JP6905265B2 - Filtering device and filtering method - Google Patents

Description

The present invention relates to a technique for separating a reference signal from a frequency-multiplexed AC signal.

Analog phase detection and numerical phase detection (also referred to as digital phase detection) are known as techniques for performing phase detection (also referred to as synchronous detection) for an AC signal.

The analog phase detection, when the angular frequency of the signal to be demodulated and omega _0, multiplied by 2cosω ₀ t or 2sinω ₀ t to the original signal, removing the double vibration component (i.e. cos2ω ₀ t and sin2ω ₀ t) 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 the numerical phase detection, if the integrated vibration frequency (in short, the number of periods used for the interval integration) is small, there is a problem that the noise removal performance is remarkably deteriorated. On the other hand, if the integrated vibration frequency is increased, there arises a problem that it takes time to extract the signal component. That is, in numerical phase detection, there is a trade-off relationship between shortening the processing time and noise removal performance.

Therefore, the present inventor has proposed a technique capable of performing low noise signal extraction processing in a short time while using numerical phase detection in a preceding related application (PCT / JP2017 / 909539 ).

By the way, as a result of further research, the present inventor has found that the processing time can be shortened when the frequency interval satisfies a predetermined condition in the detection of a frequency-multiplexed AC signal.

The present invention has been made based on the above-mentioned new findings. A main object of the present invention is to provide a technique capable of performing a process of separating a specific frequency component from a frequency-multiplexed AC signal in a short time.

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

(Item 1)
A filtering device for separating a reference signal from a frequency-multiplexed AC signal.
It has a detection part and a linear combination part.
The detection unit is configured to acquire a plurality of detection results according to the integrated number of vibrations by performing numerical phase detection on the AC signal.
The linear combination portion is configured to perform a linear combination of the plurality of detection results using linear coefficients according to the filter characteristics.
A filtering device in which the frequency components of the AC signal are arranged symmetrically with respect to the frequency of the reference signal.

(Item 2)
It also has an output section
The filtering device according to item 1, wherein the output unit is configured to output the result obtained by the linear combination at the linear combination unit.

(Item 3)
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. 2. The filtering device according to 2.

(Item 4)
A filtering method for filtering frequency-multiplexed AC signals.
A step of acquiring a plurality of detection results according to the integrated vibration frequency by performing numerical phase detection on the AC signal, and
It includes a step of filtering the AC signal by performing a linear combination of the plurality of detection results using a linear coefficient according to the filter characteristics.
It said frequency component in the AC signal, filtering methods are arranged at positions which are symmetrical about the frequency of criteria signals.

(Item 5)
By using the relationship between the linear coefficient a linear coefficient determination method used for the filtering method of claim 4, the entire passage gain in the numerical phase detection, a filter characteristic of interest, the A method for determining linear coefficients that includes steps to calculate linear coefficients.

(Item 6)
A computer program for causing a computer to perform each step according to item 4 or 5.

This computer program is 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.

According to the present invention, it is possible to perform a process of separating a specific frequency component from a frequency-multiplexed AC signal in a short time.

It is a block diagram which shows the outline of the filtering apparatus which concerns on one Embodiment of this invention. It is a flowchart for demonstrating the filtering method performed using the filtering apparatus of FIG. It is explanatory drawing for demonstrating the time required to separate the frequency-multiplexed signal frequency-converted to 1,2,3,4,5 Hz by the down conversion from each other by the OFDM method. Explain the time required to separate frequency-multiplexed signals frequency-converted to 11, 12, 13, 14, 15 Hz by down-conversion from each other by the OFDM method (OFDM) or by the method according to the previous related application (Previous method). It is explanatory drawing for this. It is explanatory drawing for demonstrating the time for separating the signals similar to FIG. 4 from each other by the method of Example 1. FIG. It is an explanatory diagram for explaining the time for separating the frequency-multiplexed signals frequency-converted to 11, 12, 13, 14, 15 Hz by down conversion from each other by the method according to the previous related application (Previous method). , This is an example using a secondary filter. It is explanatory drawing for demonstrating the time for separating a signal similar to FIG. 4 from each other by the method of Example 2, and is an example using a quadratic filter.

Hereinafter, the filtering device according to the embodiment of the present invention will be described with reference to FIG. This filtering device is for separating a reference signal from a frequency-multiplexed AC signal.

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

(Detection section)
The detection unit 1 is configured to acquire a plurality of detection results according to the integrated number of vibrations by performing numerical phase detection on the AC signal. The details of the operation of the detection unit 1 will be described later.

(Linear combination)
The linear combination unit 2 has a configuration in which a plurality of detection results obtained by the detection unit 1 are linearly combined using linear coefficients according to the filter characteristics. The details of the operation of the linear combination 2 will also be described later.

(Output section)
The output unit 3 is configured to output the result obtained by the linear combination in the linear combination unit 2. The output destination of the output unit 3 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 4 is configured to calculate the linear coefficient used in the linear combination unit 2 by using the relationship between the linear counts, the overall passing gain in the numerical phase detection, and the target filter characteristic. There is. The method for determining the linear coefficient will also be described later.

(AC signal)
The AC signal of this embodiment has a plurality of frequency components. These frequency components are arranged at positions symmetrical with respect to the frequency of the reference signal (signal to be separated). This point will also be described in detail later.

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

(Step SA-1 in FIG. 2)
First, the linear coefficient determination unit 4 determines the linear coefficient according to the target filtering characteristic. The determination of the linear coefficient is made using the relationship between the linear counts, the overall pass gain in numerical phase detection, and the desired filter characteristics. A specific example of determining the linear coefficient will be described later.

(Step SA-2 in FIG. 2)
Before, before, or at the same time as the above-mentioned step SA-1, the detection unit 1 performs numerical phase detection on the input AC signal. Thereby, in the present embodiment, it is possible to acquire a plurality of detection results according to the integrated vibration frequency. The details of this detection method will also be described later.

(Step SA-3 in FIG. 2)
Then, the linear combination 2 performs a linear combination of a plurality of detection results using linear coefficients according to the filter characteristics. This makes it possible to perform desired filtering on the AC signal.

(Step SA-4 in FIG. 2)
Then, the output unit 3 outputs the obtained filtering result.

(Principle of filtering device)
Hereinafter, the principle of the filtering device in the present embodiment will be described in detail, and then specific examples will be described.

In the related application of the present inventor (PCT / JP2017 / 009539) described above, the linear coupling of the detection results by a plurality of integrated vibration frequencies is utilized by utilizing the fact that the characteristics of the passing gain differ depending on the integrated vibration frequency in the numerical phase detection. It was shown that it is possible to have a passing gain characteristic that is not found in the detection by a single integrated vibration frequency. In the following description, conditions that can shorten the time required for separating a plurality of frequency components by utilizing this pass gain characteristic are presented. Hereinafter, the formula (**) in the related application will be referred to in the form of formula A- (**).

で与えられる。なお、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、ｎ＝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

For numerical phase detection by integration with n (n = natural number) times the demodulation angular frequency ω ₀

Given in. The same argument can be made when n = half-integer, but for the sake of simplicity, only the case where n = natural number is considered. Also, for simplification, the angular frequency will be changed thereafter.

Overall when linearly combining the detection results by the cumulative number of vibrations of multiple (m)

調では得られないような様々な周波数特性の通過利得を実現することができる。とりうるnに欠番があっても構わないが、ここでは簡単化のため欠番がないものとして扱う。

It is possible to realize the passing gain of various frequency characteristics that cannot be obtained by the key. It doesn't matter if there is a missing number in n, but for the sake of simplicity, it is treated as if there is no missing number.

とする。Ａ−（７）, Ａ−（８）より

であるため

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

And. From A- (7), A- (8)

Because

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.

が導かれるため

が成り立つ。すなわち

が成り立てば、（１）式が成り立つと言える。従って、Ａ−（１４）とＡ−（２１）

タが完成する。つまり、この式を解いて線形係数ａ_ｎを決定することにより、所望の検波を行うことができる。 From A- (7), A- (8)

To be guided

Is established. That is,

If, it can be said that Eq. (1) holds. Therefore, A- (14) and A- (21)

Ta is completed. That is, by determining the linear coefficients a _n by solving this equation, it is possible to perform the desired detection.

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。つまり、この式を解いて線形係数ａ_ｎを決定することにより、所望の検波を行うことができる。

Needs to hold. here

To hold

The filter is ready. That is, by determining the linear coefficients a _n by solving this equation, it is possible to perform the desired detection.

無数にある。従って除去したい周波数をうまく選べば先行の関連出願の方法よりも積算時間を短縮することが可能である。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。以下その方法を示す。

There are countless. Therefore, if the frequency to be removed is properly selected, the integration time can be shortened as compared with the method of the previous related application. This is effective when the frequency set to be used can be selected in advance such as broadband communication. 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。なお、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。つまり、κを基準信号（周波数多重信号から分離されるべき信号）の周波数とすると、基準信号の周波数を中心として対称となる周波数に他の信号を設定しておけば、それら他の信号を同時に除去することができる。また、多重化される周波数の間隔を等間隔とすれば、どの周波数を基準信号とした場合でもこの対称性を維持できるので好ましい。 Therefore

Will be. Than this,

It means that the components are also removed at the same time. This also holds true even when the integration period is a set of half-integers. In other words, assuming that κ is the frequency of the reference signal (the signal that should be separated from the frequency division signal), if another signal is set to a frequency that is symmetrical about the frequency of the reference signal, those other signals can be set at the same time. Can be removed. Further, if the intervals of the frequencies to be multiplexed are set to equal intervals, this symmetry can be maintained regardless of which frequency is used as the reference signal, which is preferable.

成り立つことを示す。一般性を失わないように

とおくと、

となる。従って、

の関係が成り立つ。さらに、前記したＡ−（４１）に従えば、実部の通過利得に

Show that it holds. Don't lose generality

If you say

Will be. Therefore,

The relationship holds. Further, according to A- (41) described above, the passing gain of the real part is obtained.

っていることを意味する。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いることが望ましい。さらに、先行の関連出願において示されるように、最低周波数／最高周波数（＜１）が、なるべく１に近い方が望ましい。そうすることにより、既述した関連出願の方式よりも、信号の検波（復調）処理に要する時間を更に短縮することができる。

It means that it is. In order to make good use of this relational expression, it is desirable that the frequencies are arranged at regular intervals. Further, as shown in the preceding related application, it is desirable that the minimum frequency / maximum frequency (<1) is as close to 1 as possible. By doing so, the time required for signal detection (demodulation) processing can be further shortened as compared with the method of the related application described above.

In the above description, _{the acquisition of G n} ^CC or G _n ^SS used for filtering corresponds to the example of "acquisition of a plurality of detection results according to the integrated number of vibrations", and is executed by the detection unit 1 in this example. NS. In addition, calculating the coefficient of the linear combination of the detection results according to the purpose of filtering (by computer or artificially) corresponds to the example of "determining the linear coefficient", and in this example, it is performed by the linear coefficient determining unit 4. Will be executed. Further, in the above example, the detection is performed by the linear combination 2 performing a linear combination of a plurality of detection results using the determined linear coefficient. The detection result is output by the output unit 3.

(Example 1)
For example, consider the transmission and reception of data using an AC signal that multiplexes five frequencies of 1001, 1002, 1003, 1004, and 1005 Hz. When the frequency is converted to 1, 2, 3, 4, 5 Hz by down conversion, the OFDM method requires 1 second to separate the signals from each other (see FIG. 3). Similarly, when the frequency is converted to 11, 12, 13, 14, 15 Hz, the required time is still 1 second, which is the same (see OFDM in Fig. 4). On the other hand, in the method according to the related application described above, detection can be performed in a time of 5 cycles each, and for each frequency, 5/11 = 0.4545…, 5/12 = 0.4166…, 5/13 = 0.3846, respectively. …, 5/14 = 0.3571…, 5/15 = 0.3333… seconds, which can significantly reduce the time (see Previous method in Fig. 4). However, when detecting a 13 Hz signal using the method described in the present embodiment, the condition for removing (that is, dropping) the 12 Hz signal is to drop the 14 Hz signal at the same time, and further drop the 11 Hz signal. When added, the 15 Hz signal also drops at the same time. Therefore, the required integration time is sufficient for vibration for three cycles. Similarly, when detecting a signal of 12, 14 Hz, vibration for 4 cycles is sufficient. When detecting a signal of 11, 15 Hz, vibration for 5 cycles is used in this example. Therefore, the required time is 5/11 = 0.4545…, 4/12 = 0.3333…, 3/13 = 0.2307…, 4/14 = 0.2857…, 5/15 = 0.3333… seconds (see Present method 1 in Fig. 5). ), The time required for demodulation as a whole is further shortened as compared with the related application described above, and as a result, there is an advantage that more data can be sent per unit time.

る。従来のOFDM法では、使用しない1〜10 Hzの周波数に対してもそれぞれ零点を与えるので積算振動回数を無駄に多く必要とするが、既述の関連出願および本出願では、その無駄を減らしたことにより短時間での信号の分離を可能にした。

NS. In the conventional OFDM method, zero points are given to frequencies of 1 to 10 Hz that are not used, so a large number of integrated vibrations is required unnecessarily. However, in the related application and the present application described above, the waste is reduced. This made it possible to separate signals in a short time.

(Example 2)
A high-order notch filter is effective in suppressing the influence of frequency fluctuations caused by signal changes. The conventional OFDM method does not have the function of a high-order filter, but the technique of the present embodiment has made this possible. In this embodiment, even if redundancy of a high-order filter function is added, demodulation in a shorter time than the OFDM method is generally possible depending on how the frequency is taken, and more information is sent accordingly. Will be able to.

従って9周期分のデータがそれぞれの周波数で必要になるため、各々の周波数で9/11 = 0.8181…, 9/12 = 0.7500…, 9/13 = 0.6923…, 9/14 = 0.6428…, 9/15 = 0.6000…秒の積算時間となるがこれらはいずれもOFDM法の場合の1秒より短い（図６のPrevious method 2参照）。 Here, consider a quadratic filter. The conditions of the multiplexed signal are the same as those in the first embodiment, and a case where the frequency is converted to 11, 12, 13, 14, 15 Hz is considered. In the method of the related application described above, in addition to one conditional expression (A- (14)) corresponding to one frequency to be extracted, the zero derivative becomes zero corresponding to the other four frequencies. Four conditional expressions

Therefore, data for 9 cycles is required for each frequency, so 9/11 = 0.8181…, 9/12 = 0.7500…, 9/13 = 0.6923…, 9/14 = 0.6428…, 9 / for each frequency. The integration time is 15 = 0.6000… seconds, but these are all shorter than 1 second in the case of the OFDM method (see Previous method 2 in Fig. 6).

On the other hand, when detecting a signal of 13 Hz using the second-order filter according to the method of the present embodiment, the condition that the 0-time differential and the 1-time differential of the passing gain at 12 Hz become zero is those of 14 Hz. The same applies to the relationship between 11 Hz and 15 Hz. Therefore, when detecting a 13 Hz signal, in addition to one conditional expression (A- (14)) corresponding to that frequency, 0 derivative is performed corresponding to two frequencies (11 Hz, 12 Hz). Each

12Hzの場合は、前記した３つの周波数とは13, 14, 15 Hzに相当し、11 Hzは13 Hzを落とす条件で落ちる。他方、抽出したい周波数が14Hzの場合は、前記した３つの周波数とは11, 12, 13 Hzに相当し、15 Hzは13 Hzを落とす条件で落ちる。 Similarly, in the case of detection at 12 and 14 Hz, one conditional expression (A- (14)) corresponding to the frequency and three conditional expressions in which the zero derivative is zero for each of the three frequencies.

In the case of 12 Hz, the above three frequencies correspond to 13, 14, 15 Hz, and 11 Hz drops under the condition of dropping 13 Hz. On the other hand, when the frequency to be extracted is 14 Hz, the above three frequencies correspond to 11, 12, 13 Hz, and 15 Hz drops under the condition of dropping 13 Hz.

Therefore, according to the method of the present embodiment described above, the time required for detection is 9/11 = 0.8181…, 7/12 = 0.5833…, 5/13 = 0.3846…, 7/14 = 0.5000…, 9 /, respectively. 15 = 0.6000… seconds, which is even shorter overall than the related application described above (see Present method 2 in FIG. 7).

The content of the present invention is not limited to each of the above-described embodiments. 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 linear coefficient is calculated by the linear coefficient determining unit 4, but for example, the linear coefficient may be a default value calculated in advance according to the purpose of filtering. Alternatively, the linear coefficient can be dynamically changed according to the purpose of filtering.

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 one functional element.

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

1 Detection part 2 Linear combination part 3 Output part 4 Linear coefficient determination part

Claims (6)

A filtering device for separating a reference signal from a frequency-multiplexed AC signal.
It has a detection part and a linear combination part.
The detection unit is configured to acquire a plurality of detection results according to the integrated number of vibrations by performing numerical phase detection on the AC signal.
The linear combination portion is configured to perform a linear combination of the plurality of detection results using linear coefficients according to the filter characteristics.
A filtering device in which the frequency components of the AC signal are arranged symmetrically with respect to the frequency of the reference signal. It also has an output section
The filtering device according to claim 1, 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 determining 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. Or the filtering device according to 2. A filtering method for filtering frequency-multiplexed AC signals.
A step of acquiring a plurality of detection results according to the integrated vibration frequency by performing numerical phase detection on the AC signal, and
It includes a step of filtering the AC signal by performing a linear combination of the plurality of detection results using a linear coefficient according to the filter characteristics.
It said frequency component in the AC signal, filtering methods are arranged at positions which are symmetrical about the frequency of criteria signals.
The relationship between the linear coefficient a linear coefficient determination method used for the filtering method according to claim 4, the passing the entire gain in the numerical phase detection, by using the filter characteristics of interest, A method for determining a linear coefficient, comprising a step of calculating the linear coefficient.
A computer program for causing a computer to perform each step according to claim 4 or 5.

Images