Signal separation filter and signal separation filter design method

Abstract

To provide a signal separation filter which can separate a quasi-periodic signal and a quasi-aperiodic signal with high accuracy from a signal containing a periodic signal (quasi-periodic signal) whose amplitude fluctuates at a frequency lower than a predetermined separation frequency, and an aperiodic signal (quasi-aperiodic signal) whose amplitude fluctuates at a frequency higher than the predetermined separation frequency, and a method for designing a signal separation filter.SOLUTION: A signal separation filter has a feedforward path of two or more stages which includes, on a shoulder thereof, a dead time element having a separation target period which is a target period of a separation target signal. The signal separation filter separates at least any one of a quasi-periodic signal and a quasi-aperiodic signal from an input signal including the quasi-periodic signal whose amplitude in the separation target period fluctuates at a frequency lower than a predetermined separation frequency and the quasi-aperiodic signal whose amplitude in the separation target period fluctuates at a frequency higher than the separation frequency.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a signal separation filter and a design method for a signal separation filter, and more particularly to a signal separation filter that separates a periodic signal or a non-periodic signal from an input signal and a design method for the same. [Background technology]

[0002] There is a demand for technology to separate signals of a specific frequency from an input signal in various fields, including machine control, process control, and communications. For example, in robot control, there is a demand for separating and removing periodic noise from an input signal to improve control characteristics. In the communications field, there is also a demand for extracting signals of the required communication signal frequency.

[0003] In order to meet such demands, various filters such as band-stop filters that separate periodic signals from input signals have been developed (for example, Patent Document 1). [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2020-95332 Summary of the Invention [Problem to be solved by the invention]

[0005] In Patent Document 1, a moving average filter is designed to remove vibration components from the vibration waveform using weights calculated based on data from acquired vibration waveforms at multiple points in time. However, in reality, separation of periodic signals in more complex situations is required. For example, in an industrial robot collaborating with humans, there are cases where it is desirable to use periodic signals that provide motion information associated with the robot's repetitive tasks, or non-periodic signals that provide motion information associated with unexpected contact with humans, or both periodic and non-periodic signals. Furthermore, in detecting abnormal products during product inspection processes, there are cases where it is desirable to use periodic signals that provide information on normal products, or non-periodic signals that provide information on abnormal products, or both periodic and non-periodic signals.

[0006] Furthermore, the amplitude of the periodic signal is not necessarily constant and often fluctuates over time. The filter of Patent Document 1 does not take into consideration fluctuations in the amplitude of the vibration waveform to be removed, so it is difficult to accurately remove the vibration waveform (periodic signal) when the amplitude of the vibration waveform fluctuates.

[0007] The present invention has been made in view of the above circumstances, and aims to provide a signal separation filter and a method for designing a signal separation filter that can accurately separate quasi-periodic signals and quasi-non-periodic signals from signals that include periodic signals whose amplitudes fluctuate at frequencies lower than a predetermined separation frequency (hereinafter referred to as quasi-periodic signals) and non-periodic signals whose amplitudes fluctuate at frequencies higher than a predetermined separation frequency (hereinafter referred to as quasi-non-periodic signals). [Means for solving the problem]

[0008] In order to achieve the above object, a signal separation filter according to a first aspect of the present invention comprises: On each level, A time element that includes the target period of the signal to be separated. and a gain that uses the output of the dead time element as an input. a feedforward path of two or more stages including The amplitude of the separation target period includes a quasi-periodic signal that fluctuates at a frequency lower than a predetermined separation frequency, and a quasi-non-periodic signal that fluctuates at a frequency higher than the separation frequency. The signal is used as the input signal, The feedforward path is The first stage dead time element receives the input signal, The delay elements in the second and subsequent stages use the output of the previous delay element as input, configured to output a quasi-periodic signal or a quasi-non-periodic signal by adding the output signals of the respective stages; The gain of each stage in the feedforward path is When a quasi-periodic signal is output from the input signal, calculations are performed to configure a low-pass filter for the input signal lifted based on the separation target period; When a quasi-non-periodic signal is output from the input signal, calculations are performed to configure a high-pass filter for the input signal lifted based on the separation target period.

[0009] In addition, the signal separation filter is On each level, A time element that includes the separation target period and a gain that uses the output of the dead time element as an input. An IIR filter with two or more stages of feedback paths including the law of nature, The feedback path is The delay elements in the second and subsequent stages use the output of the previous delay element as input, a quasi-periodic signal or a quasi-non-periodic signal is output by adding an output signal of each stage and an output signal of the feedforward path; The gain of each stage in the feedback path is When a quasi-periodic signal is output from the input signal, calculations are performed to configure a low-pass filter for the input signal lifted based on the separation target period; When outputting a quasi-non-periodic signal from the input signal, a high-pass filter is calculated for the input signal lifted based on the separation target period. This may also be the case.

[0010] Also, According to the second aspect of the present invention The signal separation filter is a quasi-periodic signal that is an output of a signal separation filter according to a first aspect; a differential signal with respect to the input signal, output as a quasi-non-periodic signal, or a quasi-aperiodic signal that is an output of a signal separation filter according to a first aspect; a differential signal with respect to the input signal, quasi-periodic signal Output as

[0011] In addition, the present invention 3 Design method of signal separation filter relating to the viewpoint The law , an input signal including a quasi-periodic signal whose amplitude in a separation target period, which is a target period of the 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, using the separation target period; a low-pass filter for the lifted input signal based on the separation frequency; Or a high-pass filter Generate, Generated low-pass filter or By inverse lifting the high-pass filter, the quasi-periodic signal or a quasi-non-periodic signal Generate a filter to separate A method for designing a signal separation filter, comprising: The signal separation filter includes a feedforward path of two or more stages, each stage including a dead time element having a separation target period, which is a target period of the signal to be separated, and a gain having an output of the dead time element as an input; The feedforward path is The first stage dead time element receives the input signal, The delay elements in the second and subsequent stages use the output of the previous delay element as input, configured to output a quasi-periodic signal or a quasi-non-periodic signal by adding the output signals of the respective stages; The gain of each stage in the feedforward path is When a quasi-periodic signal is output from the input signal, calculations are performed to configure a low-pass filter for the input signal lifted based on the separation target period; When a quasi-non-periodic signal is output from the input signal, calculations are performed to configure a high-pass filter for the input signal lifted based on the separation target period. [Effects of the Invention]

[0012] According to the signal separation filter and signal separation filter design method of the present invention, a periodic signal separation filter and aperiodic signal separation filter are constructed using a high-order filter that allows for amplitude fluctuations in the periodic signals to be separated, making it possible to accurately separate quasi-periodic signals and quasi-non-periodic signals from an input signal. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a conceptual diagram showing lifting according to an embodiment of the present invention. [Figure 2] FIG. 10 is a Venn diagram showing the relationship of lifted state functions. [Figure 3] 1 is a conceptual diagram illustrating a design flow of a signal separation filter according to an embodiment. [Figure 4]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 5] 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 6] FIG. 10 is a Bode diagram showing the characteristics of an IIR filter when the order is changed. [Figure 7] FIG. 10 is a Bode diagram showing the characteristics of an IIR filter when the order and separation frequency are changed. [Figure 8] FIG. 2 is a diagram illustrating an example of an FIR filter according to an embodiment. [Figure 9] FIG. 10 is a Bode diagram showing the characteristics of an FIR filter when the order is changed. [Figure 10] FIG. 10 is a Bode diagram showing characteristics of complementary FIR filters when the order is changed. [Figure 11] Graphs showing the operational results of an IIR filter and an FIR filter according to a numerical example, where (A) is a graph of an input signal, (B) to (E) are graphs of quasi-periodic and quasi-aperiodic states, (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 12] 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. DETAILED DESCRIPTION OF THE INVENTION

[0014] Hereinafter, a periodic signal separation filter according to an embodiment of the present invention will be described with reference to the drawings. First, a quasi-periodic signal handled in this embodiment will be described.

[0015] Consider the following state x(t):

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[0016] 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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[0017] Also, the inverse lifting function L -1 is defined as follows:

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[0018] Figure 1 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:

number

[0019] Lifted state function x τ The discrete time Fourier transform F of is as shown below.

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[0020] 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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[0021] 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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[0022] Figure 2 shows the relationship between the above sets. As shown in Figure 2 and the following formula, the universal set S is made up of three sets S0, S P , S A is the union of

number

number

[0023] 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

number

[0024] Furthermore, the lifted periodic aperiodic state function x τpa (t) is defined as follows:

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[0025] Also, the periodic aperiodic state x pa (t) is defined as follows:

number

number

[0026] The state x(t) can be summarized as follows:

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[0027] 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:

number

[0028] Also, the lifted state x τThe Z transform of (k) is expressed by the following formula:

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[0029] The relationship between the two z-transforms is as follows:

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[0030] 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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[0031] The above filter is Z-transformed with respect to k as shown in the following equation:

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[0032] 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.

number

[0033] 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 3).

[0034] 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.

[0035] Also, the z-transformed periodic pass filter F p (z -1 ) and aperiodic pass filter F a (z -1 ) can be expressed as follows:

number

[0036] (IIR filter) Next, an IIR (Infinite Impulse Response) filter will be described as a specific example of the above filter.

[0037] 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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[0038] 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:

number

[0039] 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. 4(A) and an example of a high-order filter in FIG. 4(B). As shown in FIGS. 4(A) and 4(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.

[0040] 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.

[0041] Furthermore, as shown in FIG. 5, 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 an output signal of the IIR filter, as the other of the quasi-periodic signal and the quasi-aperiodic signal.

[0042] Figure 6 shows the Nth-order IIR period-pass filter F p and IIR aperiodic pass filter F a 6 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 6, the period pass filter F p (z -1 ) by increasing the order, the attenuation becomes steeper and the band-stop characteristics can be deepened.

[0043] 7 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 7, 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.

[0044] 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 8. Therefore, FIR filters are inherently stable, unlike IIR filters.

[0045] 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.

[0046] In this embodiment, for comparison, 20th, 30th, and 50th order FIR low-pass filters and high-pass filters were 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 9, the higher the order, the steeper the slope. Also, as shown in the gain diagram in Figure 9, the FIR filter exhibits a higher order and a steeper slope than the IIR filter shown in Figure 6.

[0047] 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.

number

[0048] 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:

number

[0049] As shown in the Bode diagram of Figure 10, 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 at the passband frequency is zero, which shows that the phase delay is improved compared to the FIR aperiodic pass filter shown in Figure 9.

[0050] (Numerical example) Next, a numerical example of the periodic signal separation filter according to the embodiment will be described. In this numerical example, for comparison, three IIR filters of first to third orders and one FIR filter will be evaluated. The sampling time T s is 0.001 s, the period Π is 200π, and the separation frequency ρ~ is 1 rad / s.

[0051] The FIR filter used is a 50th-order FIR filter designed using the firceqrip() function of MATLAB (registered trademark). The input signal in this example is a signal in which a quasi-periodic signal is added to a quasi-non-periodic signal at 5 seconds, as shown in Figure 11(A).

[0052] As shown in Figures 11(B) to 11(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 12, the interference between quasi-periodic signals and quasi-aperiodic signals in the 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 is significantly reduced.

[0053] 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.

[0054] As described above, according to the signal separation filter and signal separation filter design method of this embodiment, the signal separation filter is configured using a high-order filter that allows for amplitude fluctuations in the periodic signals to be separated. More specifically, the signal separation filter of this embodiment is equipped with two or more stages of feedforward paths that include a time delay element that overlaps the separation target period, which is the target period of the signal to be separated, and therefore is able to accurately separate quasi-periodic signals and quasi-non-periodic signals from the input signal.

[0055] 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.

[0056] Furthermore, the signal separation filter according to this embodiment separates periodic signals that include harmonics, and therefore, unlike a notch filter, can also separate harmonic components of the signals that are the target of separation.

[0057] Although the signal separation filter according to the present embodiment is configured to separate a quasi-periodic signal or a quasi-aperiodic signal from an input signal, the present invention is not limited thereto, and a quasi-periodic filter and a quasi-aperiodic filter may be combined to output the quasi-periodic signal and the quasi-aperiodic signal. Furthermore, the signal separation filter according to the present invention may include a quasi-periodic filter or a quasi-aperiodic filter, and may output the quasi-periodic signal and the quasi-aperiodic signal by converting the difference signal between the separated quasi-periodic signal or the quasi-aperiodic signal and the input signal into a quasi-aperiodic signal or a quasi-aperiodic signal. [Industrial Applicability]

[0058] The present invention is suitable for use as a periodic signal separation filter that separates periodic signals and non-periodic signals from an input signal, particularly in fields such as robot control and anomaly detection where the period of the periodic signal to be separated fluctuates.

Claims

1. A feedforward path having two or more stages, each of which includes a dead time element having a separation target period, which is a target period of a signal to be separated, and a gain having an input that is the output of the dead time element, 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-non-periodic signal whose amplitude in the separation target period fluctuates at a frequency higher than the separation frequency; The feedforward path is The first stage dead time element receives the input signal, The delay elements in the second and subsequent stages use the output of the previous delay element as input, configured to output a quasi-periodic signal or a quasi-non-periodic signal by adding the output signals of the respective stages; The gain of each stage in the feedforward path is When a quasi-periodic signal is output from the input signal, calculations are performed to configure a low-pass filter for the input signal lifted based on the separation target period; When outputting a quasi-non-periodic signal from the input signal, a high-pass filter is calculated for the input signal lifted based on the separation target period. A signal separation filter comprising:

2. An IIR filter having two or more stages of feedback paths, each stage including a dead time element including the separation target period and a gain having an output of the dead time element as an input, The feedback path is The delay elements in the second and subsequent stages use the output of the previous delay element as input, a quasi-periodic signal or a quasi-non-periodic signal is output by adding an output signal of each stage and an output signal of the feedforward path; The gain of each stage in the feedback path is When a quasi-periodic signal is output from the input signal, calculations are performed to configure a low-pass filter for the input signal lifted based on the separation target period; When outputting a quasi-non-periodic signal from the input signal, a high-pass filter is calculated for the input signal lifted based on the separation target period.

2. The signal separation filter according to claim 1.

3. A signal separation filter according to claim 1 or 2, wherein a differential signal between the quasi-periodic signal output from the signal separation filter and the input signal is output as a quasi-non-periodic signal, or a signal separation filter according to claim 1 or 2, which outputs a differential signal between the quasi-nonperiodic signal and the input signal as a quasi-periodic signal; A signal separation filter comprising:

4. an input signal including a quasi-periodic signal whose amplitude in a separation target period, which is a target period of the 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, using the separation target period; generating a low-pass or high-pass filter for the lifted input signal based on the separation frequency; A signal separation filter design method for generating a filter for separating a quasi-periodic signal or a quasi-non-periodic signal by performing inverse lifting on a generated low-pass filter or high-pass filter, The signal separation filter includes two or more stages of feedforward paths, each stage of which includes a dead time element having a separation target period, which is a target period of the signal to be separated, and a gain having an output of the dead time element as an input; The feedforward path is The first stage dead time element receives the input signal, The delay elements in the second and subsequent stages use the output of the previous delay element as input, configured to output a quasi-periodic signal or a quasi-non-periodic signal by adding the output signals of the respective stages; The gain of each stage in the feedforward path is When a quasi-periodic signal is output from the input signal, calculations are performed to configure a low-pass filter for the input signal lifted based on the separation target period; When outputting a quasi-non-periodic signal from the input signal, a high-pass filter is calculated for the input signal lifted based on the separation target period. A method for designing a signal separation filter.

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