and 3B, a common time zone T from each of N impulse response sample sequences h _j (n− (j−1) P) (j = 1 to N). M samples (in this example, M = 7) are sampled, the time direction is the row arrangement direction, the impulse response arrangement direction is the column arrangement direction, and each impulse response sample An impulse response matrix R = {r _ij } (i = 1 to M, j = 1 to N) of M rows and N columns (in this example, 7 rows and 5 columns) whose values are matrix elements r _ij is created (step S3 ). More specifically, as shown in FIG. 3A, the observation point 1 that is the start point of the time zone T, and each observation point obtained by dividing the time zone T by M-1 (in this example, observation points 2 to 6) M sample values located at an observation point M (observation point 7 in this example) that is the end point of the time zone T are represented by N impulse response sample sequences h _j (n− (j−1) P) (j = 1 to N) to create an impulse response matrix R = {r _ij } (i = 1 to M, j = 1 to N).

In this example, one impulse response is a waveform that is attenuated in the front-rear direction around the maximum peak point, and that is symmetrical in the front-rear direction with the maximum peak point as the axis of symmetry. A set of impulse responses h _{1 to} h ₅ used for generating the impulse response matrix R = {r _ij } (i = 1 to M, j = 1 to N) is a maximum peak point of the central impulse response h _3. The waveform is symmetrical in the longitudinal direction as the axis of symmetry. And, in this example, the impulse response h ₁ to h _5, as shown in FIG. 3 (a), the maximum peak of the impulse response h ₁ that occurs earliest and largest peak of the impulse response h ₅ occurring most later Is at least inside the common time zone T, the length of the common time zone T is determined.

  In the waveform analysis method according to this example, the waveform analysis is performed using the impulse response matrix R obtained by the matrix generation process 100 described above. Hereinafter, the contents of each process after step S4 will be specifically described using the sound signal of the piano sound (first example) as an analysis target signal, and then an analysis example of the drum sound (second example) will be described. .

First, acquired by the analysis object signal x ₀ be analyzed signal x (step S4). Figure 4 illustrates the waveforms of the analysis object signal x _0. The analysis object signal x ₀ obtains a steady sinusoidal components constituting the audio signal waveform of the piano sound (C4) by CLSM, signals obtained by removing the sinusoidal components from the original piano sound signal, i.e., a sine wave This is the sound signal of the rising section of the piano sound that cannot be expressed by the synthesis of (a sound signal indicating the initial vibration waveform of the string immediately after the hammer hits the string). The sampling frequency of the analysis object signal _{x 0} is 12 kHz.

Next, the amplitude pulse train calculation process 101 will be described. First, the maximum peak point (maximum peak occurrence time) is obtained from the analysis target signal x (step S11). In FIG. 4, the maximum peak (negative peak) obtained by the first execution of step S11 is indicated by a circle. Next, an analysis period is set, and a signal matrix S = {s _i } (i = 1 to M) is acquired from the analysis target signal within the analysis period (step S12). More specifically, an analysis period is defined as a period having the same maximum length as that of the common time zone T, centered on the maximum peak obtained in step S11. Then, the signals to be analyzed that belong to the analysis period are sampled at the same sampling cycle as when the impulse response was sampled in order to obtain the impulse response matrix R (that is, 1/5 downsampling), and M signals. (Sample M = 7 in this example) is acquired and a signal matrix S = {s _i } (i = 1 to M) is created.

Next, the matrix A = {a _i } (i = 1 to N) satisfying the linear equation R · A = S, where the matrix A = {a _i } (i = 1 to N) of N rows and 1 column. An estimation calculation is performed, and an amplitude pulse train is generated using the estimated values of the respective elements of the matrix A = {a _i } (i = 1 to N) of N rows and 1 column (step S13). More specifically, a pseudo inverse matrix R ⁻¹ of an impulse response matrix R = {r _ij } (i = 1 to M, j = 1 to N) is obtained, and this pseudo inverse matrix R ⁻¹ is obtained as a signal matrix S = By multiplying {s _i } (i = 1 to M), a matrix A ′ which is a least square error solution of the matrix A = {a _i } (i = 1 to N) is calculated, and this matrix A ′ = { Amplitude pulse train composed of each amplitude pulse indicated by each element of a ′ _i } (i = 1 to N) is generated.

Next, in the process of step S21 which is the synthesizing process 102, N impulse responses h _j (n−) using the amplitudes a ′ _i (i = 1 to N) of the amplitude pulses of the amplitude pulse train obtained in step S13 as weighting factors. (J-1) Multiply each by P) and add each multiplication result to generate a composite signal.

Next, the output control process 103 will be described. First, the combined signal generated in step S21 is subtracted from the analysis target signal to generate a residual signal E (step S31). Next, the energy | E | ² of the residual signal E is calculated. If the energy | E | ² is smaller than the allowable value LMT, the waveform analysis is terminated. If the energy | E | ² is larger than the allowable value LMT, the residual signal E is calculated. The analysis target signal x is set, and the process returns to step S11 to repeat the processing from step S11 to step S32 (step S32). In the process in which the processes from step S11 to step S32 are repeated, in step S32, the amplitude pulse trains obtained each time step S13 is executed are superimposed on a common time axis, and the original signals to be analyzed are mutually phased. An amplitude pulse train (pulse train indicating the generation timing and amplitude of each impulse response) to be expressed as a linear combination of a plurality of shifted impulse responses is calculated.

  FIG. 5 shows the amplitude pulse train obtained by the first amplitude pulse train calculation process (step S13). In FIG. 5, the amplitude pulse train is shown as a sample train having a sampling frequency of 12 kHz. FIG. 6 shows respective waveforms of the analysis target signal (broken line) before the first amplitude pulse train calculation process (step S13) and the synthesized signal (thick line) obtained by the first synthesis process (step S21). It is shown. FIG. 7 is an enlarged view of a part of the waveform of the residual signal E obtained in the first output control process (step S31). 6 is compared with FIG. 7, it is confirmed that the maximum peak portion (negative peak) of the analysis target signal x (broken line) shown in FIG. 6 is largely removed in the residual signal E shown in FIG. 7. can do. That is, it can be seen that a composite signal (solid line) that accurately approximates the maximum peak (negative peak) near 13 ms of the analysis target signal x (broken line) in FIG. 6 is calculated. FIG. 8 shows the entire residual signal E with a wider display range in the time axis direction than FIG. As shown in FIG. 8, since the energy level of the residual signal E is still high only by executing the amplitude pulse train calculation process, the synthesis process, and the output control process once, the amplitude pulse train calculation process, the synthesis process, and the output are performed 20 times in total. By repeating the control process, most components of the initial vibration waveform of the piano string were removed from the analysis target signal x.

FIG. 9 shows a waveform of the residual signal E after the amplitude pulse train calculation process, the synthesis process, and the output control process are repeated 20 times. FIG. 10 illustrates an amplitude pulse train obtained by repeating the amplitude pulse train calculation process, the synthesis process, and the output control process 20 times (the amplitudes obtained in each of the 20 repetitions of the amplitude pulse train calculation process, the synthesis process, and the output control process). The pulse trains are superimposed on a common time axis). FIG. 11 shows a waveform of a composite signal obtained by convolving the amplitude pulse train and the impulse response sample train h ₀ (n = −NMAX to + NMAX) shown in FIG. Composite signal shown in FIG. 11 is adapted to an approximation better time waveforms of the initial portion of up to about 75ms of analysis object signal x ₀ shown in FIG.

  Next, paying attention to the power spectrum of each signal, the effect of executing the waveform analysis processing according to the present embodiment will be examined. FIG. 12 shows a power spectrum of a synthesized signal (synthesized signal shown in FIG. 11) synthesized by using an amplitude pulse train obtained by superimposing the amplitude pulse trains obtained by 20 times of amplitude pulse train calculation processing, synthesis processing, and output control processing. . FIG. 13 shows the power spectrum of the piano sound signal (C4). FIG. 14 shows a power spectrum of a synthesized signal synthesized using a sine wave component obtained by applying CLSM to a piano sound signal (conventional example). FIG. 15 shows a synthesized signal obtained by adding the synthesized signal obtained by CLSM (FIG. 14) and the synthesized signal obtained by 20 amplitude pulse train calculation processes, the synthesized process, and the output control process (FIG. 12) in the time domain. The power spectrum is shown. FIG. 16 shows the power spectrum of the residual signal E after the 20th amplitude pulse train calculation process, synthesis process, and output control process. Comparing FIG. 13, FIG. 14 and FIG. 15, in addition to CLSM, by executing waveform analysis processing according to the present embodiment (specifically, amplitude pulse train calculation processing, synthesis processing and output control processing over 10 times), It can be seen that the component of the initial vibration waveform of the string is added to the synthesized signal, and the power spectrum (FIG. 15) of the synthesized signal approaches the power spectrum of the C4 piano sound that is the original sound. The power spectrum of the residual signal E (that is, the component that has not been approximated in the analysis target signal) is sufficiently lower than the power spectrum (FIG. 15) of the combined signal (component that has been approximated). I understand that. As described above, according to the present embodiment, it is possible to accurately synthesize an initial vibration waveform of a string that could not be obtained by synthesizing a sine wave.

Next, the result of carrying out the same examination as above for the drum sound (second example) will be shown. Figure 17 shows a second example of the analysis object signal x _0. The analysis object signal x ₀ obtains a sine wave component of the constant part of a sound signal waveform of drum sound by CLSM, signals obtained by removing the sinusoidal components from the original drum sound signals, i.e., expressed in the synthesis of the sine wave This is a sound signal of a rising section of the drum sound that cannot be performed (a sound signal indicating an initial vibration waveform of the striking surface immediately after the stick hits the striking surface of the drum). In FIG. 17, the maximum peak of the analysis target signal x detected at the time of the first execution of step S11 is indicated by a circle.

  FIG. 18 shows the amplitude pulse train obtained by the first amplitude pulse train calculation process (step S13). FIG. 19 shows respective waveforms of the analysis target signal (broken line) before the first amplitude pulse train calculation process (step S13) and the synthesized signal (solid line) obtained by the first synthesis process (step S21). It is shown. FIG. 20 shows the waveform of the residual signal E obtained by the first output control process (step S31). Comparison of FIG. 19 and FIG. 20 confirms that the maximum peak portion (positive peak) of the analysis target signal x (thin line) shown in FIG. 19 is largely removed in the residual signal E shown in FIG. can do. That is, it can be seen that a composite signal (solid line) that accurately approximates the maximum peak (positive peak) near 3 ms of the analysis target signal x (broken line) in FIG. 19 is calculated. FIG. 21 shows the entire residual signal E with a wider display range in the time axis direction than FIG. As shown in FIG. 21, since the energy level of the residual signal E is still high only by executing the amplitude pulse train calculation process, the synthesis process, and the output control process once, the amplitude pulse train calculation process, the synthesis process, and the output are performed a total of 10 times. By repeating the control process, most components of the initial vibration waveform of the striking surface of the drum were removed from the analysis target signal x.

FIG. 22 shows the waveform of the residual signal E after the amplitude pulse train calculation process, the synthesis process, and the output control process are repeated 10 times. FIG. 23 shows an amplitude pulse train obtained by repeating the amplitude pulse train calculation process, the synthesis process, and the output control process 10 times (the amplitude pulse train obtained in each iteration of the 10 amplitude pulse train calculation processes, the synthesis process, and the output control process). Are superimposed on a common time axis). FIG. 24 shows the waveform of the composite signal obtained by convolving the amplitude pulse train and the impulse response sample train h ₀ (n = −NMAX to + NMAX) shown in FIG. The combined signal shown in FIG. 24 is adapted to that accurately approximates the time waveform of the initial portion of up to about 40ms of analysis object signal x ₀ shown in FIG. 17.

  Next, paying attention to the power spectrum of each signal, the effect of executing the waveform analysis processing according to the present embodiment will be examined. FIG. 25 shows a power spectrum of a synthesized signal (synthesized signal shown in FIG. 24) synthesized by using an amplitude pulse train obtained by superimposing the amplitude pulse trains obtained by the 10 amplitude pulse train calculation processes, the synthesis process, and the output control process. . FIG. 26 shows the power spectrum of the drum sound signal. FIG. 27 shows a power spectrum of a synthesized signal synthesized using a sine wave component obtained by applying CLSM to a drum sound signal. FIG. 28 shows a synthesized signal obtained by adding in the time domain the synthesized signal obtained by CLSM (FIG. 27) and the synthesized signal obtained by 10 amplitude pulse train calculation processes, the synthesized process and the output control process (FIG. 25). The power spectrum is shown. FIG. 29 shows the power spectrum of the residual signal E after the 10th amplitude pulse train calculation processing, synthesis processing, and output control processing. When comparing FIG. 26, FIG. 27 and FIG. 28, in addition to CLSM, by executing waveform analysis processing according to the present embodiment (specifically, amplitude pulse train calculation processing, synthesis processing and output control processing over 10 times) It can be seen that the component of the initial vibration waveform of the drum is added to the composite signal, and the power spectrum (FIG. 28) of the composite signal approaches the power spectrum (FIG. 26) of the drum sound that is the original sound. The power spectrum (FIG. 29) of the residual signal E (that is, the component that has not been approximated in the analysis target signal) is sufficiently lower than the power spectrum (FIG. 28) of the synthesized signal (component that has been approximated). You can see that As described above, according to the present embodiment, the initial vibration waveform of the drum that could not be obtained by the synthesis of the sine wave can be synthesized with high accuracy.

Next, the example which utilized this embodiment for the analysis of the reflected sound of a wall is shown. Figure 30 shows a waveform of the reflected sound signals of the wall is a third example of the analysis object signal x _0. FIG. 31 shows an amplitude pulse train obtained by executing waveform analysis processing (specifically, amplitude pulse train calculation processing, synthesis processing, and output control processing) once for this analysis target signal. The amplitude pulse train shown in FIG. 31 represents the intensity (including positive and negative signs representing in-phase or opposite phase) of a mirror image sound source or a virtual sound source that forms a reflected wave. Here, by considering the reflected sound arriving at time t = 0 as reflected sound from the virtual sound source generated on the reflecting wall surface, the reflected sound arriving later than time t = 0 is the virtual sound existing inside the reflecting wall. It can be understood as representing reflected sound from a sound source. Therefore, the reflected sound from the virtual sound source which is considered to exist farther in the reflection wall as the reflected sound arrives later is shown. As described above, according to the present embodiment, the waveform analysis processing (specifically, the processing of steps S11 to S32 in FIG. 2) is performed on the reflected sound from the wall observed at the sound receiving point, so that FIG. It can be understood that the reflected sound as shown is a synthesis of reflected waves by the five virtual sound sources shown in FIG.

  As described above, according to the present embodiment, the waveform analysis process (specifically, the amplitude pulse train calculation process, the synthesis process, and the output control process) is repeatedly performed, so that the sine wave synthesis model can be analyzed. The time waveform and spectrum of the initial vibration part of the instrument sound waveform that could not be analyzed can be analyzed. Further, according to the present embodiment, the amplitude pulse generation timing is set in the amplitude pulse train calculation process (steps S11 to S13) by setting the analysis period according to the maximum peak point of the component that has not been approximated in the analysis target signal. Since the necessary degree of freedom is secured and the analysis period is determined, the amplitude pulse train is calculated using a plurality of impulse responses each having a maximum peak point at each fixed position in the analysis period. An analysis result with sufficient accuracy can be obtained with a small amount of calculation. The waveform analysis method according to the present embodiment is effective not only for analysis and synthesis of natural sound but also for analysis of reflected sound from the wall surface, and is also effective as a means for modeling acoustic space. Therefore, an effect can be expected for the room acoustic design and the acoustic material evaluation.

<Other embodiments>
Although one embodiment of the present invention has been described above, various other embodiments are conceivable for the present invention. For example:

(1) For example, a waveform analysis program is prepared so that impulse responses of a plurality of types of bandpass filters having different passbands are prepared, a desired impulse response is selected from the impulse responses, and the waveform analysis method according to the above embodiment can be executed. It may be configured.

(2) The waveform analysis program may be configured so that the number of rows M of the impulse response matrix and the length of the analysis period can be arbitrarily selected.

(3) The rows and columns of the impulse response matrix in the above embodiment may be interchanged. More specifically, in the matrix generation process, N impulse responses are arranged with a time shift, M samples belonging to a common time zone are sampled from each impulse response, and the time direction is set as the column arrangement direction. Then, an impulse response matrix of N rows and M columns is generated with the arrangement direction of the impulse responses as the row arrangement direction and the sample values of the impulse responses as matrix elements. In the amplitude pulse train calculation process, the length of the analysis period is set as the length of the common time zone, and the multiplication result of the impulse response matrix of N rows and M columns is within the analysis period of the component that has not been approximated in the analysis target signal. A matrix of 1 row and N columns, which is M samples, is calculated, and an amplitude pulse sequence of M samples is generated using each amplitude pulse indicated by each element of the matrix of 1 row and N columns. In this aspect, the same effect as the above embodiment can be obtained.

(4) In the above-described embodiment, a period of a predetermined time length is set as the analysis period, with the maximum peak point of the component that has not been approximated in the analysis target signal being centered. However, this is an example, and the length of the period before the maximum peak point in the analysis period may be different from the length of the period after the maximum peak point.

100: Matrix generation processing, 101: Amplitude pulse train generation processing, 102: Synthesis processing, 103: Output control processing.

Claims (8)

A method of calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the signal to be analyzed as an impulse response of each bandpass filter as a linear combination of a plurality of impulse responses shifted in time from each other Because
The process of calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the component that has not been approximated in the analysis target signal as a linear combination of a plurality of impulse responses is repeated, and the amplitude pulse train generated in this repetition A waveform analysis method characterized by calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the signal to be analyzed as a linear combination of a plurality of impulse responses by superimposing them. A method of calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the signal to be analyzed as an impulse response of each bandpass filter as a linear combination of a plurality of impulse responses shifted in time from each other Because
A period of a predetermined time length including the maximum peak point appearing in the component that has not been approximated in the signal to be analyzed is an analysis period, and the component that has not been approximated in the signal to be analyzed within the analysis period is a plurality of primary impulse responses. By repeating the process of calculating the amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximation as a combination, and superimposing the amplitude pulse train generated in this repetition, the signal to be analyzed is subjected to a plurality of primary impulse responses. A waveform analysis method characterized by calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximation as a combination.   In the process of calculating an amplitude pulse train for approximating an incomplete component in the analysis target signal in the analysis period as a linear combination of a plurality of impulse responses, a maximum peak point is set at each fixed position in the analysis period. The waveform analysis method according to claim 2, wherein an amplitude pulse train is calculated by using a plurality of impulse responses each having the following. A period having a predetermined time length including the maximum peak point in the analysis target signal is set as an analysis period, and an amplitude pulse train composed of a plurality of amplitude pulses discretely generated in the analysis period, each of the band pass filters Among the signal waveforms that are impulse responses and are obtained by adding a plurality of impulse responses weighted by the amplitude of each amplitude pulse at the generation timing of each amplitude pulse in the amplitude pulse train, the signal waveform within the analysis period is the signal to be analyzed An amplitude pulse train calculating process for calculating an amplitude pulse train that approximates the signal waveform in the analysis period in
A synthesis process for generating a synthesized signal by adding a plurality of impulse responses weighted by the amplitude of each amplitude pulse at the generation timing of each amplitude pulse in the amplitude pulse string calculated by the amplitude pulse string calculation process;
Until the residual signal level obtained by subtracting the synthesized signal from the analysis target signal falls within an allowable range, the residual signal is used as a new analysis target signal, and the amplitude pulse train calculation process and the synthesis process are repeated, An output control process for superimposing the amplitude pulse trains obtained by the repetition. The N impulse responses are arranged at different times, M samples belonging to a common time zone are sampled from each impulse response, the time direction is the row arrangement direction, and the impulse responses are arranged in columns. And an impulse response matrix of M rows and N columns with each impulse response sample as a matrix element, or a time direction as a column arrangement direction, and an arrangement direction of each impulse response as a row arrangement direction, A matrix generation process for generating an N-by-M impulse response matrix having the samples of each impulse response as matrix elements;
In the amplitude pulse train calculation process, the length of the analysis period is set to the length of the common time zone, and the multiplication result of the impulse response matrix of M rows and N columns or N rows and M columns is obtained in the analysis target signal. An N-row 1-column or 1-row N-column matrix, which is M samples within the analysis period, is calculated, and M is used by using each amplitude pulse indicated by each element of the N-row 1-column or 1-row N-column matrix. The waveform analysis method according to claim 3, wherein the amplitude pulse train including the samples is generated.   The waveform analysis method according to claim 1, wherein the impulse response is an impulse response of an ideal low-pass filter. An apparatus for calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the signal to be analyzed as an impulse response of each band-pass filter as a linear combination of a plurality of impulse responses shifted in time from each other Because
The process of calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the component that has not been approximated in the analysis target signal as a linear combination of a plurality of impulse responses is repeated, and the amplitude pulse train generated in this repetition An amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the signal to be analyzed as a linear combination of a plurality of impulse responses by superimposing the signal to be analyzed is calculated. A process of calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the analysis target signal as an impulse response of each band-pass filter, which is a linear combination of a plurality of impulse responses that are shifted in time from each other Because
The process of calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the component that has not been approximated in the analysis target signal as a linear combination of a plurality of impulse responses is repeated, and the amplitude pulse train generated in this repetition , By causing the computer to execute a process of calculating an amplitude pulse train indicating the generation timing and amplitude of each impulse response for approximating the analysis target signal as a linear combination of a plurality of impulse responses. program.

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