JP2023039461A - Signal separation filter and method for designing signal separation filter - Google Patents

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

The present invention relates to a signal separation filter and a design method of the signal separation filter, and more particularly to a signal separation filter for separating a periodic signal or an aperiodic signal from an input signal and a design method thereof.

2. Description of the Related Art In various fields such as machine control, process control, and communication, there is a demand for a technique for separating a signal with a predetermined frequency from an input signal. For example, in robot control, it is required to separate and remove periodic noise from input signals in order to improve control characteristics. Further, in the field of communication, it is required to extract a signal of a frequency of a necessary communication signal.

In order to meet such demands, various filters such as a band-stop filter for separating a periodic signal from an input signal have been developed (for example, Patent Document 1).

JP 2020-95332 A

In Patent Literature 1, weights calculated based on acquired vibration waveform data at a plurality of time points are used to design a moving average filter that removes the vibration component of the vibration waveform. However, in reality, separation of periodic signals in more complicated situations is required. For example, in an industrial robot that cooperates with humans, if you want to use periodic signals that are motion information associated with repeated robot tasks, or if you want to use non-periodic signals that are motion information associated with sudden contact with humans, There are cases where it is desired to use both of these periodic signals and non-periodic signals. Also, in the detection of abnormal products in the product inspection process, if you want to use periodic signals that are information about normal products, and if you want to use non-periodic signals that are information about abnormal products, you can use both of these periodic signals and non-periodic signals. There are cases where you want to use it.

Further, the amplitude of the periodic signal is not necessarily constant, and often fluctuates over time. Since the filter of Patent Document 1 does not take into consideration the fluctuation of the amplitude of the vibration waveform to be removed, it is difficult to remove the vibration waveform (periodic signal) with high accuracy when the amplitude of the vibration waveform fluctuates.

The present invention has been made in view of the above-mentioned circumstances, and provides a periodic signal whose amplitude varies at a frequency lower than a predetermined separation frequency (hereinafter referred to as a quasi-periodic signal), and a signal whose amplitude varies at a frequency higher than the predetermined separation frequency. It is an object of the present invention to provide a signal separation filter capable of accurately separating a quasi-periodic signal and a quasi-aperiodic signal from a signal including a non-periodic signal (hereinafter referred to as a quasi-aperiodic signal), and a method of designing the signal separation filter. do.

In order to achieve the above object, a signal separation filter according to a first aspect of the present invention comprises:
Equipped with a two or more stage feedforward path including a dead time element with a separation target period that is a target period of the separation target 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-aperiodic signal whose amplitude in the separation target period fluctuates at a frequency higher than the separation frequency, Separating at least one of the quasi-periodic signal and the quasi-aperiodic signal.

Also, the signal separation filter is
An IIR filter comprising two or more stages of feedback paths including dead time elements bearing the separation target period,
You can do it.

Also, the signal separation filter is
outputting a difference signal between one of the separated quasi-periodic signal and the quasi-aperiodic signal and the input signal as the other of the quasi-periodic signal and the quasi-aperiodic signal;
You can do it.

Further, in the method for designing a signal separation filter according to the second aspect of the present invention,
A quasi-periodic signal whose amplitude in the separation target period, which is the target period of the separation target signal, fluctuates at a frequency lower than a predetermined separation frequency, and a quasi-aperiodic signal whose amplitude in the separation target period fluctuates at a frequency higher than the separation frequency. lifting the input signal containing and using the separation target period;
generating a low-pass filter and/or a high-pass filter for the lifted input signal based on the separation frequency;
Inverse lifting the generated low-pass and high-pass filters to generate a filter for separating at least one of the quasi-periodic signal and the quasi-aperiodic signal.

According to the signal separation filter and the signal separation filter design method of the present invention, the periodic signal separation filter and the non-periodic signal separation filter are configured using a high-order filter that allows amplitude fluctuations of the periodic signal to be separated. It is possible to accurately separate the quasi-periodic signal and the quasi-aperiodic signal from the input signal.

The conceptual diagram which shows the lifting which concerns on embodiment of this invention. FIG. 4 is a Venn diagram showing the relationship of lifted state functions; FIG. 4 is a conceptual diagram showing the design flow of the signal separation filter according to the embodiment; It is a figure which shows the example of the IIR filter which concerns on embodiment, (A) is an example of a 1st order filter, (B) is an example of a high order filter. FIG. 4 is a diagram showing an example of a filter that outputs a quasi-aperiodic signal or a quasi-periodic signal as a difference signal between the quasi-periodic signal or the quasi-aperiodic signal and the input signal; 4 is a Bode diagram showing the characteristics of an IIR filter when the order is changed; FIG. FIG. 4 is a Bode diagram showing the characteristics of an IIR filter when the order and separation frequency are changed; It is a figure which shows the example of the FIR filter which concerns on embodiment. FIG. 4 is a Bode diagram showing the characteristics of an FIR filter when the order is changed; FIG. 4 is a Bode plot showing the characteristics of complementary FIR filters with varying orders; 7 is a graph showing operation results of an IIR filter and an FIR filter according to numerical examples, (A) is a graph of an input signal, (B) to (E) are graphs of a quasi-periodic state and a quasi-aperiodic state, (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. 7 is a graph showing the interference between a quasi-periodic signal and a quasi-aperiodic signal for operation results of an IIR filter and an FIR filter according to numerical examples.

Hereinafter, periodic signal separation filters according to embodiments of the present invention will be described with reference to the drawings. First, a quasi-periodic signal handled in this embodiment will be described.

Consider the following state x(t).

A lifting function L below is defined using a target period (separation target period) Π of the separation target signal. The lifting function L is a linear mapping that gives the lifted state x _τ (k) from the state x(t).

Also, the inverse lifting function L ⁻¹ is defined as follows.

FIG. 1 is a conceptual diagram showing the relationship between time t, period Π, etc., related to the lifting function. Hereinafter, x is also referred to as a state function, and x _τ is also referred to as a 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 equation below.

ただし、ω＝ω~ΠＴであり、ω［rad/sample］は正規化された角周波数、ω~［rad/s］は角周波数、Ｔ［s］はサンプリング時間を表す。ここで、ｔのサンプリング時間はＴであり、ｋのサンプリング時間はΠＴである。 The discrete-time Fourier transform F of the lifted state function x _τ is as shown below.

where ω=ω˜ΠT, ω[rad/sample] is the normalized angular frequency, ω˜[rad/s] is the angular frequency, and T[s] is the sampling time. where the sampling time of t is T and the sampling time of k is ΠT.

In this embodiment, a set S ₀ of zero functions, a set S _P of lifted state functions having quasi-periodicity, and a set S _A of lifted state functions having quasi-aperiodicity are defined as follows.

Here, quasi-periodicity and quasi-aperiodicity are defined as low and high frequencies of the lifted state function _xτ . Also, ρ [rad/sample] is the normalized separation frequency that is the boundary between the lifted quasi-periodic state function and the lifted quasi-aperiodic state function, and the separation frequency ρ ~ [rad/s] is given by the following equation is represented by

また、集合Ｓ_Ｐ、Ｓ_Ａは、Ｓ_０を含まない。

FIG. 2 shows the relationship of each set described above. As shown in FIG. 2 and the equations below, the universal set S is the union of the three sets S ₀ , S _P , S _A .

Also, the sets S _P and S _A do not include S ₀ .

リフティッド準周期状態関数ｘ_τｐの逆リフティング出力とリフティッド準非周期状態関数ｘ_τａの逆リフティング出力は、それぞれ準周期状態ｘ_ｐ（ｔ）、準非周期状態ｘ_ａ（ｔ）として以下のように定義される。

ここで、準周期状態ｘ_ｐ（ｔ）と準非周期状態ｘ_ａ（ｔ）とは、それぞれ低周波、高周波ではないことに注意を要する。 The lifted quasi-periodic state function x _τp and the lifted quasi-aperiodic state function x _τa are defined by the following equations using the above sets S ₀ , S _P , and S _A .

The inverse lifting output of the lifted quasi-periodic state function x _τp and the inverse lifting output of the lifted quasi-aperiodic state function x _τa are defined as the quasi-periodic state x _p (t) and the quasi-aperiodic state x _a (t) respectively as Defined.

Note that the quasi-periodic state x _p (t) and the quasi-aperiodic state x _a (t) are not low frequency and high frequency, respectively.

Further, a lifted periodic aperiodic state function x _τpa (t) is defined as the following equation.

上記の周期非周期状態ｘ_ｐａ（ｔ）は、準周期状態と準非周期状態との和である。

Also, the periodic aperiodic state x _pa (t) is defined by the following equation.

The above periodic aperiodic state x _pa (t) is the sum of the quasi-periodic state and the quasi-aperiodic state.

The state x(t) can be summarized as follows.

Next, a filter for separating a quasi-periodic signal and a quasi-aperiodic signal from an input signal will be described. First, we define the z-transform of the state x(t) and the lifted state x _τ (k). The z-transform of state x(t) is expressed by the following equation.

Also, the Z transform of the lifted state x _τ (k) is represented by the following equation.

Also, the relationship between the above two z-transforms is as follows.

The lifted periodic pass function and the lifted aperiodic pass function can then be expressed using linear time-invariant polynomials, as shown in the following equations.

ただし、ａ_ｉ及びｂ_ｉはＦ_τｐ（Ｚ^－１）をローパスフィルタとするように決定され、ｃ_ｉ、ｄ_ｉはＦ_τａ（Ｚ^－１）をハイパスフィルタとするように決定される。 The above filter is Z-transformed in k as shown in the equation below.

where a _i and b _i are determined to make F _τp (Z ⁻¹ ) a low-pass filter, and c _i and d _i are determined to make F _τa (Z ⁻¹ ) a high-pass filter.

これらの通過フィルタは、入力信号から周期信号と非周期信号とを分離するフィルタとして用いることができる。 By the inverse Z-transform Z ⁻¹ and the inverse lifting function L ⁻¹ , the periodic pass filter and the non-periodic pass filter are given by the following equations, respectively.

These pass filters can be used as filters to separate periodic and non-periodic signals from the input signal.

As mentioned above, the quasi-periodic states contained in state x can be thought of as low-frequency functions in the lifted state by lifting state x with a given 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 the periodic signal and then performing inverse lifting transform, it is possible to design a filter capable of separating a quasi-periodic signal having a predetermined amplitude fluctuation. (Fig. 3).

Also, the quasi-aperiodic state included in the state x can be considered as a high-frequency function in the lifted state by lifting the state x using a predetermined period Π. In other words, the quasi-aperiodic signal is a signal that changes at a high frequency every period (period Π). Therefore, in the lifted state, a filter capable of separating quasi-aperiodic signals can be designed by designing a desired high-pass filter based on the separation frequency of the aperiodic signal and then performing inverse lifting transform.

Also, the z-transformed periodic pass filter F _p (z ⁻¹ ) and the aperiodic pass filter F _a (z ⁻¹ ) can be expressed as follows.

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

ただし、ｓ~は以下の式に示すように、Ｚ^－１の双一次変換によって与えられる近似ラプラス演算子であり、ρ~は式（１）に示す分離周波数である。

The Nth-order IIR low-pass filter and IIR high-pass filter can be used as the lifted periodic pass filter and the lifted aperiodic pass filter shown in the following equations.

where s~ is the approximate Laplacian operator given by the bilinear transformation of Z ^-1 , as shown below, and ρ~ is the separation frequency shown in equation (1).

Using the z-transform definition above, the IIR periodic pass filter and the IIR aperiodic pass filter are given by the following equations, respectively.

The IIR periodic pass filter and the IIR non-periodic pass filter represented by the above equations (4) and (5) are similar to the example of the first-order filter in FIG. 4A and the example of the high-order filter in FIG. 4B. is realized in As shown in FIGS. 4A and 4B, the periodic signal separation filter according to the present embodiment has z ^−Π (expressed in a discrete time system) in the feedforward path of each stage and the feedback path of each stage. contains the represented dead time element. That is, the feedforward path of each stage and the feedback path of each stage include dead time elements shouldered by the period Π representing the separation target period of the quasi-periodic signal to be separated.

Further, the IIR periodic pass filter and the IIR non-periodic pass filter shown in the above equations (4) and (5) are quasi-periodic signal separation filters that separate periodic signals having a predetermined amplitude fluctuation by the separation frequency ρ. Or it operates as a quasi-aperiodic signal separation filter that separates aperiodic signals.

Further, as shown in FIG. 5, the signal separation filter that outputs the quasi-periodic signal and the quasi-aperiodic signal separates one of the quasi-periodic signal and the quasi-aperiodic signal, which are the output signals of the IIR filter, from the input signal. may be output as the other of the quasi-periodic signal and the quasi-aperiodic signal.

FIG. 6 shows Bode plots of an Nth-order IIR periodic pass filter _Fp and an IIR aperiodic pass filter _Fa . The filter according to FIG. 6 has a sampling time T _s of 0.001 s (seconds), a period Π of 200 π, and a separation frequency ρ˜1 rad/s. As shown in FIG. 6, by increasing the order of the periodic pass filter F _p (z ⁻¹ ), the attenuation becomes steeper and the band stop characteristic can be deepened.

FIG. 7 is a Bode diagram when the order N and the separation frequency ρ˜ are changed. The filter according to FIG. 7 has a sampling time T _s of 0.001 s and a period Π of 200π. As shown in FIG. 7, the bandpass frequency of the filter can be broadened by increasing the filter separation frequency ρ~. Also, these IIR filters can reduce the order and computational cost compared to FIR (Finite Impulse Response) filters.

Next, an FIR filter as a separation filter according to this embodiment will be described. The FIR filter is realized as shown in FIG. 8 by setting a _i and c _i of the denominator polynomials of equations (2) and (3) to zero. Therefore, FIR filters are inherently stable, unlike IIR filters.

In the present embodiment, the Parks-McClellan algorithm is applied to the lifted periodic pass filter F _τp (Z ⁻¹ ) and the lifted aperiodic pass filter F _τa (Z ⁻¹ ) to form equiripple FIR low-pass filters and FIR high-pass filters. design. In this example, the coefficients b _i and d _i of the filters in Equations (2) and (3) were calculated using the firceqrip( ) function of MATLAB (registered trademark).

In the present embodiment, 20th, 30th, and 50th FIR low-pass filters and high-pass filters were created for comparison. FIG. 9 is a Bode plot of an Nth-order FIR periodic pass filter F _p (z ⁻¹ ) and an FIR non-periodic pass filter F _a (z ⁻¹ ). The filter according to FIG. 9 has a sampling time T _s of 0.001 s, a period Π of 200 π, and a separation frequency ρ˜1 rad/s. As shown in FIG. 9, the higher the order, the steeper the slope. Further, as shown in the gain diagram of FIG. 9, the FIR filter exhibits a higher order and steeper slope than the IIR filter shown in FIG.

In the FIR aperiodic pass filter described above, there is a lag (phase lag) in the passband frequency, and the aperiodic state output by the FIR aperiodic pass filter is lagging. In order to solve this phase delay problem, as another embodiment of the non-periodic pass filter, consider a filter complementary to the periodic pass filter expressed by the following equation.

For example, first-order IIR periodic pass filters and IIR non-periodic pass filters based on equations (4) and (5) are complementary filters expressed by the following equations.

As shown in the Bode plot of FIG. 10, the above filter can improve the phase lag of the FIR aperiodic pass function. More specifically, the phase at the passband frequency of the complementary FIR non-periodic pass filter is zero, indicating that the phase lag is improved compared to the FIR non-periodic pass filter shown in FIG. Recognize.

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

As the FIR filter, a 50th-order FIR filter designed using the MATLAB (registered trademark) firceqrip( ) function is used. The input signal according to this example is a signal in which a quasi-aperiodic signal is added to a quasi-periodic signal at a time point of 5s (seconds), as shown in FIG.

As shown in FIGS. 11B to 11E, it can be seen that the quasi-periodic signals and the quasi-aperiodic signals are properly separated in each of the IIR filters and FIR filters. Also, as shown in FIG. 12, the interference between the quasi-periodic signal and the quasi-aperiodic signal in the IIR filter is 100 minutes in the case of the second-order and third-order filters compared to the case of the first-order filter. is about 1 or less, and it can be seen that the interference can be greatly reduced.

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

As described above, according to the signal separation filter and the design method of the signal separation filter according to the present embodiment, the signal separation filter is configured using a high-order filter that allows amplitude fluctuations of the periodic signal to be separated. . More specifically, the signal separation filter according to the present embodiment has two or more stages of feedforward paths including dead time elements with the separation target period, which is the period of the target of the signal to be separated. A quasi-periodic signal and a quasi-aperiodic signal can be accurately separated from a signal.

In addition, a filter that separates quasi-periodic and quasi-aperiodic signals is designed by generating a low-pass filter or high-pass filter based on the lifted signal using the separation target period Π, which is the target period of the separation target signal. Therefore, a highly accurate signal separation filter can be easily generated.

In addition, since the signal separation filter according to the present embodiment is intended to separate a periodic signal including harmonics, it is possible to separate the harmonic components of the signal to be separated unlike the notch filter.

Although the signal separation filter according to the present embodiment separates a quasi-periodic signal or a quasi-aperiodic signal from an input signal, the present invention is not limited to this. A signal and a quasi-aperiodic signal may be output. Further, the signal separation filter according to the present invention includes a quasi-periodic filter or a quasi-aperiodic filter, and uses a difference signal between the separated quasi-periodic signal or quasi-aperiodic signal and the input signal as the quasi-aperiodic signal or quasi-periodic signal. Accordingly, a quasi-periodic signal and a quasi-aperiodic signal may be output.

INDUSTRIAL APPLICABILITY The present invention is suitable for a periodic signal separation filter that separates a periodic signal and an aperiodic signal from an input signal. In particular, it is suitable for a periodic signal separation filter when the period of a periodic signal to be separated fluctuates in fields such as robot control and anomaly detection.

Claims (4)

Equipped with a two or more stage feedforward path including a dead time element with a separation target period that is a target period of the separation target 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-aperiodic signal whose amplitude in the separation target period fluctuates at a frequency higher than the separation frequency, separating at least one of the quasi-periodic signal and the quasi-aperiodic signal;
A signal separation filter characterized by: An IIR filter comprising two or more stages of feedback paths including dead time elements bearing the separation target period,
2. The signal separation filter according to claim 1, wherein: outputting a difference signal between one of the separated quasi-periodic signal and the quasi-aperiodic signal and the input signal as the other of the quasi-periodic signal and the quasi-aperiodic signal;
3. The signal separation filter according to claim 1 or 2, characterized in that: A quasi-periodic signal whose amplitude in the separation target period, which is the target period of the separation target signal, fluctuates at a frequency lower than a predetermined separation frequency, and a quasi-aperiodic signal whose amplitude in the separation target period fluctuates at a frequency higher than the separation frequency. lifting the input signal containing and using the separation target period;
generating a low-pass filter and/or a high-pass filter for the lifted input signal based on the separation frequency;
inverse lifting the generated low-pass and high-pass filters to generate a filter that isolates the quasi-periodic and/or quasi-aperiodic signals;
A method of designing a signal separation filter, characterized by:

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