JP2014081352A - Frequency analysis device, signal processing apparatus using the device, and high-frequency measurement instrument using the apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a frequency analysis device capable of outputting a conversion result for a target frequency regardless of a sampling frequency.SOLUTION: A frequency analysis device includes: a sampling part 1 for sampling for an input analog signal to generate sampling data; a data conversion part 5 for converting the sampling data into re-sampling data that is sampling data corresponding to a target frequency of the analog signal; and an FFT process part 6 for applying high-speed Fourier transformation processing to the re-sampling data to output a conversion result for each frequency. The sampling data generated by the sampling part 1 is converted into re-sampling data corresponding to a target frequency of an analog signal, and high-speed Fourier transformation is applied to the re-sampling data. Therefore, it is possible to output a conversion result for a target frequency regardless of the sampling frequency.

Description

  The present invention relates to a frequency analysis device that performs fast Fourier transform processing, a signal processing device that uses the frequency analysis device, and a high-frequency measurement device that uses the signal processing device.

  2. Description of the Related Art Conventionally, a high-frequency measuring device that is arranged on a transmission line through which high-frequency power is transmitted and detects various high-frequency parameters has been developed (for example, Patent Document 1). The high-frequency measuring device detects a high-frequency current flowing through the transmission line and a high-frequency voltage generated in the transmission line, and calculates the amplitude and phase of the detected fundamental component of the voltage signal and current signal, respectively. Then, a high frequency parameter is calculated from these calculated data. Note that the high-frequency parameters are, for example, impedance, reflection coefficient, traveling wave power, reflected wave power, and the like.

  FIG. 11 is a diagram for explaining an example of a voltage signal processing device provided in a conventional high-frequency measurement device. The voltage signal processing apparatus shown in the figure calculates the amplitude and phase of the fundamental component of the voltage signal. The voltage signal processing apparatus includes a sampling unit 100 and an FFT processing unit 600 that perform frequency analysis, and a calculation unit 700 that performs calculation based on the frequency analysis result. In the present application, processing for a signal in which a plurality of frequency components are mixed and decomposition into a spectrum for each frequency is referred to as “frequency analysis”. A current signal processing device that performs signal processing of current signals has the same configuration.

The sampling unit 100 performs sampling. The sampling unit 100 receives the detected voltage signal v, performs N-point sampling (N is a power of 2) at the sampling frequency f _s , and samples N pieces of sampled data x _i (i = 0, 1). ,..., N−1) are output to the FFT processing unit 600.

The FFT processing unit 600 performs a fast Fourier transformation process. The FFT processing unit 600 performs a fast Fourier transform process on the sampling data x _i input from the sampling unit 100, and the conversion result X _k (k = 0, 1,..., N / 2-1) is calculated by the calculation unit 700. Output to.

The calculation unit 700 calculates the amplitude and phase of the fundamental wave component of the voltage signal v. Based on the conversion result X _k input from the FFT processing unit 600, the calculation unit 700 detects the one having the largest spectrum power | X _k |. If the spectrum power | X _a | when k = a is maximized, the calculation unit 700 calculates and outputs the amplitude and phase of the fundamental component of the voltage signal v based on the conversion result X _a .

JP 2004-93257 A

The conversion result X _k output by the FFT processing unit 600 by the FFT processing is discrete, and the conversion result X _k is output only for a frequency that is an integral multiple of the resolution of the sampling frequency f _s . Accordingly, when the frequency of the fundamental wave component (hereinafter referred to as “fundamental frequency”) is an integer multiple of the resolution of the sampling frequency f _s , the conversion result X _k for the fundamental frequency is output. Is not an integral multiple of the resolution of the sampling frequency f _s , the conversion result X _k for the fundamental frequency is not output, but is distributed and output in the conversion result X _k for the frequencies before and after the fundamental frequency.

In this case, since the frequency (frequency f _a when k = _a ) at which the spectrum power | X _k | becomes maximum does not match the fundamental frequency, the amplitude and phase calculated by the calculation unit 700 based on the conversion result X _a Does not accurately indicate the amplitude and phase of the fundamental component.

  The present invention has been conceived under the circumstances described above, and it is an object of the present invention to provide a frequency analyzer that can output a conversion result for a target frequency regardless of the sampling frequency. Yes.

  In order to solve the above problems, the present invention takes the following technical means.

  The frequency analysis apparatus provided by the first aspect of the present invention includes a sampling unit that performs sampling on an input analog signal to generate sampling data, and the sampling data is a target of the analog signal. Data conversion means for converting into resampling data that is sampling data corresponding to the frequency, and FFT processing means for performing fast Fourier transform processing on the resampling data and outputting a conversion result for each frequency It is characterized by.

  The “target frequency” is a frequency to be subjected to frequency analysis. For example, when performing frequency analysis of the fundamental wave component, “target frequency” is the fundamental frequency, and when performing frequency analysis of the nth harmonic component, “target frequency” is the frequency of the nth harmonic. is there. “Sampling data corresponding to the target frequency” means sampling data (resampling data) sampled at a sampling frequency (resampling frequency) when the target frequency is an integral multiple of the resolution of the sampling frequency. ).

  In a preferred embodiment of the present invention, the apparatus further comprises resampling frequency calculating means for calculating a resampling frequency that is a sampling frequency corresponding to the target frequency, wherein the data converting means includes the sampling frequency of the sampling means and Conversion is performed based on the resampling frequency.

  The “sampling frequency corresponding to the target frequency” is a sampling frequency (resampling frequency) when the target frequency is an integral multiple of the resolution of the sampling frequency.

In a preferred embodiment of the present invention, when the sampling frequency is f _s and the resampling frequency is f _r , the data conversion means is configured to output the sampling data x _i (i = 0, 1,..., N−1) is converted into the resampling data r _n (n = 0, 1,..., N−1).

  In a preferred embodiment of the present invention, a second FFT processing unit that performs a fast Fourier transform process on the sampling data and outputs a conversion result for each frequency, and a frequency output by the second FFT processing unit Frequency estimation means for estimating the target frequency based on each conversion result.

  In a preferred embodiment of the present invention, the frequency estimation means detects an approximate frequency that is a frequency when the spectrum power, which is the magnitude of the conversion result output from the second FFT processing means, reaches a maximum value. Detecting means, comparing means for comparing a spectral power for a frequency obtained by adding a frequency resolution to the approximate frequency, and a spectral power for a frequency obtained by subtracting the frequency resolution from the approximate frequency; and the comparison for the maximum value. Ratio calculating means for calculating the ratio of the spectrum power determined to be larger by the means, and estimating the target frequency based on the ratio calculated by the ratio calculating means.

  In a preferred embodiment of the present invention, the frequency estimation means further comprises storage means for storing in advance a correspondence relationship between the correction amount from the approximate frequency and the ratio, and the comparison means provides frequency resolution. When it is determined that the spectrum power of the added frequency is larger, the frequency obtained by multiplying the correction amount corresponding to the ratio by the frequency resolution and added to the approximate frequency is estimated as the target frequency, When the comparison means determines that the spectrum power of the frequency obtained by subtracting the frequency resolution is larger, the frequency obtained by multiplying the correction amount corresponding to the ratio by the frequency resolution and subtracting the frequency from the approximate frequency, Estimated as the target frequency.

In a preferred embodiment of the present invention, the frequency estimation means calculates an approximate frequency that is a frequency when the spectrum power, which is the magnitude of the conversion result output from the second FFT processing means, reaches _a maximum value sa. Comparison comparing detection means for detecting, spectral power s _{a + 1} for a frequency obtained by adding frequency resolution to the approximate frequency, and spectral power s _a-1 for a frequency obtained by subtracting the frequency resolution from the approximate frequency. And when the comparison means determines that s _{a + 1} ≧ s _a-1 ,
A frequency obtained by multiplying Δk calculated by the above frequency resolution and adding to the approximate frequency is estimated as the target frequency, and s _{a + 1} <s _a-1 is determined by the comparison unit Is
Is multiplied by the frequency resolution and subtracted from the approximate frequency to estimate the target frequency.

  In a preferred embodiment of the present invention, a frequency detecting means for detecting the target frequency is further provided.

  In a preferred embodiment of the present invention, the target frequency is a frequency of a fundamental wave component of the analog signal.

  In a preferred embodiment of the present invention, the data conversion means and the FFT processing means are provided for each of a plurality of target frequencies.

  The signal processing device provided by the second aspect of the present invention includes a frequency analysis device provided by the first aspect of the present invention and a conversion result for the target frequency output by the FFT processing means. And an arithmetic means for calculating the amplitude and phase of the frequency component of interest of the analog signal.

  The high-frequency measuring device provided by the third aspect of the present invention is arranged on a transmission line through which high-frequency power is transmitted, and detects a high-frequency voltage signal and a high-frequency current signal. A signal processing apparatus provided by the aspect, the voltage signal processing apparatus calculating the amplitude and phase of the target frequency component of the high-frequency voltage signal, and the signal processing apparatus provided by the second aspect of the present invention A current signal processing device that calculates an amplitude and a phase of the target frequency component of the high-frequency current signal, and an amplitude of the target frequency wave component of the high-frequency voltage signal output by the voltage signal processing device And the phase and the amplitude and phase of the target frequency component of the high-frequency current signal output from the current signal processing device. Characterized in that an arithmetic unit for calculating the data.

  According to the present invention, the sampling data generated by the sampling means is converted into resampling data corresponding to the frequency targeted for the analog signal, and fast Fourier transform processing is performed on the resampling data. Therefore, the conversion result for the target frequency can be output regardless of the sampling frequency.

  Other features and advantages of the present invention will become more apparent from the detailed description given below with reference to the accompanying drawings.

It is a functional block diagram for demonstrating the frequency analyzer which concerns on 1st Embodiment. It is a figure for _{demonstrating} the estimation method of the frequency fin. It is a figure for demonstrating the relationship between a spectrum power ratio and a correction amount. It is a figure for demonstrating sampling data and resampling data. It is a figure for demonstrating the high frequency measuring apparatus which concerns on 1st Embodiment. It is for demonstrating the simulation result which input the voltage signal into the voltage signal processing apparatus. It is a figure showing the amount of frequency deviation and spectrum power which were normalized. It is a functional block diagram for demonstrating the frequency analyzer which concerns on 2nd Embodiment. It is a functional block diagram for demonstrating the frequency analyzer which concerns on 3rd Embodiment. It is a functional block diagram for demonstrating the frequency analyzer which concerns on 4th Embodiment. It is a figure for demonstrating an example of the voltage signal processing apparatus with which the conventional high frequency measuring device is provided.

  Hereinafter, embodiments of the present invention will be specifically described with reference to the drawings, taking as an example a voltage signal processing apparatus including a frequency analysis apparatus according to the present invention.

  FIG. 1 is a functional block diagram for explaining the frequency analysis device according to the first embodiment, and shows a voltage signal processing device including the frequency analysis device. A voltage signal processing apparatus A shown in the figure receives a voltage signal v that is an analog signal obtained by detecting a high-frequency voltage generated in a transmission line, and calculates the amplitude and phase of a fundamental wave component of the voltage signal v. The voltage signal processing apparatus A includes a sampling unit 1, an FFT processing unit 2, a frequency estimation unit 3, a resampling frequency calculation unit 4, a data conversion unit 5, an FFT processing unit 6, and a calculation unit 7 that constitute a frequency analysis device. It has.

The sampling unit 1 performs sampling. The sampling unit 1 performs N-point sampling (N is a power of 2, for example, “2048” in the present embodiment) with respect to the input voltage signal v at the sampling frequency f _s and is sampled. N sampling data x _i (i = 0, 1,..., N−1) are output to the FFT processing unit 2 and the data conversion unit 5. The sampling frequency f _s is set to a predetermined value. The sampling unit 1 also performs quantization, and the sampling data x _i is digital data.

The FFT processing unit 2 performs a fast Fourier transform process. The FFT processing unit 2 performs fast Fourier transform processing on the sampling data x _i input from the sampling unit 1, and outputs the conversion result X _k to the frequency estimation unit 3. The conversion result X _k is calculated by the following equation (1). Note that a low-pass filter may be provided before the FFT processing unit 2 to remove high-frequency components.

The frequency estimator 3 estimates the fundamental frequency of the voltage signal v. First, the frequency estimation unit 3 calculates a frequency at which the spectrum power | X _k | is maximum based on the conversion result X _k input from the FFT processing unit 2. When N-point sampling is performed at the sampling frequency f _s , the frequency resolution f ₁ is f ₁ = f _s / N. Further, the spectrum power of the frequency f _k (= k · f ₁ ) is | X _k |. If the spectrum power | X _a | when k = a is maximized, the frequency at this time is f _a (= a · f ₁ ). Spectral power | X _{a + 1} | at frequency f _{a + 1} (= (a + 1) · f ₁ ) or Spectral power at frequency f _a-1 (= (a-1) · f ₁ ) | X _a-1 | is the next largest after the spectral power | X _a |. The frequency estimation unit 3 calculates the fundamental frequency of the voltage signal v based on the maximum spectral power | X _a | and the next largest spectral power | X _{a + 1} | (or spectral power | X _a-1 |). to estimate the f _in.

Figure 2 is a diagram for explaining a method of estimating the fundamental frequency f _in, it shows a spectrum power of each frequency.

FIG. 5A shows the case of | X _{a + 1} | ≧ | X _a-1 |. In this case, the fundamental frequency f _in, a value close to the frequency f _a of between frequency _{f a (= a · f 1} ) and the frequency _{f a + 1 (= (a} + 1) · f 1). That is, (shown by dashed lines in FIG.) Spectral power should appear in a position of the fundamental frequency f _in have appeared are dispersed in the position of the frequency f _a and the frequency f _{a + 1.} As the fundamental frequency f _in is close to the frequency f _a, spectral power | X _a | becomes larger, the spectral power | X a _{+ 1} | is small. Therefore, the spectral power | X _a | and spectral power | X a _{+ 1} | from and can determine the difference between the fundamental frequency f _in the frequency f _a. In this embodiment, a correction amount Δk that defines the difference as Δk · f ₁ is defined, and a spectrum power ratio R (= | X _{a +)} that is a ratio of the spectrum power | X _{a + 1} | to the spectrum power | X _a | ₁ | / | X _a |), the correction amount Δk is calculated.

  FIG. 3 is a diagram for explaining the relationship between the spectral power ratio R and the correction amount Δk.

  The figure shows the relationship between the spectral power ratio R and the correction amount Δk when the fundamental frequency of the voltage signal v is changed around 13.56 MHz. Specifically, the spectral power ratio R is calculated by changing the correction amount Δk by 0.01 and is tabulated and complemented by linear interpolation. The frequency estimation unit 3 calculates the correction amount Δk from the spectral power ratio R by linear interpolation based on the table (hereinafter referred to as “conversion table”), and outputs the correction amount Δk to the resampling frequency calculation unit 4.

_{| X a + 1 | <|} X a-1 | if, as shown in FIG. 2 (b), the fundamental frequency f _in, the frequency _{f a-1 (= (a} -1) · f 1) and the frequency It becomes a value close to the frequency f _a between f _a (= a · f ₁ ). That is, (shown by dashed lines in FIG.) Spectral power should appear in a position of the fundamental frequency f _in have appeared are dispersed in the position of the frequency f _a-1 and the frequency f _a. As the fundamental frequency f _in is close to the frequency f _a, spectral power | X _a | becomes larger, the spectral power | X _a-1 | is small. Therefore, the spectral power | X _a | and spectral power | X _a-1 | from and can calculate the difference between the fundamental frequency f _in the frequency _{f a (Δk · f 1)} . In this case, the relationship between the spectral power ratio R (= | X _a-1 | / | X _a |) and the correction amount Δk is the same as that in FIG. 3, so the frequency estimation unit 3 uses the same conversion table, The correction amount Δk is calculated from the spectral power ratio R by linear interpolation.

The frequency estimation unit 3 records a conversion table for each basic frequency of the voltage signal v that can be input. Note that the relationship between the spectral power ratio R and the correction amount Δk is the same regardless of the frequency, and the same upward conversion curve is used as in FIG. Also good. Further, the correction amount Δk may be calculated by a simple calculation formula (Δk = 0.5R) by approximating the relationship between the spectrum power ratio R and the correction amount Δk with a straight line indicated by a broken line in FIG. In these cases, the accuracy of the correction amount Δk is deteriorated, but the storage capacity for the conversion table can be reduced. Further, the correction amount Δk may be calculated by another calculation method. Further, instead of using the spectral power ratio R, the correction amount Δk is calculated using the difference between the spectral power | X _a | and the spectral power | X _{a + 1} | (or spectral power | X _a-1 |). You may do it.

Is the fundamental frequency f _in (hereinafter, referred to as "estimated frequency f _in".) Was estimated by the frequency estimation unit 3, from the correction amount .DELTA.k, it becomes: (2). The frequency estimation unit 3 outputs the calculated correction amount Δk to the resampling frequency calculation unit 4.

Returning to FIG. 1, the resampling frequency calculation unit 4, and calculates the resampling frequency f _r is the sampling frequency corresponding to the estimated frequency f _in. Resampling frequency calculator 4 calculates the resampling frequency f _r on the basis of the correction amount Δk inputted from the frequency estimation unit 3, and outputs the data conversion unit 5. The frequency estimation unit 3 to the resampling frequency calculation unit 4 are also input with information indicating the value of a and which of | X _{a + 1} | and | X _a-1 | is greater.

If an integral multiple of the resolution of the estimated frequency f _in resampling frequency f _r, by FFT processing sampling data obtained by sampling the voltage signal v at the resampling frequency f _r, the conversion result of the estimated frequency f _in can do. In this embodiment, the resampling frequency f _r greater than the sampling frequency f _s, in order to be as close as possible, the following equation (3), calculates the resampling frequency f _r. The method of calculating the resampling frequency f _r is not limited to this. For example, the denominator of the following equation (3) may be “a”, “a−1”, “a + 1”, or other integers.

The above (2) and (3), f _r can be expressed by the following equation (4). Therefore, the calculation instead of entering a correction amount Δk from the frequency estimation unit 3, the (2) Enter the estimated frequency f _in calculated based on the formula, the resampling frequency f _r on the basis of the following equation (4) You may make it do.

The data conversion unit 5 converts sampling data. Data converter 5 is input from the sampling unit 1, the sampling frequency f _s of sampled sampling data _{x i (i = 0,1, ...} , N-1) if the, sampled at the resampling frequency f _r To the resampling data r _n (n = 0, 1,..., N−1). Specifically, the data conversion unit 5 includes sampling data x _i (i = 0, 1,..., N−1) input from the sampling unit 1 and a resampling frequency f input from the resampling frequency calculation unit 4. _r, and on the basis of the preset and has the sampling frequency f _s, is calculated by the following formula (5) the nature using the sinc function, the resampling data _{r n (n = 0,1, ...} , n-1) a doing.

  The calculation method of the above equation (5) will be described below.

The equation for Fourier transforming f (t) is the following equation (6), and the equation for inverse Fourier transforming F (ω) is the following equation (7).

Substituting the above equation (6) into the above equation (7),

When the above equation (8) is rewritten into discrete display, the following equation (9) is obtained. The following equation (9) means that f (t) is reproduced from the sampled discrete data f (k) using convolution of a delta function. That is, an interpolated value at an arbitrary time can be expressed using the sampled discrete data f (k).

  As a sampling function, a Sinc function that is an approximate function of the delta function δ (t) can be used.

When the frequency spectrum of the continuous waveform f (t) is limited to W [Hz] or less, it is completely represented by a sequence of f (t) values sampled every 1 / (2 W) seconds from the sampling theorem. . Therefore, when the sampling function is defined as a Sinc function from the above equation (9), it is expressed by the following equation (10).

  A method for deriving the above equation (10) will be described below.

f (t) was sampled every time interval T f _s (t) is expressed by the following equation (11).

Referring to the relationship of the following equation (12) that is the formula of the superposition integral theorem, when f _s (t) of the above equation (11) is Fourier transformed, F _s (ω) is as shown in the following (13).

F _s (ω) is in the interval _{(-ω 0 / 2~ω 0/2} ), is a periodic function equal to (1 / T) F (ω ). Note that the frequency band of f (t) is limited to (−W to W) [Hz]. By using the square window function Pω _c (ω) shown in the following equation (14), 2πW = ω _{As c} , the following equation (15) is obtained.

When the inverse Fourier transform is performed on the above equation (15), f (t) is expressed by the following equation (16) with reference to the formula of the superposition integral theorem of the above equation (12).

Here, a Fourier transform pair can be calculated as follows.

When the Fourier transform pair of the above equation (17) is used, the above equation (16) becomes the following equation (18) from ω _c = 2πW and T = 1 / (2W).

  As described above, data of an arbitrary time can be restored by using discrete data and a Sinc function.

In the above equation (18) (the above equation (10)), 2W = f _s and arbitrary time t = (1 / f _r ) i, the following equation (19) is obtained. Since the Sinc function is an even function, Sinc (x) = Sinc (−x).

From the above (19), discrete data f (n / f _s) of the sampling data _{x i (i = 0,1, ...} , N-1) when that resampling data r _n (n = 0, 1 ,..., N−1) can be calculated by the above equation (5).

From the above equation (3), f _s / f _r = a / (a + Δk) (or a / (a−Δk)), so the above equation (5) can be expressed by a and Δk. Therefore, instead of entering the resampling frequency f _r from the resampling frequency calculator 4, the correction amount Δk from the frequency estimation unit 3, the values of a, and | X a _{+ 1} | and | X _a-1 | which of large or a type information indicating, may be calculated resampling data r _n.

FIG. 4 is a diagram for explaining the sampling data x _i and the resampling data r _{n obtained} by converting the sampling data x _i by the data converter 5.

In the figure, the points indicated by diamonds indicate sampling data x _i (i = 0, 1,..., N−1) obtained by sampling a sine wave signal at a predetermined sampling frequency f _s . Based on the sampling data x _i , the resampling frequency _fr is calculated by the FFT processing unit 2, the frequency estimation unit 3, and the resampling frequency calculation unit 4. That are represented by squares, the resampling frequency f _r resampled data converted by the data conversion unit 5 based on _{r n (n = 0,1, ...} , N-1) shows a. Resampling data r _n are also located in the same sine wave on the sampling data x _i. Further, since the resampling frequency f _r is greater than the sampling frequency f _s, distance resampled data r _n is narrower than the interval of the sampling data x _i.

Returning to FIG. 1, the FFT processing unit 6 performs fast Fourier transform processing. FFT processing section 6 performs fast Fourier transform processing on resampling data r _n inputted from the data converter 5, the conversion result _{R k (k = 0,1, ...} , N / 2-1) the operation Output to unit 7. The conversion result R _k is calculated by the following equation (20).

The calculation unit 7 calculates the amplitude and phase of the fundamental wave component of the voltage signal v. Based on the conversion result R _k input from the FFT processing unit 6, the calculation unit 7 detects the one having the maximum spectrum power | R _k |. When the resampling frequency _fr is calculated by the first expression of the above expression (3) (that is, when | X _{a + 1} | ≧ | X _a-1 |), the spectral power when k = a | Since R _a | is maximized, the calculation unit 7 calculates and outputs the amplitude and phase of the fundamental component of the voltage signal v based on the conversion result R _a . Amplitude | R _a | to be calculated based on the phase θ from that the real part of R _a Re (R _a) and an imaginary part Im (R _a), is calculated by the following equation (21).

On the other hand, when the resampling frequency _fr is calculated by the second expression of the above expression (3) (that is, in the case of | X _{a + 1} | <| X _a-1 |), when k = a−1 R _a-1 | | spectral power of the so becomes maximum, the arithmetic unit 7 calculates and outputs the amplitude and phase of the fundamental wave component of the voltage signal v based on the conversion result R _a-1.

  FIG. 5 is a diagram for explaining a high-frequency measuring device including the voltage signal processing device A. The high-frequency measuring device shown in the figure includes a voltage signal processing device A, a current signal processing device B, a high-frequency detection device C, and an arithmetic device D.

  The high-frequency detection device C is arranged on the transmission line E through which high-frequency power is transmitted, and detects a high-frequency current flowing through the transmission line E and a high-frequency voltage generated in the transmission line E. The high frequency detection device C outputs the detected voltage signal v, which is an analog signal, to the voltage signal processing device A, and outputs the detected current signal i, which is an analog signal, to the current signal processing device B. The current signal processing device B receives the current signal i from the high frequency detection device C and calculates the amplitude and phase of the fundamental wave component of the current signal i. The configuration of the current signal processing device B is the same as that of the voltage signal processing device A (see FIG. 1). The arithmetic unit D uses various amplitudes and phases of the fundamental component of the voltage signal v calculated by the voltage signal processor A and the amplitude and phase of the fundamental component of the current signal i calculated by the current signal processor B. Calculate the parameters.

In this embodiment, the resampling data r _n outputted from the data converting unit 5 (n = 0,1, ..., N-1) is adapted to sampling data when sampled at the resampling frequency f _r. Since the estimated frequency f _in (estimated fundamental frequency of the voltage signal v) is an integral multiple of the resolution of the resampling frequency _fr , the conversion result R _k (k = 0, 1) output by the FFT processing unit 6 , ..., the N / 2-1), which include the estimated frequency f _in. Therefore, the calculation unit 7 can accurately calculate the amplitude and phase of the fundamental wave component of the voltage signal v.

  FIG. 6 is a diagram for explaining a simulation result when the voltage signal v is input to the voltage signal processing apparatus A.

A voltage signal v having a frequency of 13.56 MHz was input to the sampling unit 1 with a phase shifted by 30 °. Sampling frequency f _s = 125 MHz and sampling point number N = 2048. FIG middle column describes a phase calculated by the estimated frequency f _in and the arithmetic unit 7 which is estimated by the frequency estimation unit 3 theta, column of the FIG right, the actual value (FIG left Column)). As shown in the figure, the maximum frequency error was about 40 Hz, and the maximum phase error was about 0.12 °. A sufficiently practical value can be calculated.

  In the present embodiment, the case where the frequency estimation unit 3 calculates the correction amount Δk using the spectral power ratio R and the conversion table has been described. However, the present invention is not limited to this, and the correction amount Δk is calculated by another method. You may do it. An embodiment in which the frequency estimation unit 3 calculates the correction amount Δk using a calculation formula will be described below.

Also in this case, the frequency estimation unit 3 determines the maximum spectral power | X _a | and the next largest spectral power | X _{a + 1} | (or based on the conversion result X _k input from the FFT processing unit 2. Spectral power | X _a-1 |) is detected. Hereinafter, the spectral power | X _k | is described as s _k .

In this embodiment, since the sampling data x _i is not multiplied by a special window function, the square wave shown in the following equation (22) is multiplied as a window function.

When the above equation (22) is Fourier transformed, the following equation (23) is obtained, and when ω = 2πf, the following equation (24) is obtained. Note that normalization is performed so that the maximum value is “1” when f = 0.

When the frequency deviation from the fundamental frequency f _in and those normalized [delta], S ([delta]) that the spectral power of the frequency spectrum normalized corresponding thereto may be expressed by the following equation (25). [Delta] = 0 becomes the time of the fundamental frequency f _in, is maximized at this time S (0) = 1.

When the maximum spectral power is s _a and the next largest spectral power is s _{a + 1} (s _{a + 1} ≧ s _a-1 ), when δ = −Δk corresponds to the frequency f _a , S (− .delta.k) is obtained by normalizing the s _a reference (FIG. 7 (a)). Further, when δ = 1−Δk corresponds to the frequency f _{a + 1} , S (1−Δk) is obtained by normalizing s _{a + 1} . Note that l is a constant for normalization. Therefore, the following formulas (26) and (27) are derived from the above formula (25), and the following formula (28) is derived.

When the maximum spectral power is s _a and the next largest spectral power is s _a-1 (s _{a + 1} <s _a-1 ), when δ = Δk corresponds to the frequency f _a , S (Δk) Becomes _a normalized version of sa (see FIG. 7B). Further, when δ = Δk−1, this corresponds to the frequency f _a−1 , and S (Δk−1) is obtained by normalizing s _a−1 . Therefore, the following formulas (29) and (30) are derived from the above formula (25), and the following formula (31) is derived.

The frequency estimation unit 3 uses the above equation (28) when s _{a + 1} ≧ s _a−1 , and uses the above equation (31) when s _{a + 1} <s _a−1 . A compensation amount Δk is calculated. The basic frequency f _in can be calculated from the above equation (2).

Further, in the first embodiment has been estimated estimated frequency f _in the frequency estimation unit 3 is not limited thereto, may be detected to estimate the frequency f _in the other way. The case of detecting the estimated frequency f _in the other way as the second embodiment will be described below.

FIG. 8 is a functional block diagram for explaining the frequency analysis device according to the second embodiment. In the figure, the same or similar elements as those of the voltage signal processing apparatus A (see FIG. 1) according to the first embodiment are denoted by the same reference numerals. As shown in FIG. 8, the voltage signal processing device A1 is different from the voltage signal processing device A according to the first embodiment _in that the estimated frequency fin is detected from the voltage signal v.

The frequency detector 8 detects the fundamental frequency of the input signal. Frequency detection unit 8 is input a voltage signal v, detecting the estimated frequency f _in the fundamental frequency of the voltage signal v, and outputs the detected estimated frequency f _in the resampling frequency calculator 4 '. The frequency detection method may be a conventional detection method, which counts pulses between points where the AC signal crosses the zero level, and calculates the frequency by taking the reciprocal of the count value. There may be a method using PLL (Phase Locked Loop). The frequency detection by the frequency detection unit 8 is performed at the same timing as the sampling by the sampling unit 1. Instead of providing the frequency detection unit 8 in the voltage signal processing device A1, the basic frequency of the voltage signal v is detected by the frequency detection device outside the voltage signal processing device A1, and the resampling frequency calculation unit 4 ′ You may make it input.

Resampling frequency calculator 4 'calculates the resampling frequency f _r is input to the estimated frequency f _in the frequency detecting unit 8. Resampling frequency calculator 4 'may be made of any of the above (4) equation, to calculate the resampling frequency f _r. "A" of the denominator may be the estimated frequency f _in to use the nearest integer divided by the frequency resolution _{f 1 (= f s / N} ).

In the second embodiment, like the first embodiment, the estimated frequency f _in resampling frequency f _r which corresponds is calculated, resampling data output from the data conversion unit 5 r _{n (n} = 0,1 , ..., the sampling data in the case where N-1) is sampled at the resampling frequency f _r. Therefore, also in 2nd Embodiment, there can exist an effect similar to 1st Embodiment.

In the above first and second embodiments, the description has been given of the case of converting the sampling data x _i for the data converter 5 is input from the sampling unit 1 to the resampling data r _n, not limited to this. For example, the sampling unit 1 is configured to perform sampling at the resampling frequency f _r which is calculated by the resampling frequency calculator 4 (4 ') may not be provided with the data converter 5. However, as the sampling unit 1 can correspond to the resampling frequency f _r which is calculated by the resampling frequency calculator 4 (4 '), it is necessary to considerably higher clock frequency. Reducing the precision of the resampling frequency f _r in accordance with the clock frequency, decrease the accuracy of the operation result of the arithmetic unit 7. With the data conversion unit 5, irrespective of the performance of the sampling unit 1 can generate the appropriate resampling data r _n.

In the first and second embodiments, the case where the frequency analysis device according to the present invention is used in a voltage signal processing device has been described. However, the present invention is not limited to this. The frequency analysis apparatus according to the present invention can also be used when performing frequency analysis of any AC signal. For example, in the voltage signal processing apparatus A (see FIG. 1), instead of calculating the amplitude and phase in the calculation unit 7, the conversion result R _k (k = 0, 1,..., N / 2) output from the FFT processing unit 6 -1) may be displayed as a spectrum.

  In the first and second embodiments, the case where the voltage signal processing apparatus A (A1) calculates the amplitude and phase of the fundamental wave component of the voltage signal v has been described. However, the present invention is not limited to this. The voltage signal processing device A (A1) may calculate the amplitude and phase of the harmonic component of the voltage signal v.

For example, when calculating the amplitude and phase of the nth harmonic component, the calculation unit 7 corresponds to a frequency component of n times the fundamental frequency in the conversion result R _k input from the FFT processing unit 6. What is necessary is just to perform calculation using. That is, when the resampling frequency _fr is calculated by the first expression (that is, in the case of | X _{a + 1} | ≧ | X _a-1 |), the spectrum when k = a is obtained. The power | R _a | is maximized, and the frequency at this time is the fundamental frequency. Therefore, the calculating part 7 should just calculate based on conversion result _Rna . Specifically, the amplitude is calculated based on | R _na |, and the phase θ is calculated by replacing “R _a ” with “R _na ” in the equation (21). On the other hand, when the resampling frequency _fr is calculated by the second expression of the above expression (3) (that is, in the case of | X _{a + 1} | <| X _a-1 |), when k = a−1 Spectrum power | R _a-1 | becomes maximum, and the frequency at this time is the fundamental frequency. Therefore, the calculation unit 7 may perform the calculation based on the conversion result Rn _(a-1) . Specifically, the amplitude is calculated based on | R _{n (a-1)} |, and the phase θ is calculated by replacing “R _a ” with “R _{n (a-1)} ” in the above equation (21). .

When the amplitude and phase of the harmonic component are calculated only by the calculation processing of the calculation unit 7 described above, if there is an error in the fundamental frequency estimated by the frequency estimation unit 3 (frequency detection unit 8), higher-order harmonic components The accuracy of the result of the calculation will deteriorate. Therefore, the frequency estimation unit 3 may calculate the correction amount Δk using only the conversion result X _k input from the FFT processing unit 2 in the frequency band corresponding to the harmonic component (first embodiment). In case of form). In this case, the correction amount Δk is intended for the harmonic frequencies, because it is converted into resampled data r _n based on this calculation result of the accuracy in the calculation unit 7 is improved. Note that a band pass filter may be provided in the previous stage of the FFT processing unit 2 so that only the harmonic component is input to the FFT processing unit 2. In the case of the second embodiment, the frequency detecting unit 8 detects the harmonic frequencies instead of the fundamental frequency may be output to the resampling frequency calculator 4 'as the estimated frequency f _in.

  Next, a voltage signal processing device capable of calculating the amplitude and phase of the fundamental component and the amplitude and phase of the harmonic component will be described as a third embodiment.

  FIG. 9 is a functional block diagram for explaining the frequency analysis apparatus according to the third embodiment. In the figure, the same or similar elements as those of the voltage signal processing apparatus A (see FIG. 1) according to the first embodiment are denoted by the same reference numerals. As shown in FIG. 9, the voltage signal processing device A2 has a configuration for calculating the amplitude and phase of the harmonic component (a resampling frequency calculation unit 4 ″, a data conversion unit 5 ′, which is a configuration surrounded by a broken line in FIG. 9), In the first embodiment, an FFT processing unit 6 ′ and a calculation unit 7 ′) are added, and the frequency estimation unit 3 ′ switches and outputs two types of correction amounts Δk and Δk ′. This is different from the voltage signal processing apparatus A.

The frequency estimation unit 3 ′ calculates a correction amount Δk for the fundamental frequency using the conversion result X _k and outputs the correction amount Δk to the resampling frequency calculation unit 4, and the frequency band corresponding to the harmonic component in the conversion result X _k Is used to calculate the correction amount Δk ′ for the harmonic frequency and switch the state to be output to the resampling frequency calculation unit 4 ″. Note that a filter is provided in the previous stage of the FFT processing unit 2 as a low-pass filter. You may make it switch the state which allows only a fundamental frequency component to pass, and the state which allows only a harmonic component to pass as a band pass filter.

The resampling frequency calculator 4 ″, the data converter 5 ′, the FFT processor 6 ′, and the calculator 7 ′ are respectively the resampling frequency calculator 4, the data converter 5, the FFT processor 6, and the calculator. 7 to be the same functional blocks. resampling frequency calculator 4 "on the basis of the 'correction amount Δk input from' frequency estimating unit 3 calculates the resampling frequency f _r '. The re-sampling frequency calculation unit 4 ″ is during the period when the correction amount Δk ′ is not input from the frequency estimation unit 3 ′ (while the frequency estimation unit 3 ′ inputs the correction amount Δk to the resampling frequency calculation unit 4). The previous resampling frequency f _r ′ held is output (the same applies to the resampling frequency calculation unit 4), and the data conversion unit 5 ′ converts the resampling data r _n converted based on the resampling frequency f _r ′. ', The FFT processing unit 6' performs fast Fourier transform processing on the resampling data r _n 'and outputs a conversion result R _k ', and the calculation unit 7 'generates a harmonic based on the conversion result R _k '. Calculate the amplitude and phase of the wave component.

  When processing a plurality of harmonic components (for example, the third harmonic and the fifth harmonic) in addition to the fundamental wave component, a necessary number of configurations surrounded by a broken line shown in FIG. 9 are provided to estimate the frequency. The unit 3 ′ may calculate the correction amount Δk ′ for each harmonic frequency, and switch and output it.

In the case of the third embodiment, since the frequency estimation unit 3 ′ alternately calculates the correction amount Δk and the correction amount Δk ′ and switches the output, the resampling frequency _fr and the resampling frequency _fr ′ are fixed. There is a period. When the frequency of the voltage signal v varies, the accuracy of the calculation result in this fixed period is deteriorated. A voltage signal processing apparatus capable of calculating the correction amount Δk and the correction amount Δk ′ simultaneously will be described below as a fourth embodiment.

  FIG. 10 is a functional block diagram for explaining the frequency analysis device according to the fourth embodiment. In the figure, the same or similar elements as those of the voltage signal processing apparatus A (see FIG. 1) according to the first embodiment are denoted by the same reference numerals. As shown in FIG. 10, the voltage signal processing device A3 has a configuration for calculating the amplitude and phase of the harmonic component (an FFT processing unit 2 ′, a frequency estimation unit 3 ″ that is a configuration surrounded by a broken line in the same figure, resampling). It differs from the voltage signal processing apparatus A according to the first embodiment in that a frequency calculation unit 4 ″, a data conversion unit 5 ′, an FFT processing unit 6 ′, and a calculation unit 7 ′) are added.

The FFT processing unit 2 ′, the frequency estimation unit 3 ″, the resampling frequency calculation unit 4 ″, the data conversion unit 5 ′, the FFT processing unit 6 ′, and the calculation unit 7 ′ are respectively the FFT processing unit 2 and the frequency estimation unit 3 These are functional blocks similar to the resampling frequency calculation unit 4, the data conversion unit 5, the FFT processing unit 6, and the calculation unit 7. The FFT processing unit 2 ′ performs a fast Fourier transform process on the sampling data x _i input from the sampling unit 1, and outputs the transformation result X _k ′ to the frequency estimation unit 3 ″. A correction amount Δk ′ for the harmonic frequency is calculated using only the conversion result X _k ′ in the frequency band corresponding to the harmonic component, and is output to the resampling frequency calculation unit 4 ″. "the frequency estimation unit 3 '' on the basis of the resampling frequency f _r 'correction amount Δk inputted from calculated. resampled data data converter 5' is the resampling frequency f _r 'was converted on the basis of r _n ′ is output, the FFT processing unit 6 ′ performs fast Fourier transform processing on the resampling data r _n ′ and outputs a conversion result R _k ′, and the calculation unit 7 ′ outputs the conversion result R _k ′. Base Computing the amplitude and phase of the harmonic components Te.

  Note that a low-pass filter may be provided before the FFT processing unit 2 so as to pass only the fundamental frequency component, and a band-pass filter may be provided before the FFT processing unit 2 ′ so as to pass only the harmonic component. .

  When processing a plurality of harmonic components (for example, third and fifth harmonics) in addition to the fundamental wave component, a necessary number of configurations surrounded by a broken line shown in FIG. 10 may be provided. .

  The frequency analysis device according to the present invention, the signal processing device using the frequency analysis device, and the high-frequency measurement device using the signal processing device are not limited to the above-described embodiments. The specific configuration of each part of the frequency analysis device according to the present invention, the signal processing device using the frequency analysis device, and the high-frequency measurement device using the signal processing device can be varied in design in various ways.

A, A1, A2, A3 Voltage signal processing device 1 Sampling unit 2 FFT processing unit 3, 3 ′, 3 ″ frequency estimation unit 4, 4 ′, 4 ″ resampling frequency calculation unit 5, 5 ′ data conversion unit 6, 6 'FFT processing unit 7, 7' calculation unit 8 frequency detection unit B current signal processing unit C high frequency detection unit D calculation unit E transmission line

Claims (12)

Sampling means for sampling the input analog signal and generating sampling data;
Data conversion means for converting the sampling data into resampling data that is sampling data corresponding to a target frequency;
FFT processing means for performing a fast Fourier transform process on the resampling data and outputting a conversion result for each frequency;
A frequency analysis apparatus comprising: Re-sampling frequency calculating means for calculating a resampling frequency that is a sampling frequency corresponding to the target frequency;
The data conversion means performs conversion based on the sampling frequency of the sampling means and the resampling frequency.
The frequency analysis apparatus according to claim 1. Said data conversion means, the sampling frequency f _s, if the resampling frequency is f _r, on the basis of the following equation, the sampling data _{x i (i = 0,1, ...} , N-1) the Converted into resampling data r _n (n = 0, 1,..., N−1),
The frequency analysis apparatus according to claim 2.
A second FFT processing means for performing a fast Fourier transform process on the sampling data and outputting a conversion result for each frequency;
Frequency estimation means for estimating the target frequency based on a conversion result for each frequency output by the second FFT processing means;
Further equipped with,
The frequency analysis apparatus according to claim 1. The frequency estimation means includes
Detecting means for detecting an approximate frequency that is a frequency when the spectrum power, which is the magnitude of the conversion result output by the second FFT processing means, reaches a maximum value;
Comparison means for comparing the spectrum power for the frequency obtained by adding frequency resolution to the approximate frequency and the spectrum power for the frequency obtained by subtracting the frequency resolution from the approximate frequency;
A ratio calculating means for calculating a ratio of the spectrum power determined to be larger by the comparing means with respect to the maximum value;
With
Estimating the target frequency based on the ratio calculated by the ratio calculating means;
The frequency analysis apparatus according to claim 4. The frequency estimation means includes
Storage means for storing in advance the correspondence between the correction amount from the approximate frequency and the ratio;
If it is determined by the comparison means that the spectrum power of the frequency obtained by adding the frequency resolution is larger, the frequency obtained by multiplying the correction amount corresponding to the ratio by the frequency resolution and adding the frequency to the approximate frequency, Estimate as the target frequency,
When the comparison means determines that the spectrum power of the frequency obtained by subtracting the frequency resolution is larger, the frequency obtained by multiplying the correction amount corresponding to the ratio by the frequency resolution and subtracting the frequency from the approximate frequency, Estimate as the target frequency,
The frequency analysis apparatus according to claim 5. The frequency estimation means includes
Detecting means for detecting an approximate frequency that is a frequency when the spectrum power, which is the magnitude of the conversion result output by the second FFT processing means, reaches _a maximum value sa;
A comparison means for comparing a spectral power s _{a + 1} for a frequency obtained by adding a frequency resolution to the approximate frequency and a spectral power s _a-1 for a frequency obtained by subtracting the frequency resolution from the approximate frequency;
With
When the comparison means determines that s _{a + 1} ≧ s _a-1 ,
A frequency obtained by multiplying Δk calculated by the frequency resolution and adding to the approximate frequency is estimated as the target frequency,
When the comparison means determines that s _{a + 1} <s _a-1 ,
A frequency obtained by multiplying Δk calculated by the frequency resolution and subtracting from the approximate frequency is estimated as the target frequency.
The frequency analysis apparatus according to claim 4. A frequency detection means for detecting the target frequency;
The frequency analysis apparatus according to claim 1.   The frequency analysis device according to claim 1, wherein the target frequency is a frequency of a fundamental wave component of the analog signal. For each of a plurality of target frequencies, the data conversion means and the FFT processing means are provided.
The frequency analysis apparatus according to claim 1. A frequency analysis device according to any one of claims 1 to 10,
An arithmetic means for calculating the amplitude and phase of the target frequency component of the analog signal based on the conversion result for the target frequency output by the FFT processing means;
A signal processing apparatus comprising: A high-frequency detector arranged on a transmission line through which high-frequency power is transmitted to detect a high-frequency voltage signal and a high-frequency current signal;
The signal processing device according to claim 11, wherein the voltage signal processing device calculates the amplitude and phase of the target frequency component of the high-frequency voltage signal;
The signal processing device according to claim 11, wherein the current signal processing device calculates the amplitude and phase of the target frequency component of the high-frequency current signal;
From the amplitude and phase of the target frequency component of the high-frequency voltage signal output from the voltage signal processing device and the amplitude and phase of the target frequency component of the high-frequency current signal output from the current signal processing device An arithmetic device for calculating various high-frequency parameters;
A high-frequency measuring device comprising: