JP7024983B1 - Filtering device and filtering method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To accurately realize demodulation in numerical phase detection. SOLUTION: A sampling unit 1 samples an AC signal at a sampling cycle corresponding to each frequency to be extracted. Here, the sampling cycle is set so that one cycle or a half cycle of each frequency to be extracted is an integral multiple of the sampling cycle. The filter unit 3 performs filtering on the AC signal by performing numerical phase detection on the sampled AC signal, and acquires a frequency component to be extracted. [Selection diagram] Fig. 1

Description

The present invention relates to a technique for filtering an AC signal.

As a technique for performing phase detection (also referred to as synchronous detection) for an AC signal, analog phase detection and numerical phase detection (also referred to as digital phase detection) are known.

In analog phase detection, assuming that each frequency of the signal to be demolished is ω ₀ , the original signal is multiplied by 2cos ω ₀ t or 2 sin ω ₀ t, and the double vibration component (that is, cos 2 ω ₀ t and sin 2 ω ₀ t) is removed. By doing so, a constant component that does not depend on time is extracted. Here, in the analog phase detection, since the component of the double vibration is removed by the low-pass filter, there is a problem that long-time integration is required.

On the other hand, in the numerical phase detection, since the component of the double vibration can be removed by using the interval integral of an integral multiple or a half-integer multiple of the reference period, there is an advantage that the signal component can be extracted in a short time.

By the way, in numerical phase detection, if the integrated vibration frequency (in short, the number of cycles used for interval integration) is small, there is a problem that the noise removal performance is significantly deteriorated. On the other hand, if the integrated vibration frequency is increased, there arises a problem that it takes time to take out the signal component. That is, in the numerical phase detection, the shortening of the processing time and the noise removal performance are in a trade-off relationship.

Therefore, the present inventor has proposed in Patent Document 1 below a technique capable of performing low noise signal extraction processing in a short time while using numerical phase detection. That is, the technique of Patent Document 1 below utilizes the fact that the characteristics of the passing gain differ depending on the integrated vibration frequency in the numerical phase detection, and takes a linear coupling of the detection results by a plurality of integrated vibration frequencies to obtain a single integrated vibration. It was shown that it is possible to have a pass gain characteristic that is not found in detection by the number of times.

Further, as a development of the technology of the following Patent Document 1, the present inventor sets the position of the frequency component to a specific position in the following Patent Document 2, so that the time required for separating the multiplexed frequency component is shortened. I showed you how you can do it.

International Publication 2018/163334 Gazette Japanese Patent No. 6905265

By the way, in these techniques, the AC signal to be filtered is generally a continuous function with respect to time. On the other hand, the actual signal acquisition (that is, sampling) is performed discretely. Then, in the separate demodulation of a plurality of frequencies, it becomes necessary to adjust the sampling method so that the integrated vibration frequency of an integer value (or a half integer value) can be realized. The patent document 1 (paragraph 0090) proposes a solution in which the frequency is set so that the reciprocal of the frequency is an integral multiple of the reciprocal of the sampling rate. However, in this case, if an attempt is made to match the conditions of the frequency arrangement for efficient filtering as in Patent Document 2, the restrictions on the frequencies that can be taken become strict.

The present invention has been made in view of the above circumstances. A main object of the present invention is to provide a technique for accurately realizing demodulation in numerical phase detection. Another object of the present invention is to provide a technique capable of increasing the degree of freedom in setting the frequency to be extracted in the numerical phase detection.

The means for solving the above-mentioned problems can be described as the following items.

(Item 1)
A filtering device for filtering AC signals.
It has a sampling unit, a detection unit, and a linear combination unit.
The sampling unit is configured to sample the AC signal at a sampling cycle corresponding to each frequency to be extracted.
Here, the sampling cycle is set so that one cycle or a half cycle of each frequency to be extracted is an integral multiple of the sampling cycle.
The detection unit is configured to acquire a plurality of detection results according to the integrated vibration frequency by performing numerical phase detection on the sampled AC signal.
The linear combination portion is a filtering device configured to perform a linear combination of the plurality of detection results using linear coefficients according to the filter characteristics.

(Item 2)
The filtering device according to item 1, wherein the sampling unit performs sampling of the AC signal in parallel at a sampling cycle corresponding to each frequency to be extracted.

(Item 3)
The filtering device according to item 1, wherein the sampling unit changes the sampling cycle so as to follow the fluctuation of the frequency of the AC signal.

(Item 4)
The filtering device according to any one of items 1 to 3, wherein the frequency components to be extracted in the AC signal are arranged at equal intervals.

(Item 5)
It also has an output section.
The filtering device according to any one of items 1 to 4, wherein the output unit is configured to output the result obtained by the linear combination at the linear combination unit.

(Item 6)
In addition, it has a linear coefficient determination unit.
The linear coefficient determining unit is configured to calculate the linear coefficient by using the relationship between the linear coefficients, the overall passing gain in the numerical phase detection, and the target filter characteristic. 5. The filtering device according to any one of 5.

(Item 7)
The filtering device according to any one of items 1 to 6, wherein at least two of the sampling cycles corresponding to the different frequencies are common.

(Item 8)
It is a filtering method for filtering AC signals.
The step of sampling the AC signal at the sampling cycle corresponding to each frequency to be extracted, and here, the sampling cycle is such that one cycle or a half cycle of each frequency to be extracted is an integral multiple of the sampling cycle. Is set to
A step of acquiring a plurality of detection results according to the integrated vibration frequency by performing numerical phase detection on the sampled AC signal, and
A filtering method including a step of performing a linear combination of the plurality of detection results using linear coefficients according to the filter characteristics.

(Item 9)
It is a filtering method for filtering AC signals.
The step of sampling the AC signal at the sampling cycle corresponding to each frequency to be extracted, and here, the sampling cycle is such that one cycle or a half cycle of each frequency to be extracted is an integral multiple of the sampling cycle. Is set to
A filtering method including a step of filtering the AC signal by performing numerical phase detection on the sampled AC signal and acquiring a frequency component to be extracted.

(Item 10)
A computer program for causing a computer to perform each step according to item 8 or 9.

This computer program can be applied to an appropriate recording medium (for example, an optical recording medium such as a CD-ROM or a DVD disk, a magnetic recording medium such as a hard disk or a flexible disk, or a magneto-optical recording medium such as an MO disk). Can be stored. This computer program can be transmitted via a communication line such as the Internet.

(Item 11)
A filtering device for filtering AC signals.
It has a sampling unit and a filter unit.
The sampling unit has a configuration in which the AC signal is sampled at a sampling cycle corresponding to each frequency to be extracted. Here, the sampling cycle is one cycle or a half cycle of each frequency to be extracted. It is set to be an integral multiple of the period,
The filter unit is a filtering device configured to filter the AC signal by performing numerical phase detection on the sampled AC signal and acquire a frequency component to be extracted.

According to the present invention, it is possible to accurately realize demodulation in numerical phase detection. Further, according to the present invention, it is possible to increase the degree of freedom in setting the frequency to be extracted in the numerical phase detection.

It is a block diagram which shows the outline of the filtering apparatus which concerns on one Embodiment of this invention. It is a block diagram which shows the outline of the filter part in the filtering apparatus of FIG. It is a flow chart for demonstrating the filtering method performed using the filtering apparatus of FIG. It is explanatory drawing for demonstrating the procedure of sampling and demodulating a mixed signal which mixed AC signals. It is explanatory drawing for demonstrating the procedure of sampling a plurality of AC signals having equal frequency intervals in comparison with the OFDM method. In these figures, the numbers on the vertical axis represent frequency (Hz), and the vertical axis represents the amplitude for each frequency. It is explanatory drawing for demonstrating the example which applied the filtering method of this embodiment to frequency sweep. The vertical axis in these figures shows the normalized signal strength.

Hereinafter, the filtering device according to the embodiment of the present invention will be described with reference to FIG.

(Configuration of Filtering Device of the Present Embodiment)
The filtering device of the present embodiment includes a sampling unit 1 and a filter unit 3 as a main configuration (see FIG. 1). Further, the filtering device of the present embodiment includes a sampling rate storage unit 2, an output unit 4, and a linear coefficient determination unit 5 as additional elements.

(Sampling section)
The sampling unit 1 is configured to sample an AC signal at a sampling cycle corresponding to each frequency to be extracted. Here, the sampling cycle is set so that one cycle of each frequency to be extracted is an integral multiple of the sampling cycle. Here, the appropriate sampling periods for different frequencies are usually considered to be different from each other. However, as long as the condition that "one cycle of each frequency to be extracted is an integral multiple of the sampling cycle" is satisfied, any of the sampling cycles may be common. Therefore, the number M of sampling cycles corresponding to N frequencies may be any of N = M, N> M, and M = 1. The detailed sampling operation will be described later.

(Sampling rate storage)
The sampling rate storage unit 2 stores the sampling period corresponding to the frequency to be extracted (which is usually known). The sampling rate storage unit 2 provides the sampling unit 1 with a predetermined sampling period.

(Filter part)
The filter unit 3 of the present embodiment is composed of a detection unit 31 and a linear combination unit 32 (see FIG. 2).

The detection unit 31 acquires a plurality of detection results according to the integrated vibration frequency by performing numerical phase detection on the sampled AC signal.

The linear combination unit 32 performs a linear combination of a plurality of detection results using linear coefficients according to the filter characteristics.

The detection unit 31 and the linear combination unit 32 can be configured basically in the same manner as in Patent Document 1 or 2 described above. The detailed operation of the filter unit 3 will also be described later.

(Output section)
The output unit 4 is configured to output the result obtained by the linear combination in the linear combination unit 32. The output destination of the output unit 4 is, for example, a display or a printer, but other than that, some storage means or a remote device may be used. In this embodiment, sending data to some device is also included in the concept of output.

(Linear coefficient determination part)
The linear coefficient determination unit 5 is configured to calculate the linear coefficient used in the linear combination unit 32 by using the relationship between the linear coefficients, the overall passing gain in the numerical phase detection, and the target filter characteristic. There is. The method for determining the linear coefficient may be the same as that in Patent Document 1.

(Procedure of filtering method of this embodiment)
Next, a filtering method using the above-mentioned filtering device will be described with reference to FIG.

(Steps SA-1 and SA-2 in FIG. 3)
Upon receiving the input of the AC signal as the detection target, the sampling unit 1 receives the sampling period corresponding to the frequency to be extracted from the sampling rate storage unit 2, and samples the AC signal in this sampling period. Here, the sampling cycle is set so that one cycle of each frequency to be extracted is an integral multiple of the sampling cycle.

(Step SA-3 in FIG. 3)
Then, by performing numerical phase detection on the sampled AC signal, a plurality of detection results corresponding to the integrated vibration frequency are acquired. After that, a linear combination of a plurality of detection results is performed using a linear coefficient according to the filter characteristics. As for these numerical phase detections and linear combinations, the methods described in Patent Document 1 or Patent Document 2 described above can be used, so detailed description thereof will be omitted. The linear coefficient used is determined by the linear coefficient determining unit 5 in the same manner as in Patent Document 1. After that, the output unit 4 outputs the obtained filtering result.

(Principle of filtering device)
Here, the principle of the filtering device in the present embodiment will be described in detail, and then specific examples will be described. In the following, the citation of the formula in Patent Document 1 will be referred to as A- (**), and the citation of the formula in Patent Document 2 will be referred to as B- (**).

で与えられる（注意：ｎ＝半整数の場合も同様の議論は可能であるがここでは簡単化のため自然数の場合のみを考える。）。また簡単化のため以後角振動数を無次

(Note: The same argument is possible when n = half-integer, but for the sake of simplicity, only the case of natural numbers is considered here). Also, for simplification, the angular frequency will be changed to non-order.

という条件を課せば自動的にＡ－（１５）が成り立つ。 Generally, the passing gain of the signal component to be detected needs to be finite and equal in the real part and the imaginary part. For simplicity

If the condition is imposed, A- (15) is automatically established.

が成り立てばこれらのノイズを全て除去できることになる。

If holds true, all of these noises can be removed.

が成り立てばＢ－（１）が言える。従って、Ａ－（１４）とＡ－（２１）の連立

求める特性のフィルタが完成する。

If holds true, then B- (1) can be said. Therefore, a simultaneous system of A- (14) and A- (21)

The filter with the desired characteristics is completed.

が成り立つ必要性がある。ここで

が成り立つため

フィルタが出来上がる。

Needs to hold. here

To hold

The filter is ready.

数にある。従って除去したい周波数をうまく選べば、より積算時間を短縮することが可能である（前記特許文献２参照）。これは、ブロードバンド通信などのように使用する周波数の組をあらかじめ選べる場合に有効である。以下その方法の概要を示す。

In number. Therefore, if the frequency to be removed is properly selected, the integration time can be further shortened (see Patent Document 2). This is effective when the frequency set to be used can be selected in advance such as broadband communication. The outline of the method is shown below.

From A- (8) and A- (12)

となる。これより、

成分も同時に除去されることを意味する（このことは積算周期が半整数の組の場合でも同様に成り立つ。）。 Therefore,

Will be. Than this,

This means that the components are also removed at the same time (this is true even if the integration period is a set of half-integers).

と置くと、

となる。従って、

And put it

Will be. Therefore,

ることを意味する。この関係式をうまく利用するには、各々の周波数が一定間隔に並んでいてとりうる周波数帯域の中で高周波側に片寄せされているのが望ましい。そうすることで前記特許文献１の方式よりも全体の積算時間を更に短縮することが出来る。

Means that. In order to make good use of this relational expression, it is desirable that the respective frequencies are arranged at regular intervals and are offset to the high frequency side in the possible frequency band. By doing so, the total integration time can be further shortened as compared with the method of Patent Document 1.

整数倍でなければいけない。なお、ｎ=半整数の系列の場合、「復調すべき信号の半周期がサンプリング周期の整数倍になる」ようにする。本実施形態の説明においては、煩雑を避けるためｎ＝整数を仮定しているが、ｎ＝半整数の場合は、前記の通り、１周期を半周期と読み替えればよい。ちなみに、離散的Fourier変換（DFT）を基本とした直交周波数分割多重方式(orthogonal frequency- division multiplexing, OFDM)では、Δｔの整数倍の区間の中で、最初と最後の位相が同じになる周波数のみを扱うので、そもそもこういった問題は起きない（後述の図５（ｂ）参照）。 In the above theoretical explanation, the signal is treated as a continuous function with respect to time. On the other hand, since the actual signal acquisition is performed discretely on both the vertical and horizontal axes, it is necessary to consider the influence of deviation from the ideal situation. In particular, when time-series data is acquired with a finite sampling period Δt, it is very difficult to calculate equation A− (7 to 10) unless the integration interval is exactly an integral multiple of the sampling period Δt. .. If it is not an integral multiple, various interpolation methods can be used if the phase and amplitude of the signal are known and there is no noise, but this is a case where demodulation and signal separation have already been completed and is not a solution. Therefore, with respect to an arbitrary natural number n by the method of Patent Document 1.

Must be an integral multiple. In the case of a series of n = half-integer, "the half cycle of the signal to be demodulated is an integral multiple of the sampling cycle". In the description of this embodiment, n = an integer is assumed to avoid complication, but when n = a half-integer, one cycle may be read as a half-integer as described above. By the way, in the orthogonal frequency-division multiplexing (OFDM) based on the discrete Fourier transform (DFT), only the frequencies where the first and last phases are the same in the interval of an integral multiple of Δt. In the first place, such a problem does not occur (see FIG. 5 (b) described later).

When considering the separation and demodulation of a plurality of frequencies, it is sufficient that each frequency can be selected so that the period of each frequency is an integral multiple of Δt. This means that the reciprocal of the frequency is an integer ratio. However, what Patent Document 2 suggests is that the frequencies are evenly spaced, which is a requirement for efficiently transmitting and receiving data. In this case, there arises a problem that it is difficult to satisfy that the period of each frequency is an integral multiple of Δt at the same time. The following example is shown as a method to solve this problem.

(Example 1)
First, in the method of Patent Document 1, one cycle of the frequency to be extracted needs to be an integral multiple of Δt, but one cycle of the frequency to be removed does not necessarily have to be an integral multiple of Δt. Focused on. As a result, by independently sampling and demodulating the same input signal before detection with different sampling cycles for each frequency to be extracted, one cycle is always an integral multiple of the sampling cycle for each frequency to be extracted. Can be made to be. That is, for the frequency to be extracted, both ends of the integration interval can be secured as data points.

This point will be described in more detail with reference to FIG. Consider detecting these two AC signals from a mixed signal (FIG. 4 (c)) of two AC signals (see FIGS. 4 (a) and 4 (b)). In this case, sampling (FIG. 4 (d)) in the sampling cycle corresponding to the first AC signal (FIG. 4 (a)) is performed on the mixed signal. Further, before, after, or in parallel with this, sampling (FIG. 4 (e)) in the sampling cycle corresponding to the second AC signal (FIG. 4 (b)) is performed. In FIG. 4, white circles indicate sampling points. Here, each sampling cycle is set so that one cycle of the frequency to be extracted is an integral multiple of the sampling cycle. By performing numerical phase detection using the sampled data in the filter unit 3, each AC signal can be extracted as shown in FIGS. 4 (f) and 4 (g). That is, demodulation can be performed based on the sampling data, and the original waveform can be reproduced.

(Example 2)
Next, an example in which the frequencies are arranged at equal intervals will be described with reference to FIG. In this example, it is assumed that a frequency of 11 Hz to 15 Hz is used. The number of vibration integrations required by the conventional OFDM method is shown in light gray (FIG. 5A). In the OFDM method, even if the same sampling period is used, the integration interval required for detection is an integral multiple of the sampling period for all the frequency components considered, so interpolation is not necessary in the first place (Fig. 5 (b). )). That is, there is no need to adjust the sampling period.

On the other hand, the number of vibration integrations required in the signal separation method shown in Patent Document 1 or 2 is shown in dark gray in FIG. According to this method, demodulation can be performed with data in a shorter time than the OFDM method (FIG. 5A). However, when acquiring data at a single sampling rate, it is difficult to set the integration interval required for detection for all the frequency components considered to be an integral multiple of the sampling period. In particular, it is difficult when the frequency components are arranged at equal intervals as shown in FIG. 5 (see FIG. 5 (c)).

Therefore, by using different sampling rates for each of the frequency components considered, the integration interval can always be an integral multiple of the sampling period (see FIG. 5D). After that, as in the case of the first embodiment, the sampled data points can be used to extract an AC signal having a target frequency. Therefore, according to the method of the present embodiment, it is possible to increase the degree of freedom in setting the frequency to be extracted in the numerical phase detection.

(Example 3)
The idea of linking the sampling period to the frequency to be extracted is also effective when the frequency is swept continuously / discontinuously. An example in the case of frequency sweep will be described with reference to FIG.

In the case of sweeping, the sampling rate is linked according to the change in frequency, and the sampling unit 1 samples the data so that one cycle of the frequency is always an integral multiple of the sampling cycle Δt (see FIG. 6A). ). In FIG. 6A, the horizontal axis is the actual time. For reference, FIG. 6 (b) shows a diagram in which the sampling intervals are rearranged at equal intervals. The horizontal axis of FIG. 6B is the converted time. By interlocking the sampling rate according to the change in frequency, it is possible to sample data so that one cycle of the frequency is always an integral multiple of the sampling cycle. After that, as in the case of the first embodiment, the sampled data points can be used to extract an AC signal having a target frequency.

As described above, in the method of the present embodiment, a separate sampling period is given for each frequency, so that the period of the frequency to be extracted is always an integral multiple of the sampling period, and as a result, the integration interval is accurately set for each frequency. It can be an integral multiple of the vibration period. However, as described above, it is possible to use a common sampling period for a plurality of frequencies.

Generally, in order to increase the time resolution of signal detection, it is common practice to increase the frequency used for modulation, but because the frequency band legally permitted to use is limited, such as broadcasting and telecommunications. When the frequency cannot be easily increased, the signal processing methods of Patent Documents 1 and 2 are particularly effective. For example, according to the techniques of these documents, various frequency components are used with information having a shorter time width than the orthogonal frequency-division multiplexing (OFDM) currently used in the broadcasting and communication fields. The so-called broadband signal composed of can be demodulated. Therefore, in the broadcasting / communication field including Beyond 5G, improvement in communication speed, fault tolerance, and interference resistance can be expected by improving the signal density. Further, in the medical field, high speed and high resolution can be expected in imaging devices such as ultrasonic diagnostic devices and MRI. In the field of sensors, it is considered to contribute to the improvement of sensitivity, time response and anti-mixing performance in devices required for autonomous driving technology such as electronic compass, acceleration sensor, millimeter wave radar, and ultrasonic sonar.

In the era when the numerical processing part in demodulation of broadband signals was the mainstream of single core, OFDM based on discrete Fourier transform (DFT) by fast Fourier transform (FFT) was an overwhelmingly efficient method of signal demodulation and separation. rice field. On the other hand, in the present situation where multi-core (parallel processing) is the mainstream, when the same signal is acquired and processed in parallel at different sampling cycles for each frequency to be extracted as in this embodiment, processing between each core is performed. Is advantageous because it can be done independently. For example, in the above-described second embodiment, by assigning each sampling rate to each core (that is, the sampling unit 1) and performing parallel processing, the time required for extraction of a plurality of frequencies can be shortened.

In addition, there is no method for efficiently handling numerical phase detection in a short time in the frequency sweep technique often used in millimeter wave radar and ultrasonic sonar. Even in these cases, practical application can be achieved by applying the method of the third embodiment.

The content of the present invention is not limited to the above embodiment. The present invention may make various changes to a specific configuration within the scope of the claims.

For example, in the above-described embodiment, the filter unit 3 is composed of the detection unit 31 and the linear combination unit 32, but the functions of both can be realized by one functional block. The filter unit 3 of the present embodiment includes a process that is mathematically equivalent to the above-mentioned detection and linear combination, and for example, it is not necessary to separately perform the detection and the linear combination as separate processes. In short, the filter unit 3 may be configured to filter the AC signal by performing numerical phase detection on the sampled AC signal and acquire the frequency component to be extracted.

Further, each of the above-mentioned components may exist as a functional block and may not exist as independent hardware. Further, as the mounting method, hardware or computer software may be used. Further, one functional element in the present invention may be realized by a set of a plurality of functional elements, and a plurality of functional elements in the present invention may be realized by a single functional element.

Further, the functional elements may be arranged at physically separated positions. In this case, the functional elements may be connected to each other by a network. It is also possible to realize the function by grid computing or cloud computing, or to configure the functional elements.

1 Sampling unit 2 Sampling rate storage unit 3 Filter unit 31 Detection unit 32 Linear combination unit 4 Output unit 5 Linear coefficient determination unit

Claims (11)

A filtering device for filtering AC signals.
It has a sampling unit, a detection unit, and a linear combination unit.
The sampling unit is configured to sample the AC signal at a sampling cycle corresponding to each frequency to be extracted.
Here, the sampling cycle is set so that one cycle or a half cycle of each frequency to be extracted is an integral multiple of the sampling cycle.
The detection unit is configured to acquire a plurality of detection results according to the integrated vibration frequency by performing numerical phase detection on the sampled AC signal.
The linear combination portion is a filtering device configured to perform a linear combination of the plurality of detection results using linear coefficients according to the filter characteristics. The filtering device according to claim 1, wherein the sampling unit performs sampling of the AC signal in parallel at a sampling cycle corresponding to each frequency to be extracted. The filtering device according to claim 1, wherein the sampling unit changes the sampling cycle so as to follow the fluctuation of the frequency of the AC signal. The filtering device according to any one of claims 1 to 3, wherein the frequency components to be extracted in the AC signal are arranged at equal intervals. It also has an output section.
The filtering device according to any one of claims 1 to 4, wherein the output unit is configured to output a result obtained by a linear combination at the linear combination unit. In addition, it has a linear coefficient determination unit.
Claim 1 is configured such that the linear coefficient determination unit calculates the linear coefficient by using the relationship between the linear coefficients, the overall passing gain in the numerical phase detection, and the target filter characteristic. The filtering device according to any one of 5 to 5. The filtering device according to any one of claims 1 to 6, wherein at least two of the sampling cycles corresponding to different frequencies to be extracted are common. It is a filtering method for filtering AC signals.
The step of sampling the AC signal at the sampling cycle corresponding to each frequency to be extracted, and here, the sampling cycle is such that one cycle or a half cycle of each frequency to be extracted is an integral multiple of the sampling cycle. Is set to
A step of acquiring a plurality of detection results according to the integrated vibration frequency by performing numerical phase detection on the sampled AC signal, and
A filtering method including a step of performing a linear combination of the plurality of detection results using linear coefficients according to the filter characteristics. It is a filtering method for filtering AC signals.
The step of sampling the AC signal at the sampling cycle corresponding to each frequency to be extracted, and here, the sampling cycle is such that one cycle or a half cycle of each frequency to be extracted is an integral multiple of the sampling cycle. Is set to
A filtering method including a step of filtering the AC signal by performing numerical phase detection on the sampled AC signal and acquiring a frequency component to be extracted. A computer program for causing a computer to perform each step according to claim 8 or 9. A filtering device for filtering AC signals.
It has a sampling unit and a filter unit.
The sampling unit has a configuration in which the AC signal is sampled at a sampling cycle corresponding to each frequency to be extracted. Here, the sampling cycle is one cycle or a half cycle of each frequency to be extracted. It is set to be an integral multiple of the period,
The filter unit is a filtering device configured to filter the AC signal by performing numerical phase detection on the sampled AC signal and acquire a frequency component to be extracted.

Images