JP6887585B2 - Signal analyzers, signal analysis systems, signal analysis methods, control circuits and programs - Google Patents

Description

The present invention relates to a signal analysis device, a signal analysis system, and a signal analysis method for decomposing a signal to be analyzed into a plurality of non-harmonic signals.

The short-time Fourier transform is generally used in signal analysis that decomposes the signal to be analyzed into a plurality of frequency components. However, the short-time Fourier transform has an uncertainty limit that the product of the frequency decomposition error and the time decomposition error cannot be kept below a certain level. Furthermore, it is known that the anharmonic signal, which is a signal component of a frequency whose period does not match the Fourier transform length, cannot be detected as a single frequency, the spectrum line width is widened, and the frequency resolution is further lowered. Has been done.

To solve such a problem, in the method called generalized harmonic analysis disclosed in Patent Document 1, it is possible to obtain frequency accuracy exceeding the uncertainty limit by extending the discrete-time Fourier transform. In the method disclosed in Patent Document 1, first, the parameters of the non-harmonic signal that minimizes the error with the waveform of the signal to be analyzed are estimated, and thereafter, the non-harmonic with the waveform of the residual error signal is minimized. The signal parameters are being estimated sequentially.

Japanese Patent No. 5590547

However, according to the technique disclosed in Patent Document 1, since the parameters of the anharmonic signals are determined one by one by sequential processing, it is possible to represent the analysis target signal with a small number of anharmonic signals as a whole, which is efficient. There was a problem that it was difficult to determine the combination of parameters.

The present invention has been made in view of the above, and an object of the present invention is to obtain a signal analysis apparatus capable of efficiently determining a combination of parameters capable of representing a signal to be analyzed.

In order to solve the above-mentioned problems and achieve the object, the signal analysis device according to the present invention is a signal analysis device that decomposes a signal to be analyzed into a plurality of non-harmonic signals, and defines a plurality of non-harmonic signals. An evaluation value indicating an error between the parameter candidate selection unit that selects a candidate for a parameter combination, the waveform obtained by the sum of a plurality of nonharmonic signals defined by the selected combination, and the waveform of the signal to be analyzed. It is characterized by including an evaluation unit for calculation and a combination optimization unit for determining a combination of the parameters that define a plurality of the non-harmonic signals representing the analysis target signal based on the evaluation value.

The signal analysis apparatus according to the present invention has an effect that it is possible to efficiently determine a combination of parameters that can represent the signal to be analyzed.

The figure which shows the structure of the signal analysis apparatus which concerns on Embodiment 1 of this invention. A flowchart showing the operation when the signal analyzer shown in FIG. 1 uses the simulated annealing method. The figure which shows the relationship between the cost function and the parameter transition in the parameter space used by the signal analyzer shown in FIG. The figure which shows the structure of the signal analysis system including the signal analysis apparatus shown in FIG. The figure which shows the process of the combinatorial optimization processing of the signal analysis apparatus shown in FIG. The figure which shows the analysis result of the signal analysis apparatus shown in FIG. The figure which shows the time waveform obtained based on the analysis result of the signal analysis apparatus shown in FIG. The figure which shows the structure of the signal analysis system which concerns on Embodiment 2 of this invention. The figure which shows the structure of the signal analysis system which concerns on Embodiment 3 of this invention. The figure which shows the dedicated hardware for realizing the function of the signal analysis apparatus which concerns on Embodiments 1 to 3 of this invention. The figure which shows the structure of the control circuit for realizing the function of the signal analysis apparatus which concerns on Embodiments 1 to 3 of this invention.

Hereinafter, the signal analysis apparatus, the signal analysis system, and the signal analysis method according to the embodiment of the present invention will be described in detail with reference to the drawings. The present invention is not limited to this embodiment.

Embodiment 1.
FIG. 1 is a diagram showing a configuration of a signal analysis device 10 according to a first embodiment of the present invention. The signal analysis device 10 includes a sampling unit 101, a parameter space definition unit 102, a parameter candidate selection unit 103, an evaluation unit 104, and a combinatorial optimization unit 105.

The signal analysis device 10 performs frequency analysis for decomposing the signal to be analyzed into a plurality of anharmonic signals. The sampling unit 101 outputs a signal sequence obtained by sampling the analysis target signal at equal time intervals. Allowing the parameters to be redundant, in general, assuming that the conversion frame length is L and M ≧ 1, any complex signal sequence x (t) sampled at equal time intervals is given by the following equation (1). It is represented by.

Here, assuming that the sampling time interval is Δt, the following mathematical formula (2) holds. Further, K in the mathematical formula (1) is represented by the following mathematical formula (3).

When M = 1, the following mathematical formula (4) holds, and it can be seen that the frame length and the vector length of the angular frequency ω are equal and equivalent to the discrete-time Fourier transform used in the short-time Fourier transform. On the other hand, by setting M> 1, the angular frequency ω is increased and the angular frequency resolution is made finer, which is the generalized harmonic analysis used in the present embodiment.

The parameter space definition unit 102 defines a sparse parameter space by thinning out the parameter space composed of a plurality of non-harmonic signal parameter candidates representing the analysis target signal at the frequency. In the parameter estimation in the generalized harmonic analysis, the basis vectors shown in the following mathematical formula (5) are generally not orthogonal to each other, so that the amount of calculation required to search for the optimum parameter is enormous. Therefore, in the present embodiment, by defining the parameter space by thinning out the frequency, it is possible to reduce the amount of calculation and express the signal to be analyzed with a smaller number of parameters.

The parameter candidate selection unit 103 selects a candidate for a combination of parameters that defines a plurality of non-harmonic signals from the parameter space defined by the parameter space definition unit 102. The parameter candidate selection unit 103 outputs a plurality of selected parameter candidates to the evaluation unit 104. The parameter candidate selection unit 103 selects parameter candidates by a method according to the solution method used for parameter optimization. For example, in the case of the brute force method, the parameter candidate selection unit 103 sequentially selects all combinations and outputs them to the evaluation unit 104. Further, in the case of simulated annealing method, the parameter candidate selection unit 103 selects candidates for a combination of parameters based on the set initial values and temperature. Details of the solution of the combinatorial optimization problem will be described later.

The evaluation unit 104 calculates an evaluation value indicating an error between the waveform obtained by the sum of a plurality of non-harmonic signals defined by the candidates for the combination of the selected parameters and the waveform of the signal to be analyzed.

The evaluation value can be, for example, the square norm of the error signal. When the number of angular frequencies ω is K, the evaluation value can be expressed by the following mathematical formula (6). When the parameter space definition unit 102 selects S angular frequencies ω, which are less than K, from the K angular frequencies ω, the evaluation value can be expressed by the following mathematical formula (7).

The combinatorial optimization unit 105 determines a combination of parameters that define a plurality of anharmonic signals representing the analysis target signal based on the calculated evaluation value. The method of optimizing a system having a plurality of parameters is also called a combinatorial optimization problem, and the parameter candidate selection unit 103, the evaluation unit 104, and the combinatorial optimization unit 105 use a common solution method to solve the combinatorial optimization problem. Can be solved.

Examples of the method for solving the combinatorial optimization problem include a brute force method, a gradient descent method, and a simulated annealing method. The brute force method is a method of trying all combinations and selecting the one with the best evaluation value. When the number of parameters is small, the brute force method can be used to obtain a highly accurate solution. However, the brute force method is characterized in that the convergence speed decreases exponentially as the number of parameters increases.

The gradient descent method is a method that emphasizes the convergence speed. It is said that the gradient descent method may fall into local optimization depending on the initial value. If such a drawback can be tolerated, gradient descent can be used.

In the simulated annealing method, the process of determining the acceptance / rejection of a parameter is repeatedly performed based on the evaluation value of the candidate combination of the parameters selected from the parameter space. Here, at the initial stage, parameter candidates are selected from a wide range of the parameter space, and the parameter space is gradually narrowed by adjusting the parameter called temperature, so that the parameter falls into local optimum depending on the initial value. The possibility can be reduced. Here, the temperature is a value derived from the analogy of thermodynamics, and is a real number of 0 or more. The temperature indicates that the higher the temperature, the wider the parameter search range. In simulated annealing, the parameter transition probability when the difference value of the cost evaluation function E (p), which is the evaluation value when transitioning in the parameter space, is ΔE, is set as a real number with the temperature T at the time of transition as 0 or more. , Can be expressed by the following mathematical formula (8).

By using the parameter transition probability defined in the above formula (8), the detailed equilibrium condition in the probability sampling by the Metropolis-Hastings method can be satisfied, and if the temperature change is sufficiently slow, the distribution probability is cost-evaluated in the parameter space p. It is a Boltzmann distribution that is exponentially determined with respect to the function E (p). Therefore, by gradually lowering the temperature T from high temperature to low temperature, the probability distribution on the parameter space p is exponentially concentrated in the low part of the cost evaluation function E (p), and the early stage of the optimization process. At high temperatures, the probability distribution is flat, and it is difficult to fall into local optimum, and it is possible to obtain the property of efficiently converging to overall optimum.

The combination optimization unit 105 determines whether or not the completion condition of the optimization process is satisfied based on the evaluation value. When the combination optimization unit 105 determines that the completion condition is satisfied, it completes the optimization process and sets the candidate for the combination of the selected parameters as the processing result. When the combination optimization unit 105 determines that the completion condition is not satisfied, the parameter candidate selection unit 103 causes the parameter candidate selection unit 103 to select a candidate for the next parameter combination.

FIG. 2 is a flowchart showing an operation when the signal analyzer 10 shown in FIG. 1 uses the simulated annealing method. Note that FIG. 2 is based on the premise that the processing of the sampling unit 101 and the parameter space definition unit 102 has been completed, and the operations of the parameter candidate selection unit 103, the evaluation unit 104, and the combination optimization unit 105 will be mainly described.

First, the parameter candidate selection unit 103 sets the initial parameter and the temperature T (step S101). Then, the parameter candidate selection unit 103 selects a candidate for the combination of parameters (step S102). Here, the parameter p * selected includes candidates for a plurality of amplitudes A * and a plurality of angular frequencies ω * that define a plurality of anharmonic signals.

The evaluation unit 104 determines an evaluation value indicating an error between the waveform obtained by the sum of a plurality of non-harmonic signals defined by the parameter candidate selection unit 103 using the candidates for the combination of parameters and the waveform of the signal to be analyzed. Calculate (step S103).

The combination optimization unit 105 determines whether or not the candidate combination of parameters selected by the parameter candidate selection unit 103 satisfies the adoption condition (step S104). When the adoption condition is not satisfied (step S104: No), the combination optimization unit 105 instructs the parameter candidate selection unit 103 to select the parameter candidate, and returns to the process of step S102. When the adoption condition is satisfied (step S104: Yes), the combinatorial optimization unit 105 adopts a new parameter p * and updates the temperature T (step S105).

Further, the combinatorial optimization unit 105 determines whether or not the completion condition is satisfied (step S106). When the completion condition is satisfied (step S106: Yes), the combinatorial optimization unit 105 ends the process. When the completion condition is not satisfied (step S106: No), the combinatorial optimization unit 105 instructs the parameter candidate selection unit 103 to select the parameter candidate, and returns to the process of step S102.

FIG. 3 is a diagram showing the relationship between the cost function and the parameter transition in the parameter space used by the signal analyzer 10 shown in FIG. In FIG. 3, the parameter space is schematically illustrated as one dimension, but in reality, the parameter space is a multidimensional parameter space having a plurality of axes including a plurality of complex amplitudes A and an angular frequency ω. E (p) is a cost function which is an example of an evaluation value, and is a scalar axis. p (t) is a parameter adopted at a certain time t, and p * is a parameter selected as a new candidate.

Here, when p * satisfies the adoption condition, it becomes the adopted parameter p (t + 1) at the next time t + 1. Further, ΔE is the difference of the cost function when moving in the parameter space, and P (ΔE) is the parameter transition probability determined based on ΔE and the temperature T.

FIG. 4 is a diagram showing a configuration of a signal analysis system 1 including the signal analysis device 10 shown in FIG. The signal analysis system 1 includes an antenna 11, an amplifier 12, an analog-digital converter 13, and a signal analysis device 10.

The electromagnetic wave signal received by the antenna 11 is amplified by the amplifier 12, converted into a digital signal sequence by the analog-digital converter 13, and then input to the signal analyzer 10. The signal analysis device 10 can output the combination of the estimated parameters as the analysis result. In the configuration shown in FIG. 4, the signal analyzer 10 directly processes the original signal as a real signal sequence. In this case, since the signal sequence is limited to the real number sequence and there is a dependency between the parameters, the parameter space can be defined based on the constraint condition.

FIG. 5 is a diagram showing a process of combinatorial optimization processing of the signal analysis apparatus 10 shown in FIG. The horizontal axis of FIG. 5 represents the number of optimization steps, and the vertical axis represents the angular frequency. Further, the color depth in FIG. 5 represents the natural logarithm of the absolute value of the complex amplitude, and the lighter the color, the larger the complex amplitude. FIG. 5 shows the results of an experiment using simulated annealing. With reference to FIG. 5, it can be seen that a large number of parameters can be estimated simultaneously in parallel.

FIG. 6 is a diagram showing an analysis result 51 of the signal analysis device 10 shown in FIG. FIG. 6 also shows the results of an experiment using the simulated annealing method. The horizontal axis of FIG. 6 represents the frequency, and the vertical axis represents the signal amplitude. Further, the solid line shows the analysis result 51 of the signal analysis device 10 according to the present embodiment, and the broken line shows the comparative example 52. Comparative Example 52 is an estimation result using a conventional short-time Fourier transform. The signal to be analyzed has signal components of 1.00 Hz, 1.005 Hz, 1.01 Hz, 1.02 Hz, 1.04 Hz, and 1.08 Hz. By referring to FIG. 6, it can be seen that the accuracy of the analysis result 51 of the signal analysis device 10 is higher than that of the comparative example 52.

FIG. 7 is a diagram showing a time waveform obtained based on the analysis result of the signal analysis device 10 shown in FIG. The horizontal axis of FIG. 7 represents time, and the vertical axis represents signal amplitude. It can be seen that the time waveform 53 obtained based on the analysis result of the signal analysis device 10 shown in FIG. 7 is very well matched with the time waveform 54 of the signal to be analyzed.

As described above, according to the first embodiment of the present invention, the signal analysis device 10 sets a combination of parameters that define a plurality of non-harmonic signals when the signal to be analyzed is decomposed into a plurality of non-harmonic signals. It can be solved as a combinatorial optimization problem. Therefore, it is possible to efficiently determine the combination of parameters that can represent the signal to be analyzed.

Further, the signal analysis device 10 defines the parameter space by thinning out the frequency, and then solves the combinatorial optimization problem using this parameter space. Therefore, it is possible to narrow down the candidates for the combination of parameters, reduce the processing load required for the combination optimization, and shorten the time required to obtain the solution. In addition, it becomes possible to express the signal to be analyzed with fewer parameters than when the parameter space is not thinned out, and the efficiency is improved.

As a method for solving the combinatorial optimization problem, a brute force method, a gradient descent method, a simulated annealing method, or the like can be used. The brute force method has a high optimization ability, but the convergence speed becomes slower as the number of parameters increases, so it is recommended to use it when the number of parameters is small. Since the gradient descent method has a high convergence speed, it should be used when the convergence speed is important. Simulated annealing has a good balance between optimization ability and convergence speed, and is less likely to fall into local optimization than gradient descent, so it can be used under a wide range of conditions.

Embodiment 2.
FIG. 8 is a diagram showing a configuration of a signal analysis system 2 according to a second embodiment of the present invention. The signal analysis system 1 directly processes the original analysis target signal as a real number signal sequence. On the other hand, the signal analysis system 2 can process the original analysis target signal as a complex signal sequence by frequency-shifting it to an intermediate frequency.

The signal analysis system 2 includes an antenna 21, an amplifier 22, mixers 23 and 24, a local oscillator 25, a π / 2 phase delayer 26, analog-digital converters 27 and 28, and a signal analysis device 10. The mixer 24 is an electric element that shifts the frequency of the signal to be analyzed to an intermediate frequency.

The electromagnetic wave signal received by the antenna 21 is amplified by the amplifier 22 and then branched into two mixers 23 and 24 for input. Signals are also input to each of the mixers 23 and 24 from the local oscillator 25 that oscillates at the shifting frequency. The signal input from the local oscillator 25 to the mixer 24 is phase-delayed by π / 2 radians by the π / 2 phase delayer 26. The output signal of the mixer 23 is input to the analog-digital converter 27, converted into a digital signal sequence, and input to the signal analyzer 10. The output signal of the mixer 24 is input to the analog-digital converter 28, converted into a digital signal sequence, and input to the signal analyzer 10. The signal analysis device 10 outputs the analysis result.

As described above, the signal analysis system 2 according to the second embodiment includes mixers 23 and 24 which are electric elements that shift the frequency of the signal to be analyzed to an intermediate frequency. Therefore, the signal sequence input to the signal analysis device 10 in the signal analysis system 2 is not limited to the real number sequence, and the signal analysis device 10 processes the analysis target signal as a complex signal sequence. Therefore, there is no dependency between the parameters, and the constraint condition that can be set in the case of a real number series is not set and is interpreted as a shifted angular frequency.

Embodiment 3.
FIG. 9 is a diagram showing a configuration of a signal analysis system 3 according to a third embodiment of the present invention. In the second embodiment described above, a configuration for performing frequency shifting in a system that receives an electromagnetic wave signal has been described. In the third embodiment, the processing in the system for receiving the optical signal will be described.

The signal analysis system 3 includes an optical fiber 31, a local oscillator 32, an optical element 33, photodetectors 34 and 35, amplifiers 36 and 37, analog-digital converters 38 and 39, and a signal analysis device 10. The analog-to-digital converter 38 is an I-channel analog-digital converter, and the analog-to-digital converter 39 is a Q-channel analog-digital converter.

The optical signal propagating through the optical fiber 31 is input to the optical element 33. Local oscillation light is also input to the optical element 33 from the local oscillator 32 that oscillates at the frequency to be shifted. The optical element 33 outputs two beat-up optical signals. One of the output signal lights of the optical element 33 is received by the photodetector 34, amplified by the amplifier 36, converted into a digital signal sequence by the analog-digital converter 38, and input to the signal analyzer 10. The other of the output signal lights of the optical element 33 is received by the photodetector 35, amplified by the amplifier 37, converted into a digital signal sequence by the analog-digital converter 39, and input to the signal analyzer 10. The signal analysis device 10 outputs the analysis result.

As described above, according to the signal analysis system 3 according to the third embodiment of the present invention, the function of the signal analysis device 10 can be used even in the system for receiving the optical signal. Further, the signal analysis system 3 has an optical element 33 that shifts the frequency of the signal to be analyzed to an intermediate frequency. Therefore, even in the signal analysis system 3, the signal sequence input to the signal analysis device 10 is not limited to the real number sequence, and the signal analysis device 10 processes the analysis target signal as a complex signal sequence. Therefore, there is no dependency between the parameters, and the constraint condition that can be set in the case of a real number series is not set and is interpreted as a shifted angular frequency.

Subsequently, the hardware configuration of the signal analysis device 10 according to the first to third embodiments of the present invention will be described. The sampling unit 101, the parameter space definition unit 102, the parameter candidate selection unit 103, the evaluation unit 104, and the combinatorial optimization unit 105 are realized by a processing circuit. These processing circuits may be realized by dedicated hardware, or may be control circuits using a CPU (Central Processing Unit).

When the above processing circuits are realized by dedicated hardware, these are realized by the processing circuit 90 shown in FIG. FIG. 10 is a diagram showing dedicated hardware for realizing the functions of the signal analysis apparatus 10 according to the first to third embodiments of the present invention. The processing circuit 90 is a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or a combination thereof.

When the above processing circuit is realized by a control circuit using a CPU, this control circuit is, for example, a control circuit 91 having the configuration shown in FIG. FIG. 11 is a diagram showing a configuration of a control circuit 91 for realizing the function of the signal analysis device 10 according to the first to third embodiments of the present invention. As shown in FIG. 11, the control circuit 91 includes a processor 92 and a memory 93. The processor 92 is a CPU, and is also called a central processing unit, a processing unit, an arithmetic unit, a microprocessor, a microcomputer, a DSP (Digital Signal Processor), or the like. The memory 93 is, for example, a non-volatile or volatile semiconductor memory such as a RAM (Random Access Memory), a ROM (Read Only Memory), a flash memory, an EPROM (Erasable Programmable ROM), and an EPROM (registered trademark) (Electrically EPROM). Magnetic discs, flexible discs, optical discs, compact discs, mini discs, DVDs (Digital Versatile Disks), etc.

When the above processing circuit is realized by the control circuit 91, it is realized by the processor 92 reading and executing a program stored in the memory 93 corresponding to the processing of each component. The memory 93 is also used as a temporary memory in each process executed by the processor 92.

The configuration shown in the above-described embodiment shows an example of the content of the present invention, can be combined with another known technique, and is one of the configurations without departing from the gist of the present invention. It is also possible to omit or change the part.

For example, although the configuration and operation of the signal analysis device 10 have been described above, the technique of the present invention can be realized as the signal analysis device 10 and the signal analysis method, and also to realize the functions of the signal analysis device 10. It can also be realized as a computer program of. This computer program may be provided via a communication path, or may be stored in a recording medium and provided.

1,2,3 signal analysis system, 10 signal analyzer, 11,21 antenna, 12,22,36,37 amplifier, 13,27,28,38,39 analog digital converter, 23,24 mixer, 25,32 local Oscillator, 26 π / 2 phase delayer, 31 optical fiber, 33 optics, 34,35 photodetector, 51 analysis results, 52 comparative examples, 53,54 hour waveform, 90 processing circuit, 91 control circuit, 92 processor, 93 memory , 101 sampling unit, 102 parameter space definition unit, 103 parameter candidate selection unit, 104 evaluation unit, 105 combination optimization unit.

Claims (12)

In a signal analyzer that decomposes the signal to be analyzed into multiple anharmonic signals,
A parameter candidate selection unit that selects candidates for a combination of parameters that define multiple anharmonic signals, and a parameter candidate selection unit.
An evaluation unit that calculates an evaluation value indicating an error between the waveform obtained by the sum of a plurality of non-harmonic signals defined by the selected combination and the waveform of the analysis target signal.
A combinatorial optimization unit that determines a combination of the parameters that define a plurality of the anharmonic signals representing the analysis target signal based on the evaluation value.
A signal analysis device comprising. A parameter space definition unit that defines a parameter space composed of a plurality of anharmonic signal parameter candidates by thinning out the frequency.
With more
The signal analysis apparatus according to claim 1, wherein the parameter candidate selection unit selects a candidate for a combination of the parameters from the parameter space. The signal analysis apparatus according to claim 1 or 2, wherein the combination optimization unit determines a combination of the parameters by using a brute force method. The signal analysis apparatus according to claim 1 or 2, wherein the combination optimization unit determines a combination of the parameters by using a gradient descent method. The signal analysis apparatus according to claim 1 or 2, wherein the combination optimization unit determines a combination of the parameters by using a simulated annealing method. The signal analysis apparatus according to any one of claims 1 to 5, wherein the analysis target signal is directly processed as a real number signal sequence. The signal analyzer according to any one of claims 1 to 5,
An electric element that shifts the frequency of the signal to be analyzed to an intermediate frequency,
With
The signal analysis device is a signal analysis system characterized in that the signal to be analyzed is processed as a complex signal sequence. The signal analyzer according to any one of claims 1 to 5,
An optical element that shifts the frequency of the signal to be analyzed to an intermediate frequency,
With
The signal analysis device is a signal analysis system characterized in that the signal to be analyzed is processed as a complex signal sequence. A signal analyzer that decomposes the signal to be analyzed into multiple anharmonic signals
A step of selecting a candidate combination of parameters defining the plurality of anharmonic signals, and
A step of calculating an evaluation value indicating an error between the waveform obtained by the sum of a plurality of non-harmonic signals defined by the selected combination and the waveform of the signal to be analyzed.
Based on the evaluation value, a step of determining a combination of the parameters that define the plurality of the anharmonic signals representing the analysis target signal, and a step of determining the combination of the parameters.
A signal analysis method comprising. A step of thinning out and defining a parameter space composed of a plurality of parameter candidates of the anharmonic signal in terms of frequency.
Including
The signal analysis method according to claim 9, wherein in the step of selecting a candidate for the combination of the parameters, a candidate for the combination of the parameters is selected from the parameter space. It is a control circuit for controlling a signal analysis device that decomposes a signal to be analyzed into a plurality of anharmonic signals.
A step of selecting a candidate combination of parameters defining the plurality of anharmonic signals, and
A step of calculating an evaluation value indicating an error between the waveform obtained by the sum of a plurality of non-harmonic signals defined by the selected combination and the waveform of the signal to be analyzed.
Based on the evaluation value, a step of determining a combination of the parameters that define the plurality of the anharmonic signals representing the analysis target signal, and
A control circuit, characterized in that the signal analyzer is executed. A program for controlling a signal analysis device that decomposes a signal to be analyzed into a plurality of anharmonic signals.
A step of selecting a candidate combination of parameters defining the plurality of anharmonic signals, and
A step of calculating an evaluation value indicating an error between the waveform obtained by the sum of a plurality of non-harmonic signals defined by the selected combination and the waveform of the signal to be analyzed.
Based on the evaluation value, a step of determining a combination of the parameters that define the plurality of the anharmonic signals representing the analysis target signal, and
A program characterized by causing the signal analyzer to execute the above.

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