Signal processing device and signal processing method

Abstract

To provide a signal processing device and a signal processing method capable of separating a periodic signal (quasi-periodic signal) and an aperiodic signal (quasi-aperiodic signal) which have fluctuations in amplitude from estimated values and corrected values of a Kalman filter.SOLUTION: A signal processing device 1 includes a Kalman filter 11 that outputs an estimated value and an updated value of a system 20, and a signal separation filter 12 for separating at least any one of a quasi-periodic signal and a quasi-aperiodic signal from an input signal including the quasi-periodic signal and the quasi-aperiodic signal, the amplitude of the quasi-periodic signal in a separation target period which is a target period of a separation target signal fluctuating at a frequency lower than a predetermined separation frequency, and the amplitude of the quasi-aperiodic signal in the separation target period fluctuating at a frequency higher than the separation frequency. Further, the signal separation filter 12 has a feedforward path including a dead time element with the separation target period on a shoulder thereof, receives the estimated value and the updated value as input signals, and separates at least one of the quasi-periodic signal and the quasi-aperiodic signal for each input signal.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a signal processing device and a signal processing method, and more particularly to a signal separation device and a signal separation method for separating periodic or non-periodic signals from estimates and update values ​​of a Kalman filter. [Background technology]

[0002] State estimation using a Kalman filter is utilized in a wide range of fields, such as environment estimation (for example, Patent Document 1) and vehicle state estimation (for example, Patent Document 2). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent Publication No. 2021-114968 [Patent Document 2] Patent Publication No. 2021-38989 Summary of the Invention [Problem to be solved by the invention]

[0004] The Kalman filters disclosed in Patent Documents 1 and 2 calculate state estimates in a prediction step and update values ​​of the state estimates in a filtering step. There are cases where it is necessary to understand stationary periodic signals and non-periodic signals contained in the estimates and update values ​​that are the outputs of these Kalman filters.

[0005] For example, in state estimation of an industrial robot that collaborates with humans, there are cases where it is desired to detect periodic signals that are motion information accompanying repetitive work by the robot, cases where it is desired to detect non-periodic signals that are motion information accompanying sudden contact with a person, cases where it is desired to detect both these periodic and non-periodic signals, etc. Furthermore, in estimation of abnormal products in a product inspection process, there are cases where it is desired to detect periodic signals that are information about normal products, cases where it is desired to detect non-periodic signals that are information about abnormal products, cases where it is desired to detect both these periodic and non-periodic signals, etc.

[0006] Furthermore, the amplitude of the periodic signal is not necessarily constant, but often fluctuates over time. Since a typical signal separation filter does not take into account fluctuations in the amplitude of the periodic signal contained in the signal to be separated, it is difficult to separate the periodic and non-periodic components contained in the estimated and corrected values ​​of the Kalman filter.

[0007] The present invention has been made in view of the above circumstances, and aims to provide a signal processing device and a signal processing method that are capable of separating periodic signals (quasi-periodic signals) and non-periodic signals (quasi-non-periodic signals) having amplitude fluctuations from the estimated values ​​and corrected values ​​of a Kalman filter. [Means for solving the problem]

[0008] In order to achieve the above object, a signal processing device according to a first aspect of the present invention comprises: a Kalman filter that outputs estimates and updates of the target system; a signal separation filter configured to separate at least one of a quasi-periodic signal and a quasi-non-periodic signal from an input signal including a quasi-periodic signal whose amplitude in a separation target period, which is a target period of a signal to be separated, fluctuates at a frequency lower than a predetermined separation frequency, and a quasi-non-periodic signal whose amplitude in the separation target period fluctuates at a frequency higher than the separation frequency; The signal separation filter comprises: a feedforward path including a time delay element including the separation target period; The estimated value and the updated value are used as input signals, and for each of the input signals, at least one of the quasi-periodic signal and the quasi-non-periodic signal is separated. death, The feedforward path of the signal separation filter to which the estimated value is inputted and the feedforward path of the signal separation filter to which the updated value is inputted are common. .

[0009] Moreover, the signal separation filter an IIR filter having a feedback path including a time delay element including the separation target period; This may also be the case.

[0011] A signal processing method according to a second aspect of the present invention teeth, 1. A signal processing method performed by a signal processing device, comprising: Computing estimates and updates of the target system using a Kalman filter; The signal separation filter has a feedforward path including a dead time element with a separation target period, which is a target period of a signal to be separated, and separates at least one of the quasi-periodic signal and the quasi-nonperiodic signal from an input signal including a quasi-periodic signal whose amplitude in the separation target period fluctuates at a frequency lower than a predetermined separation frequency and a quasi-nonperiodic signal whose amplitude in the separation target period fluctuates at a frequency higher than the separation frequency, using the estimated value and the updated value as the input signal, and separates at least one of the quasi-periodic signal and the quasi-nonperiodic signal for each of the input signals. death, The feedforward path of the signal separation filter to which the estimated value is inputted and the feedforward path of the signal separation filter to which the updated value is inputted are common. . [Effects of the Invention]

[0012] According to the signal processing device and signal processing method of the present invention, it is possible to separate at least one of a quasi-periodic signal whose amplitude fluctuates at a frequency lower than a predetermined separation frequency and a quasi-non-periodic signal whose amplitude fluctuates at a frequency higher than the separation frequency, by using a signal separation filter that receives as input signals the estimated values ​​and updated values ​​that are outputs of a Kalman filter. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a block diagram showing a configuration of a signal processing device according to an embodiment of the present invention; [Figure 2] FIG. 10 is a conceptual diagram showing lifting according to the embodiment. [Figure 3] FIG. 10 is a Venn diagram showing the relationship of lifted state functions. [Figure 4] 1 is a conceptual diagram illustrating a design flow of a signal separation filter according to an embodiment. [Figure 5]1A and 1B are diagrams showing examples of IIR filters according to an embodiment, where (A) is an example of a first-order filter and (B) is an example of a higher-order filter. [Figure 6] 10A and 10B are diagrams illustrating an example of a filter that outputs a quasi-aperiodic signal or a quasi-periodic signal as a difference signal between a quasi-periodic signal or a quasi-aperiodic signal and an input signal. [Figure 7] FIG. 10 is a Bode diagram showing the characteristics of an IIR filter when the order is changed. [Figure 8] FIG. 10 is a Bode diagram showing the characteristics of an IIR filter when the order and separation frequency are changed. [Figure 9] FIG. 2 is a diagram illustrating an example of an FIR filter according to an embodiment. [Figure 10] FIG. 10 is a Bode diagram showing the characteristics of an FIR filter when the order is changed. [Figure 11] FIG. 10 is a Bode diagram showing characteristics of complementary FIR filters when the order is changed. [Figure 12] 1 is an algorithm for the operation of a signal separation filter including a Kalman filter according to an embodiment. [Figure 13] 1 is a block diagram showing a configuration of a signal processing device including a Kalman filter according to an embodiment; [Figure 14] 1A and 1B are diagrams showing examples of filters that separate periodic or non-periodic signals from the output signal of a Kalman filter, where (A) is an example when an IIR filter is used, and (B) is an example when an FIR filter is used. [Figure 15] Graphs showing the operation results of an IIR filter and an FIR filter according to a numerical example, where (A) is a graph of the output and state, (B) to (E) are graphs of the updated quasi-periodic state and quasi-aperiodic state, where (B) is a graph of a 1st-order IIR filter, (C) is a graph of a 2nd-order IIR filter, (D) is a graph of a 3rd-order IIR filter, and (E) is a graph of a 50th-order FIR filter. [Figure 16] 10 is a graph showing interference between a quasi-periodic signal and a quasi-aperiodic signal for operation results of an IIR filter and an FIR filter according to a numerical example. [Figure 17]10A and 10B are graphs showing examples of the operation results of a signal processing device equipped with a Kalman filter and a first-order IIR filter, where (A) is a graph of a periodic state and an aperiodic state when no control is performed, (B) is a graph of a periodic state when control is performed, and (C) is a graph of an aperiodic state when control is performed. DETAILED DESCRIPTION OF THE INVENTION

[0014] A signal processing device and a signal processing method according to an embodiment of the present invention will be described with reference to the drawings. As shown in FIG. 1, the signal processing device 1 includes a Kalman filter 11 that performs system state estimation, and a signal separation filter 12. The Kalman filter 11 may have a known configuration. As shown in a generalized form in FIG. 1, the Kalman filter 11 calculates an estimated value based on input information obtained from a system 20, which is a system to be estimated (prediction step). The Kalman filter 11 also calculates an updated value based on sensor information obtained from the system 20 (filtering step).

[0015] The signal separation filter 12 receives as input signals the time series data of the estimated values ​​and updated values ​​calculated by the Kalman filter 11, and separates the periodic signals and non-periodic signals contained in the estimated values ​​and updated values. In this embodiment, the periodic signals to be separated may be signals whose amplitudes fluctuate. More specifically, signals whose amplitudes fluctuate at frequencies lower than a predetermined separation frequency are defined as quasi-periodic signals, and signals whose amplitudes fluctuate at frequencies higher than the predetermined separation frequency are defined as quasi-non-periodic signals.

[0016] (signal separation filter) The signal separation filter 12 according to this embodiment will be described in detail below. First, the quasi-periodic signal handled in this embodiment will be described.

[0017] Consider the following state x(t):

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[0018] Using the target period of the signal to be separated (target period for separation) Π, we define the following lifting function L. The lifting function L converts the state x(t) into the lifted state x τ (k) is a linear mapping that gives

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[0019] Also, the inverse lifting function L -1 is defined as follows:

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[0020] Figure 2 is a conceptual diagram showing the relationship between time t, period Π, etc., related to the lifting function. Hereinafter, x is the state function, x τ is also called the lifted state function. The lifted state function x τ belongs to the set S of lifted state functions, which is the set of all mappings from integers Z to real numbers R, as shown in the following equation:

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[0021] Lifted state function x τ The discrete time Fourier transform F of is as shown below.

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[0022] In this embodiment, a set of zero functions S0 and a set of lifted state functions S P , a set of lifted state functions S with quasi-nonperiodicity Ais defined as the following equation:

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[0023] Here, quasi-periodicity and quasi-aperiodicity are defined by the lifted state function x τ The low and high frequencies are defined as ρ [rad / sample], which is the normalized separation frequency that is the boundary between the lifted quasi-periodic state function and the lifted quasi-aperiodic state function. The separation frequency ρ~ [rad / s] is expressed by the following equation:

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[0024] Figure 3 shows the relationship between the above sets. As shown in Figure 3 and the following equation, the universal set S is made up of three sets S0, S P , S A is the union of

number

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[0025] Lifted quasi-periodic state function x τp and the lifted quasi-nonperiodic state function x τa is the set S0, S P , S A are defined by the following formulas:

number

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[0026] Furthermore, the lifted periodic aperiodic state function x τpa (t) is defined as follows:

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[0027] Also, the periodic aperiodic state x pa (t) is defined as follows:

number

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[0028] The state x(t) can be summarized as follows:

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[0029] Next, we will explain the filter that separates the quasi-periodic signal and the quasi-non-periodic signal from the input signal. First, we consider the state x(t) and the lifted state x τ The z-transform of (k) is defined as follows: The z-transform of the state x(t) is expressed by the following equation:

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[0030] Also, the lifted state x τThe Z transform of (k) is expressed by the following formula:

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[0031] The relationship between the two z-transforms is as follows:

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[0032] Subsequently, the lifted periodic passage function and the lifted aperiodic passage function can be expressed using linear time-invariant polynomials as shown in the following equations.

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[0033] The above filter is Z-transformed with respect to k as shown in the following equation:

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[0034] Inverse Z transformation Z~ -1 and the inverse lifting function L -1 Thus, the periodic pass filter and the non-periodic pass filter are given by the following equations, respectively.

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[0035] As mentioned above, the quasi-periodic state contained in state x can be considered as a low-frequency function in the lifted state by lifting state x with a predetermined period Π. In other words, a quasi-periodic signal is a signal that changes at a low frequency every period (period Π). Therefore, in the lifted state, by designing a desired low-pass filter based on the separation frequency of a periodic signal and then performing an inverse lifting transform, it is possible to design a filter that can separate a quasi-periodic signal with a predetermined amplitude fluctuation (Figure 4).

[0036] Furthermore, the quasi-aperiodic state contained in state x can be considered as a high-frequency function in the lifted state by lifting state x with a predetermined period Π. In other words, a quasi-aperiodic signal is a signal that changes at a high frequency every period (period Π). Therefore, in the lifted state, a desired high-pass filter can be designed based on the separation frequency of the aperiodic signal, and then a filter that can separate the quasi-aperiodic signal can be designed by performing an inverse lifting transform.

[0037] Also, the z-transformed periodic pass filter F p (z -1 ) and aperiodic pass filter F a (z -1 ) can be expressed as follows:

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[0038] (IIR filter) Next, an IIR (Infinite Impulse Response) filter will be described as a specific example of the above filter.

[0039] The N-th order IIR low-pass filter and IIR high-pass filter can be used as a lifted periodic pass filter and a lifted aperiodic pass filter as shown in the following equations.

number

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[0040] Using the definition of the z-transform above, the IIR periodic pass filter and the IIR aperiodic pass filter are given by the following equations, respectively:

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[0041] The IIR periodic pass filter and IIR non-periodic pass filter shown in the above equations (4) and (5) are realized as an example of a first-order filter in FIG. 5(A) and an example of a high-order filter in FIG. 5(B). As shown in FIGS. 5(A) and 5(B), the periodic signal separation filter according to this embodiment has z in the feedforward path of each stage and the feedback path of each stage. -Π (expression in a discrete-time system) In other words, the feedforward path and the feedback path of each stage contain a time delay element with a period Π representing the target period of the quasi-periodic signals to be separated.

[0042] Furthermore, the IIR periodic pass filter and IIR aperiodic pass filter shown in the above equations (4) and (5) operate as a separation filter for quasi-periodic signals that separate periodic signals having a predetermined amplitude fluctuation at the separation frequency ρ, or as a separation filter for quasi-aperiodic signals that separate aperiodic signals.

[0043] Furthermore, as shown in FIG. 6, a signal separation filter that outputs a quasi-periodic signal and a quasi-aperiodic signal may output a differential signal between the input signal and either the quasi-periodic signal or the quasi-aperiodic signal, which is the output signal of the IIR filter, as the other of the quasi-periodic signal and the quasi-aperiodic signal.

[0044] Figure 7 shows the Nth-order IIR period-pass filter F p and IIR aperiodic pass filter F a 7 shows the Bode diagram of the sampling time T s is 0.001 s (seconds), the period Π is 200π, and the separation frequency ρ~ is 1 rad / s. As shown in Figure 7, the period pass filter F p (z -1 By increasing the order of the filter, the attenuation becomes steeper and the band-stop characteristics can be deepened.

[0045] 8 is a Bode diagram when the order N and the separation frequency ρ are changed. s is 0.001 s and the period Π is 200π. As shown in Figure 8, the bandpass frequency of the filter can be widened by increasing the filter separation frequency ρ~. Furthermore, these IIR filters can reduce the order and computational cost compared to FIR (Finite Impulse Response) filters.

[0046] Next, an FIR filter as a separation filter according to this embodiment will be described. In the FIR filter, the a i and c i is set to zero, and is realized as shown in Figure 9. Therefore, FIR filters are inherently stable, unlike IIR filters.

[0047] In this embodiment, the lifted period pass filter F τp (Z -1 ) and lifted aperiodic pass filter F τa (Z -1 ) to design an equiripple FIR low-pass filter and an FIR high-pass filter. In this example, the coefficients b of each filter in equations (2) and (3) are calculated using the firceqrip() function of MATLAB (registered trademark). i , d i was calculated.

[0048] In this embodiment, for comparison, 20th, 30th, and 50th order FIR low-pass filters and high-pass filters are created. p (z -1 ) and FIR aperiodic pass filter F a (z -1 ) is a Bode diagram of the sampling time T s is 0.001 s, the period Π is 200π, and the separation frequency ρ~ is 1 rad / s. As shown in Figure 10, the higher the order, the steeper the slope. Also, as shown in the gain diagram in Figure 10, the FIR filter exhibits a higher order and a steeper slope than the IIR filter shown in Figure 7.

[0049] In the above-mentioned FIR non-periodic pass filter, there is a delay (phase delay) in the passband frequency, and the non-periodic state output by the FIR non-periodic pass filter is delayed. To solve the problem of this phase delay, consider a complementary filter to the periodic pass filter expressed by the following equation as another embodiment of the non-periodic pass filter.

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[0050] For example, a first-order IIR periodic pass filter and an IIR non-periodic pass filter based on equations (4) and (5) are complementary filters expressed by the following equations:

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[0051] As shown in the Bode diagram of Figure 11, the above filter can improve the phase delay of the FIR aperiodic pass function. More specifically, the phase of the complementary FIR aperiodic pass filter is zero at the passband frequency, and it can be seen that the phase delay is improved compared to the FIR aperiodic pass filter shown in Figure 10.

[0052] (Kalman filter) Next, a Kalman filter using the above-mentioned signal separation filter will be described. As a system equipped with a Kalman filter, consider the following observable linear time-invariant system including periodic and non-periodic states.

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[0053] The Kalman filter is expressed as follows:

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[0054] The periodic / aperiodic separation filter (PASF) is expressed as follows:

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[0055] The variables in the above formulas are as follows:

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[0056] Also, x^ pa (t|t-1), x^ pa (t|t), g(t), v(t), and w(t) are the predicted periodic aperiodic state, the updated periodic aperiodic state, the Kalman gain, the process noise, and the observation noise, respectively. pi , G ai , H pi , H ai , S pi , S ai is a matrix consisting of coefficients of the periodic pass filter and the non-periodic pass filter. The estimation error is defined as follows:

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[0057] e(t|t), e p (t|t), e a (t|t) represent the estimation error, periodic estimation error, and aperiodic estimation error, respectively. The error covariance matrix is ​​defined as follows:

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[0058] The Kalman filter of equation (6) and the PASF of equation (7) are integrated into an algorithm A1 shown in Fig. 12. Here, the estimated periodic state x̂ p (t|t-1), the estimated aperiodic state x^ a (t|t-1), the updated periodic state x^ p (t|t), the updated aperiodic state x^ a (t|t) is estimated as follows:

number

[0059] As shown in Algorithm A1 of FIG. 12, the Kalman filter minimizes the sum of the cyclic error covariance and the non-cyclic error covariance by minimizing the error covariance P(t|t).

[0060] In the above algorithm A1, θ p , θ aIn other words, as shown in the block diagram of the Kalman filter 11 and the signal separation filter 12 in FIG. 13 and the block diagram of an example of the signal separation filter 12 in FIGS. 14(A) and 14(B), in this embodiment, the separation filter related to the estimated value and the separation filter related to the updated value share a feedforward path and a feedback path including a time delay element. This makes it possible to reduce the filtering process. Note that the feedforward path and the feedback path may be based on either the estimated value or the updated value, but it is preferable that they are processed based on the updated value. This is because the calculation process related to these sharing uses past information, and the accuracy of past information is higher for the updated value than for the estimated value.

[0061] (Numerical example) A numerical example will be shown using a system equipped with the above-mentioned Kalman filter. In this example, a case will be described in which a periodic signal separation filter according to each embodiment is applied to a one-input, one-output control system shown in the following equation.

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[0062] In this numerical example, for comparison, three IIR filter models of first to third orders and one FIR filter model are evaluated. The common parameters of the IIR filter models are as follows:

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[0063] The first-order (N=1) parameters are as follows:

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[0064] The second-order (N=2) parameters are as follows:

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[0065] The third-order (N=3) parameters are as follows:

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[0066] The FIR filter used is a 50th-order FIR filter designed using the firceqrip() function of MATLAB (registered trademark). In this estimation example, the input is set to u(t) = 0. Figures 15(A) to 15(E) and 16 show estimation results when four optimal PASFs are used. Here, the interference shown in Figure 16 is an updated aperiodic state extracted from an updated periodic state. The input signal in this example is a signal in which a quasi-periodic signal is added to a quasi-aperiodic signal at 5 seconds (seconds), as shown in Figure 15(A).

[0067] All four PASFs estimate both periodic and aperiodic states. As shown in Figures 15(A)-(E) and 16, increasing the order of the IIR filter reduces interference. On the other hand, the interference of the 50th-order FIR model is greater than that of the 3rd-order IIR filter. Also, the updated aperiodic state of the FIR filter does not oscillate after 6 seconds, unlike the IIR filter.

[0068] As shown in Figures 15(B) to 15(E), it can be seen that each IIR filter and FIR filter can properly separate quasi-periodic signals and quasi-aperiodic signals. Also, as shown in Figure 16, the interference between quasi-periodic signals and quasi-aperiodic signals in an IIR filter is about 1 / 100 or less in the case of a first-order filter in the case of a second-order and third-order filter, and it can be seen that the interference can be significantly reduced.

[0069] Therefore, the signal separation filter according to this embodiment can accurately separate quasi-periodic signals and quasi-aperiodic signals having amplitude fluctuations. In particular, by using a second-order or higher-order signal separation filter, it is possible to configure a signal separation filter that can significantly reduce interference between quasi-periodic signals and quasi-aperiodic signals.

[0070] Next, an example of periodic-aperiodic separation control using the optimal PASF based on the first-order IIR filter will be described. In this example, the system according to the numerical example above and the proportional-integral controller shown in the following equation are used.

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[0071] The above control was enabled 10 seconds after the start. Figures 17(A) to (C) are graphs showing the control results of this example, and Figure 17(A) is a graph showing the results when no control was performed, for comparison. As shown in Figures 17(B) and (C), respectively, the periodic state x1p(t) of x1(t) and the aperiodic state x3a(t) of x3(t) are appropriately controlled after the control started at 10 seconds.

[0072] As described above, according to the signal processing device and signal processing method of this embodiment, Quasi-periodic and quasi-aperiodic signals are separated using a signal separation filter equipped with a feedforward path including a dead time element that includes the separation target period, which is the target period of the signal to be separated.This makes it possible to accurately separate quasi-periodic and quasi-aperiodic signals from the estimated and corrected values ​​of the Kalman filter.

[0073] Furthermore, by generating a low-pass filter or a high-pass filter based on a signal lifted using the separation target period Π, which is the target period of the signal to be separated, it is possible to design a filter that separates quasi-periodic signals and quasi-aperiodic signals, thereby easily generating a highly accurate signal separation filter.

[0074] Furthermore, in the signal processing device and signal processing method according to this embodiment, the periodic signal including harmonics is the target of separation, and therefore, unlike a notch filter, the harmonic components of the signal to be separated can also be separated.

[0075] Furthermore, in the signal processing device and signal processing method according to this embodiment, by integrating the Kalman filter 11 and the PASF, which is the signal separation filter 12, it is possible to estimate, without bias, the quasi-periodic state and the quasi-aperiodic state that minimize the sum of the covariance of the cyclic error and the covariance of the non-cyclic error. [Industrial Applicability]

[0076] The present invention is suitable for estimating quasi-periodic and quasi-aperiodic states using a Kalman filter, particularly in fields such as robot control and anomaly detection, where estimates and update values ​​include periodic and aperiodic signals. [Explanation of symbols]

[0077] 1 Signal processing device, 11 Kalman filter, 12 Signal separation filter, 20 System

Claims

1. a Kalman filter that outputs estimates and updates of the target system; a signal separation filter configured to separate at least one of a quasi-periodic signal and a quasi-non-periodic signal from an input signal including a quasi-periodic signal whose amplitude in a separation target period, which is a target period of a signal to be separated, fluctuates at a frequency lower than a predetermined separation frequency, and a quasi-non-periodic signal whose amplitude in the separation target period fluctuates at a frequency higher than the separation frequency; The signal separation filter comprises: a feedforward path including a time delay element including the separation target period; the estimated value and the updated value are used as input signals, and for each of the input signals, at least one of the quasi-periodic signal and the quasi-non-periodic signal is separated; the feedforward path of the signal separation filter to which the estimated value is inputted and the feedforward path of the signal separation filter to which the updated value is inputted are common. A signal processing device comprising:

2. The signal separation filter comprises: an IIR filter having a feedback path including a time delay element including the separation target period; 2. The signal processing device according to claim 1.

3. A signal processing method executed by a signal processing device, comprising: Computing estimates and updates of the target system using a Kalman filter; using a signal separation filter that has a feedforward path including a dead time element with a separation target period, which is a target period of a signal to be separated, and that separates at least one of the quasi-periodic signal and the quasi-nonperiodic signal from an input signal including a quasi-periodic signal whose amplitude in the separation target period fluctuates at a frequency lower than a predetermined separation frequency and a quasi-nonperiodic signal whose amplitude in the separation target period fluctuates at a frequency higher than the separation frequency, and using the estimated value and the updated value as the input signal, separating at least one of the quasi-periodic signal and the quasi-nonperiodic signal for each of the input signals; the feedforward path of the signal separation filter to which the estimated value is inputted and the feedforward path of the signal separation filter to which the updated value is inputted are common. A signal processing method comprising:

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