JP5674042B2 - Phase difference measurement method and phase difference measurement system, and frequency measurement method and frequency measurement system - Google Patents

Description

  The present invention relates to a phase difference measurement method and a phase difference measurement system for obtaining a phase difference of a signal to be measured from a closed curve serving as a Lissajous diagram, and a frequency measurement method and a frequency measurement system for obtaining a frequency of the signal to be measured from a closed curve serving as a Lissajous diagram. About.

  In the field of signal processing, measuring a phase difference (phase angle) with a reference frequency is an important core technology. For example, various fields such as phase difference (phase angle) measurement of electric power and electric energy, abnormality diagnosis by vibration analysis of facilities and equipment, noise analysis for evaluating noise reduction and examining countermeasures for noise causes, etc. Measurement of phase difference is important in sound source estimation in acoustic processing and analysis of overtones in musical sound processing.

  Conventionally, as a phase difference measurement method, a Lissajous method (Lissajous method) is used to draw a Lissajous diagram, a method using an FFT (Fast Fourier Transform) analyzer, a method of measuring a period from a waveform (the power / energy amount) And a method using a correlation between waveform portions (used in a speech processing system) are known.

Of the known phase difference measurement methods, in the frequency calibration, a Lissajous method may be used as a simple method for detecting a minute frequency deviation.
The Lissajous diagram is a plane figure drawn by the locus of points obtained as an ordered pair of two simple vibration waveforms when the measurement display device is set to the XY input mode. When the frequency ratio is 1, the shape is an ellipse, a circle, or a straight line according to the phase difference, and when the frequency ratio is an integer, a plurality of peaks are drawn.

  As a conventional method for obtaining the phase difference between two signals to be measured from the Lissajous diagram, for example, when sine waves having the same frequency are input to the X axis and Y axis of the measurement display device, an elliptical Lissajous diagram appears. In order to accurately calculate the phase difference at this time, each point where the figure crosses the X axis (or Y axis) is determined accurately. Then, the phase difference is calculated from the maximum amplitude in the Y-axis direction of the closed curve for drawing the Lissajous diagram and the amplitude in the Y-axis direction when the closed curve crosses the Y-axis.

  Patent Document 1 relates to a phase difference control method for a multi-axis vibration tester, and a phase difference and an output of an input signal by overlapping a Lissajous diagram normalized on a display device using signals of a plurality of systems. It is described that it is detected whether or not the phase differences of signals are uniform.

  Patent Document 2 relates to a method for reducing a periodic error of an optical interferometer, by substituting the fluctuation values of the phase angle and radius of a quadrature-transformed quadrature two-phase signal into each equation for obtaining an error, It is described that correction values for the zero point and the phase difference are obtained and corrected so that the radius of the polar coordinates is constant. In order to explain the operation principle of the optical interferometer, a Lissajous diagram is explained.

JP 2000-298149 A Japanese Patent No. 4465451

However, in the conventional Lissajous method, in order to accurately calculate the phase difference, the coordinates of the point where the figure crosses the X axis (or Y axis) must be accurately obtained. The zero cross point can be obtained by performing interpolation processing by digital signal processing, but as the locus approaches the origin, the relative speed of passing near the origin increases and the interpolation error decreases.
In the past, frequency counters have adopted the “reciprocal method”, which allows measurement of frequencies below the decimal point, but in order to accurately measure the period, a very high sampling frequency is used. It is necessary to measure. In addition, there is a concern that the detection accuracy of the “zero cross point” to be the reference of the cycle is affected by the DC offset and the detection accuracy is lowered.
In the conventional Lissajous method, in order to recognize a minute frequency deviation, for example, 0.1 / 1000 Hz, a phase difference changing at 360/10000 (degrees / second) is recognized in a short time, and fine adjustment of the frequency is performed. Need to repeat.

  Accordingly, an object of the present invention is to improve the processing method using the conventional Lissajous method, and to perform phase measurement with a phase difference measurement method and phase difference measurement system capable of performing phase difference measurement with high accuracy, and to perform frequency measurement with high accuracy. An object of the present invention is to provide a frequency measurement method and a frequency measurement system that can be used.

  The inventor of the present application has focused on the area surrounded by the closed curve drawn by the Lissajous figure, found a method capable of detecting a precise phase difference in a short time, and has completed the present invention.

  The phase difference measuring method of the present invention includes an area calculating step for calculating an area surrounded by a closed curve that becomes a Lissajous figure from two measured signals, and a normalization that normalizes the area from the amplitude values of the two measured signals. And a phase difference calculating step of calculating a phase difference between the two measured signals from the normalized area.

  In the conventional Lissajous method, only the data in the vicinity of the zero crossing in the Lissajous diagram is used for the calculation. However, according to the present invention, by calculating the area surrounded by the closed curve of the Lissajous diagram, all the Lissajous diagrams are constructed. Data will be used for calculation, and precise phase difference measurement can be performed.

  The phase difference measurement method of the present invention includes a digital conversion step for A / D converting two measured signals, and an area calculating step for calculating an area enclosed by a closed curve that becomes a Lissajous figure from the two measured signals after digital conversion. And a normalizing step for normalizing the area from the amplitude values of the two measured signals, and a phase difference calculating step for calculating a phase difference between the two measured signals from the normalized area. It is characterized by.

  According to the present invention, there is no processing for extracting a specific condition such as zero crossing, and the error in the conversion means (A / D conversion) for converting an analog signal into a digital signal is statistically equal in all positive and negative. It is diffused in the state, and the error is greatly reduced.

  The phase difference measurement system of the present invention includes an A / D converter for A / D converting each of two signals to be measured, and a computer having a measurement program. The measurement program has two digital signals after being converted. Calculate the area enclosed by the closed curve that becomes the Lissajous figure from the measurement signal, normalize the area from the amplitude value of each of the two signals under measurement, and calculate the phase difference between the two signals under measurement from the normalized area It is characterized by doing.

  According to the present invention, if there is a measured signal waveform of one cycle capable of drawing a Lissajous diagram, the phase difference between the two measured signals can be calculated by the measurement program operating on the computer. Phase difference measurement can be performed.

  The frequency measurement method of the present invention includes a phase difference generation step of filtering a signal under measurement and converting and outputting the phase difference of the signal before and after the filtering, and an area enclosed by a closed curve that becomes a Lissajous diagram from the two signals before and after the filtering An area calculating step for calculating the phase, a normalizing step for normalizing the area from the amplitude value of the signal under measurement, and a phase difference calculating step for calculating a phase difference between the two digital signals from the normalized area. And a frequency estimation step of calculating a frequency deviation from the phase difference and a filter phase shift characteristic in the filtering, and estimating a frequency of the signal under measurement from the frequency deviation and the notch frequency of the filtering.

  According to the present invention, the frequency deviation can be calculated from the phase difference and the filter phase shift characteristic in the filtering, and the frequency of the signal to be measured can be accurately obtained from the frequency deviation and the notch frequency of the filtering.

  The frequency measurement method of the present invention includes a digital conversion step for A / D converting a signal under measurement, and a phase difference generation for filtering the signal under measurement after digital conversion and converting and outputting the phase difference of the digital signal before and after the filtering. An area calculating step for calculating an area surrounded by a closed curve that becomes a Lissajous figure from the digital signal before and after the filtering, a normalizing step for normalizing the area from the amplitude value of the signal under measurement, and the normalized A phase difference calculating step of calculating a phase difference of the digital signal from an area; a frequency deviation is calculated from the phase difference and a filter phase shift characteristic in the filtering; and the signal to be measured is calculated from the frequency deviation and the notch frequency of the filtering A frequency estimation step of estimating the frequency of

  The frequency measurement system of the present invention includes an A / D converter that performs A / D conversion of a signal to be measured, and a computer that includes a measurement program. The measurement program filters the signal to be measured after digital conversion, The phase difference of the digital signal before and after the filtering is converted and output, the area enclosed by the closed curve that becomes the Lissajous diagram is calculated from the digital signal before and after the filtering, the area is normalized from the amplitude value of the signal under measurement, and normalized The phase difference of the digital signal is calculated from the measured area, the frequency deviation is calculated from the phase difference and the filter phase shift characteristic in the filtering, and the frequency of the signal under measurement is calculated from the frequency deviation and the notch frequency of the filtering. Is estimated.

  According to the present invention, there is no processing for extracting a specific condition such as zero crossing, and the error in the conversion means (A / D conversion) for converting an analog signal into a digital signal is statistically equal in all positive and negative. It is diffused in the state, and the error is greatly reduced.

  The present invention is characterized in that an IIR comb filter is used for the filtering.

  According to the present invention, by using an IIR comb filter (also called a feedback comb filter), the phase between the input and output is changed abruptly in the vicinity of the set notch frequency, so that the minimum frequency resolution is improved. .

  The present invention is characterized in that a linear phase FIR filter is used for the filtering.

  According to the present invention, by using a linear phase FIR filter, the linearity is improved and the measurable frequency band is wide.

  According to the phase difference measurement method and the phase difference measurement system of the present invention, by calculating the area surrounded by the closed curve of the Lissajous diagram, all data constituting the Lissajous diagram is used for calculation, and precise phase difference measurement is performed. Can do. Further, there is no processing for extracting a specific condition such as zero crossing, and errors in the conversion means (A / D conversion) for converting an analog signal into a digital signal are diffused in a state where the sign is statistically equal throughout. The error will be greatly reduced. Further, according to the present invention, the origin may be outside the locus due to the nature of the closed curve integral. Even if an offset is added to the signal, it is not reflected in the area calculation. Even if noise is added, the area is averaged and the influence is mitigated. As a result, the disadvantages of the zero cross method that depends on the data around the threshold are eliminated. According to the present invention, if there is a signal waveform to be measured with one cycle capable of drawing a Lissajous diagram, the phase difference between the two signals to be measured can be calculated by the measurement program operating on the computer. The phase difference can be measured with.

  According to the frequency measurement method and the frequency measurement system of the present invention, the frequency deviation is calculated from the phase difference and the phase shift characteristic in the filtering, and the frequency of the signal under measurement is accurately calculated from the frequency deviation and the notch frequency in the filtering. Can be requested. Then, by using an IIR comb filter for the filtering, the phase between the input and output is abruptly changed in the vicinity of the set notch frequency, so that the minimum frequency resolution is improved. Alternatively, by using a linear phase FIR filter, linearity is improved and the measurable frequency band is wide.

It is a block diagram explaining the phase difference measuring system of an embodiment of the invention. It is a block diagram which illustrates the composition of the measurement program concerning the above-mentioned phase difference measurement system. It is a figure which shows the method of this invention which calculates | requires the phase difference of two signals from a Lissajous figure. It is a flowchart figure which shows the phase difference measurement procedure of embodiment of this invention. It is a block diagram explaining the frequency measurement system of embodiment of this invention. It is a block diagram which illustrates the measurement program structure which concerns on the said frequency measurement system. It is a block diagram which illustrates the measurement program structure which concerns on the said frequency measurement system. It is a flowchart figure which shows the frequency measurement procedure of embodiment of this invention. FIG. 3 is a structural diagram of an IIR comb filter. It is a characteristic figure of an IIR comb type filter, (a) is a phase shift characteristic figure, and (b) is an amplitude characteristic figure. It is a time-series characteristic figure which shows the dispersion | variation in the phase difference resolution by the said frequency measurement system. It is a frequency distribution figure which shows the dispersion | variation in the phase difference resolution by the said frequency measurement system. It is a frequency deviation scatter diagram at the time of averaging the measured value for every measurement in the above-mentioned frequency measurement system. It is a figure which shows the phase change generate | occur | produced by a fine frequency difference.

  The principle of phase difference measurement according to the present invention will be described below.

(Phase difference measurement principle)
The Lissajous diagram in the case where the frequency ratio between the signal x and the signal y is 1: 1 and the phase difference φ is an ellipse / circle / line depending on the phase difference and amplitude. A method of obtaining the phase difference sin (φ) from the area drawn by the trajectory by taking this as a closed curve will be described below.

  First, the general formula of the area enclosed by the closed curve is shown in Equation 1.

  If the area surrounded by the closed curve in the Lissajous diagram shown in FIG. 3 is denoted by S, the partial area dS of the minute triangle formed by the two adjacent points and the origin in the trajectory is calculated using the outer product of the trajectory and the movement vector of the trajectory. , Expressed by the following Formula 2 or Formula 3. This partial area dS is obtained by taking the outer product of the trajectory vector (= P) and the movement vector (= dP) to be ½.

  When the partial area dS is calculated according to the outer product calculation formula, dS> 0 when the locus is counterclockwise, and dS <0 when the locus is clockwise. Further, the total area S is obtained by adding up dS and expressed by the following formula 4. The period T varies depending on the frequency of the signal under measurement and the sampling conditions.

  Here, the “Lissajous area drawn by the signal of the phase difference φ” is derived. Consider signals q1 and q2 having a phase difference φ. If the codes a1 and a2 are amplitudes and the code ω0 is an angular velocity, it is expressed by the following formula 5.

  By substituting and modifying Formula 5 and its differential form into Formula 1 using the addition theorem of trigonometric functions, the area S is expressed by Formula 6 below. Here, the integration interval is one period. It is shown that the area to be drawn is determined by the phase difference and the amplitude.

  Assuming that the aforementioned amplitudes (a1, a2) are measured by another method, the obtained closed curve area S is normalized as represented by the following Expression 7, and a normalized Lissajous area (LsRot) is obtained.

  The area obtained by Equation 7 is an area normalized so that area = 0 when the phase difference = 0 degree and area = π when the phase difference = ± 90 degrees. −π ≦ LsRot ≦ π, resulting in a dimensionless amount. From the above formulas 6 and 7, the following formula 8 is obtained.

  From Equation 8, it can be seen that the phase difference sin (φ) can be easily obtained from the normalized Lissajous area (LsRot).

  Here, the partial area dS surrounded by the closed curve that becomes the Lissajous diagram shown in FIG. 3 is expressed by the above-described Expression 2 or Expression 3 using the outer product of the locus and the movement vector of the locus. However, because of the nature of the outer product, P × P≡0 (constantly zero), and the calculation for obtaining the difference is unnecessary, so that Equation 9 can be derived.

  A phase difference measurement procedure, a phase difference measurement system, and a phase difference measurement program according to the present invention will be described below.

(Phase difference measurement procedure)
FIG. 4 is a flowchart showing a phase difference measurement procedure according to the embodiment of the present invention. The phase difference measurement method of this embodiment includes a digital conversion step S11 for A / D-converting two measured signals q1 and q2, and a closed curve that becomes a Lissajous figure from the two measured signals qd1 and qd2 after digital conversion. An area calculating step S21 for calculating the surrounding area, a normalizing step S31 for normalizing the area from the amplitude values of the two measured signals, and a phase difference between the two measured signals from the normalized area It consists of phase difference calculation step S41 which calculates. According to this embodiment, if there is a signal waveform under measurement that can draw a Lissajous diagram, the phase difference between the two signals under measurement can be calculated by the measurement program 2 operating on the computer 3 in a short time. Phase difference measurement can be performed.

(Phase difference measurement system)
FIG. 1 is a block diagram functionally illustrating a phase difference measurement system 1 according to an embodiment of the present invention. The phase difference measurement system 1 according to this embodiment includes an A / D converter 7 that performs A / D conversion on two signals under measurement q1 and q2, and a computer 3 that includes a measurement program 2 (FIG. 1). .

  In the example shown in FIG. 1, the computer 3 includes an input unit 81 that receives data input, a CPU 4 that performs arithmetic processing on the input data, a database 5 that stores and stores data after arithmetic processing, and data before and after data processing. Is displayed, and the measurement program 2 operates on the computer 3. The measurement program 2 includes a digital filter program 22 and a phase difference measurement program 23.

(Phase difference measurement program)
FIG. 2 is a block diagram illustrating the configuration of the measurement program 2 according to the phase difference measurement system 1 of the embodiment. In the example illustrated in FIG. 2, the measurement program 2 includes a digital filter program 22 and a phase difference measurement program 23. When the two signals to be measured qd1 and qd2 digitally converted in the digital conversion step S11 are input to the computer 3, an area calculation process for calculating the area enclosed by the closed curve that becomes the Lissajous diagram is performed through the digital filter 222 ( (S21) Amplitude calculation processing of each of the two measured signals qd1 and qd2 is performed (reference S211), and area normalization processing is performed to normalize the area from the amplitude values of the two measured signals (reference S21). S31) After performing a phase difference calculation process (reference S41) for calculating a phase difference between the two measured signals from the normalized area, the phase difference signal data an12 is output. Although the Lissajous diagram is not directly drawn here, for example, the Lissajous diagram may be drawn and displayed on the display before the area calculation processing S21.

  Next, the filter in the frequency measurement of the present invention will be described.

(IIR comb filter)
In general, the structure of an IIR comb filter is shown in FIG. When the number of delay stages is K and the feedback gain is a, the transfer function is expressed by the following Equation 10. j is an imaginary unit.

  When the frequency and the angular velocity are normalized by the sampling frequency fs, the normalized frequency F and the normalized angular velocity Ω are expressed by the following formula 11.

  Using the normalized angular frequency and the normalized angular velocity described above, the transfer function is expressed by the following Equation 12 using the normalized angular velocity. Hereinafter, description will be made based on the normalized expression.

  The phase shift φ of the IIR comb filter is expressed by the following Equation 13 from the above transfer function. Next, Equation 13 is modified so that the phase shift characteristic φ can be expressed as a function of Ω, and how much the phase change φ is generated by the frequency Ω is expressed by the filter phase shift characteristic φ (Ω). The filter phase shift characteristic φ (Ω) is expressed by the following formula 14.

  FIG. 10 is a characteristic diagram of the IIR comb filter. FIG. 10A is a phase shift characteristic diagram. The vertical axis of the graph indicates the input / output phase difference, and the horizontal axis of the graph indicates the relative frequency. FIG. 10B is an amplitude characteristic diagram, in which the vertical axis of the graph indicates amplitude, and the horizontal axis of the graph indicates relative frequency. Here, -1 <a <0 is used, which is an extremely sharp phase shift characteristic and an amplitude characteristic that allows only the vicinity of the notch frequency to pass at an odd multiple of the notch frequency.

  A third-order term or more obtained by Taylor expansion of the above formula 14 is rounded down, and first-order approximation is performed. An approximate expression of the phase shift φ in the vicinity of the notch frequency is expressed by the following Expression 15.

Here, the phase change rate is obtained. The phase change rate in the vicinity of f ₀ is obtained by differentiating φ by Ω, and is expressed by the following Expression 16.

Next, a frequency deviation is obtained from the obtained phase change rate. Δf is a displacement from f ₀ . The relationship between Δφ and Δf is expressed by Equation 17 below.

From Equation 17 above, it can be seen that the measured phase difference can be measured with a frequency deviation multiplied by πg ₀ (improvement of sensitivity). By transforming Equation 17 above, it can be written as Equation 18 below.

The above equation 18 is shifted and the frequency deviation (Δf / f ₀ ) is expressed by the following equation 19.

The notch frequency f ₀ of the comb filter can be determined only by the sampling frequency fs and the number of delay stages (see Equation 21). When precisely that quantified the normalized Lissajous area described above, the combined relationship of Equation 19 and the frequency deviation Δf and f _0, the formula of Equation 20 is obtained. Precise frequency discrimination is possible using simple equations such as Equation 20 and Equation 21.

Looking at the obtained Equations 20 and 21, the sampling frequency is a reference frequency (can be calibrated using a national standard). Sampling frequency calibration is possible by measuring traceable frequency standards. In other words, looking at the obtained Equations 20 and 21, K, g ₀ π ² is a pure constant. The normalized Lissajous area (LsRot) is a measured value. As for fs, an actual measurement value of a frequency operating in an actual apparatus is determined by the accuracy of a crystal oscillator mounted on hardware. Therefore, by correctly calibrating fs (which can be calibrated using the national standard), the accuracy of the sampling frequency (fs) that is actually operating can be increased, and the calculation result (theoretical value) and the actual value ( Measured value) can be brought closer.

  The frequency measurement procedure, frequency measurement system, and frequency measurement program according to the present invention will be described below.

(Frequency measurement procedure)
FIG. 8 is a flowchart showing a frequency measurement procedure according to the embodiment of the present invention. In the frequency measurement method of the present embodiment, a digital conversion step S11 for A / D converting a signal under measurement (for example, q1), and a signal under measurement (for example, qd1) after digital conversion are filtered, and the digital signal before and after the filtering is filtered. The phase difference generating step S15 for converting and outputting the phase difference of the signal, the area calculating step S21 for calculating the area enclosed by the closed curve as the Lissajous figure from the digital signal before and after the filtering, and the area from the amplitude value of the signal under measurement is normalized. Normalization step S31 to be converted, phase difference calculation step S41 to calculate the phase difference of the digital signal from the normalized area, frequency deviation is calculated from the phase difference and filter phase shift characteristics in the filtering, The frequency of the signal under measurement is calculated from the frequency deviation and the notch frequency of the filtering. Consisting frequency estimation step S51 of estimating a number.

(Frequency measurement system)
FIG. 5 is a block diagram illustrating the frequency measurement system 11 according to the embodiment of this invention. The frequency measurement system 11 of this embodiment includes an A / D converter 7 that performs A / D conversion on each of the signals under measurement q1, q2,..., Qk (k is a positive integer), and a measurement program 2. It is composed of a computer 3 (FIG. 5). Here, the same reference numerals represent the same functions, and description thereof will be omitted as appropriate. In the example shown in FIG. 5, a case where a multi-channel signal to be measured is input is described. However, one signal to be measured (for example, q1) may be used, or two signals to be measured (for example, q1 and q2). Also good.

(First frequency measurement program)
FIG. 6 is a block diagram illustrating the configuration of the measurement program 2 according to the frequency measurement system 11 of the embodiment. FIG. 6 shows an example in which one measured signal q 1 is input. The measurement program 2 includes a digital filter program 22 and a frequency measurement program 24. When the signal to be measured qd1 digitally converted in the digital conversion step S11 is input to the computer 3, it passes through the digital filter 222, converts and outputs the phase difference of the digital signal before and after the filtering, An area calculation process surrounded by a closed curve that becomes a Lissajous figure is performed from the digital signal before and after the filtering (reference S21), an amplitude calculation process of the measured signal is performed (reference S211), and the area is normalized from the amplitude value of the measured signal. Area normalization processing (reference S31), phase difference calculation processing (reference S41) for calculating the phase difference between the two measured signals from the normalized area, and the phase difference and the filtering in the filtering The frequency deviation is calculated from the filter phase shift characteristic, and from this frequency deviation and the notch frequency of the filtering. Serial performs frequency estimation process for estimating the frequency of the measured signal (code S51), and outputs the result as a frequency signal data an1. Although the Lissajous diagram is not directly drawn here, for example, the Lissajous diagram may be drawn and displayed on the display before the area calculation processing S21.

  In the frequency measurement system 11 of this embodiment, an IIR comb filter is used as the digital filter. This is because the IIR comb filter is used to sharply change the phase between the input and output in the vicinity of the set notch frequency, thereby improving the minimum frequency resolution.

(Second frequency measurement program)
FIG. 7 is a block diagram illustrating another example of the configuration of the measurement program 2 according to the frequency measurement system 11 of the embodiment. In the example illustrated in FIG. 7, the measurement program 2 includes a digital filter program 22 and a frequency measurement program 24. FIG. 7 shows an example in which two channels of signals to be measured q1 and q2 are input. When the measured signals qd1 and qd2 digitally converted in the digital conversion step S11 are respectively input to the computer 3, the digital filter 222 (comb filter 222) is passed through the preprocessing filter 221. A phase difference is generated by converting and outputting the phase difference of the digital signal before and after filtering by the comb filter 222, and an area calculation process surrounding a closed curve that becomes a Lissajous diagram is performed from the digital signal before and after the filtering (reference S21), An amplitude calculation process of the signal under measurement is performed (reference S211), an area normalization process is performed to normalize the area from the amplitude value of the signal under measurement (reference S31), and the two areas under test are calculated from the normalized areas. A phase difference calculation process (reference S41) for calculating a phase difference of the measurement signal is performed, a frequency deviation is calculated from the phase difference and a filter phase shift characteristic in the filtering, and the frequency difference is calculated from the frequency deviation and the notch frequency of the filtering. A frequency estimation process for estimating the frequency of the measurement signal is performed (reference S51), and the results are respectively obtained as frequency signal data. And outputs it as a data an1, an2. Then, an area calculation process for calculating the area enclosed by the closed curve that becomes the Lissajous figure from the digital signal that has passed through the digital filter 222 is performed (reference S21), and the amplitude calculation process for each of the two measured signals qd1 and qd2 is performed. (Reference S211), an area normalization process is performed to normalize the area from the amplitude values of the two measured signals (reference S31), and the phase difference between the two measured signals is calculated from the normalized area. After performing the calculated phase difference calculation process (reference S41), it is output as the phase difference signal data an12.

(Example)
A frequency measurement system having a block diagram shown in FIGS. 5 and 7 was prototyped. This configuration has two channels and measures each precise frequency and precise phase difference between channels.

  The pre-processing filter 221 was used to cut out an unintended frequency band. As the comb filter 222, an IIR comb filter in which a specific notch frequency is set by the delay stage number K is used. The frequency measurement system 11 measures the signal frequencies f1 and f2, and simultaneously obtains the phase difference between the two signals. Sampling was 16 bits and 44100 Hz.

  Next, the frequency measurement system 11 of the above embodiment was used to evaluate the minimum phase difference resolution, resolution variation, and precision frequency accuracy. As a test signal, a function generator (hereinafter abbreviated as FG) using a rubidium (Rb) oscillator (10 MHz) as an external frequency reference was used. The signal used was 2 channels 44100 Hz. An A / D converter 7 was used by external connection.

  This time, we intentionally created a signal with zero phase difference and measured it with this software. The measurement was performed for 10 minutes. The resolution was estimated from the mean and standard deviation of the values. A resolution of 1.1 μradian (± 3σ) in the short-time average (about 0.6 seconds) and 0.33 μradian (± 3σ) in the long-time average (about 6 seconds) were confirmed.

  FIG. 11 is a time-series characteristic diagram showing variation in phase difference resolution by the frequency measurement system 11. This is an actual observation of the phase difference between the two signals (q1, q2) generated by the signal generator. When the behavior was observed with a short-time average (about 0.6 seconds) and a long-time average (about 6 seconds), it was confirmed that the behavior was generally within the range of ± 1 μradian. FIG. 12 is a frequency distribution diagram showing variations in phase difference resolution by the frequency measurement system 11 of the above embodiment. The long-term average data is plotted on a histogram from the values in FIG. The standard deviation σ was 1.085E-07.

Next, the frequency accuracy was verified. FIG. 13 is a frequency deviation scatter diagram when the measurement values for each measurement in the frequency measurement system 11 are averaged. When frequency measurement was performed with two channels and the variation in frequency was analyzed, it was 1.5 μHz (± 3σ). It was found that the frequency after the decimal point matches up to the order of μHz. 440.998, 958, and 17 Hz (σ = 0.52 μHz) were obtained as average values of frequencies.
The error from the set frequency 441.00 Hz is caused by the frequency deviation or drift of the sampling clock crystal oscillator mounted in the A / D converter. When the A / D converter is not sufficiently stabilized, the reference sampling frequency first drifts. Therefore, the instantaneous frequency of both channels in this implementation example also drifts in the same direction, and the correlation coefficient becomes a value close to 1 (strong correlation). Various stabilization precautions were taken and finally the correlation coefficient after stabilization was 0.46. This suggests that some of the errors in both channels are generated by independent processes.

FIG. 14 is a diagram showing a phase change due to a fine frequency variation. Attempt to detect phase difference due to transmission delay in a certain line length. The speed of light is 3.0e + 8 m / sec. And a slight transmission delay.
The wavelength λ of the frequency 441.00 Hz used for the test is 680272 m. If a phase difference of 1 μradian is detectable, a difference of about 10 cm in line length can be detected. In the experiment, the function generator and the A / D converter were connected using two cables having a length of 57 cm, and the phase difference φ1 was measured. Next, the cables were replaced and connected, and the phase difference φ2 was measured. The results of φ1 = 52.5 μradian and φ2 = 810 μradian were obtained. The phase difference Δφ = 757 μ radians, far exceeding the theoretical value of 10.5 μ radians in the relative line length difference (= 1.14 m). This result captures the phase difference of the transmission delay due to the impedance of the line, not the phase difference due to the transmission delay due to the speed of light. The experiment shows again that cable length differences and delays must be fully considered.

As described above, the measurement system to which the present invention can be applied includes a frequency measurement device that replaces the frequency counter, a phase difference measurement processing unit built in the signal generator, an impedance meter that uses phase difference measurement, and a frequency characteristic of an acoustic device, in particular. Measurement of phase delay characteristics, phase difference measurement in signal processing using an array microphone, time delay measurement using phase difference measurement in a distance measuring device using a laser beam, measuring instrument using a small Doppler effect in an acoustic frequency band, singing voice There are various applications such as precision pitch discrimination of instruments and instruments, estimation of fundamental frequencies in voice processing, precision tuners used in piano tuning, and precision measurement of inharmonicity in piano tuning.
In particular, at low frequencies, the frequency below the decimal point can be obtained in a short time even for data of one wavelength to several wavelengths. Therefore, the frequency measurement and power factor measurement in the power meter, and the precise measurement of the power system frequency (50 Hz, 60 Hz) in a short time. It can be applied to power flow estimation obtained by precisely measuring the phase difference at a specific point in the power system.

1 phase difference measurement system,
2 measurement program,
22 Digital filter program,
23 phase difference measurement program,
24 frequency measurement program,
3 computers,
4 CPU,
7 A / D converter,
11 Frequency measurement system,
q1, q2, ..., qk Signal to be measured (k = positive integer)

Claims (8)

  An area calculating step for calculating an area surrounded by a closed curve that becomes a Lissajous figure from two measured signals, a normalizing step for normalizing the area from amplitude values of the two measured signals, and the normalized area A phase difference measurement method comprising: a phase difference calculation step of calculating a phase difference between the two signals under measurement.   A digital conversion step for A / D converting each of the two signals to be measured, an area calculating step for calculating an area enclosed by a closed curve that becomes a Lissajous figure from the two signals to be measured after digital conversion, and each of the two signals to be measured A phase difference measuring method comprising: a normalizing step of normalizing the area from the amplitude value of the signal; and a phase difference calculating step of calculating a phase difference between the two measured signals from the normalized area.   A phase difference generating step of filtering the signal under measurement, converting and outputting the phase difference of the signal before and after the filtering, and an area calculating step of calculating an area surrounded by a closed curve that becomes a Lissajous diagram from the two signals before and after the filtering; In the normalization step of normalizing the area from the amplitude value of the signal under measurement, the phase difference calculation step of calculating the phase difference of the two digital signals from the normalized area, the phase difference and the filtering A frequency measurement method comprising: calculating a frequency deviation from a filter phase shift characteristic, and estimating a frequency of the signal under measurement from the frequency deviation and the notch frequency of the filtering.   A digital conversion step for A / D converting the signal under measurement, a phase difference generation step for filtering the signal under measurement after digital conversion, and converting and outputting the phase difference of the digital signal before and after the filtering, and the digital before and after the filtering An area calculating step for calculating an area surrounded by a closed curve that becomes a Lissajous diagram from a signal, a normalizing step for normalizing the area from an amplitude value of the signal under measurement, and a phase difference of the digital signal from the normalized area Calculating a phase difference from the phase difference and a filter phase shift characteristic in the filtering, and estimating a frequency of the signal under measurement from the frequency deviation and the notch frequency of the filtering A frequency measurement method characterized by comprising:   An A / D converter for A / D converting each of the two signals to be measured and a computer having a measurement program, and the measurement program is a closed curve that becomes a Lissajous figure from the two signals to be measured after digital conversion. A phase difference measurement characterized in that an area to be enclosed is calculated, the area is normalized from the amplitude value of each of the two signals under measurement, and the phase difference between the two signals under measurement is calculated from the normalized area. system.   An A / D converter that performs A / D conversion of a signal to be measured and a computer having a measurement program, the measurement program filters the signal to be measured after digital conversion, and the digital signal before and after the filtering is filtered. Converting and outputting a phase difference, calculating an area surrounded by a closed curve as a Lissajous figure from the digital signal before and after the filtering, normalizing the area from the amplitude value of the signal under measurement, and calculating the digital signal from the normalized area A frequency deviation is calculated from the phase difference and a filter phase shift characteristic in the filtering, and a frequency of the signal under measurement is estimated from the frequency deviation and the notch frequency of the filtering. Frequency measurement system.   7. The frequency measurement system according to claim 6, wherein an IIR comb filter is used for the filtering.   The frequency measurement system according to claim 6, wherein a linear phase FIR filter is used for the filtering.

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