WO2016006079A1 - ピーク周波数検出装置、方法およびプログラム - Google Patents
ピーク周波数検出装置、方法およびプログラム Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
- G01R19/04—Measuring peak values or amplitude or envelope of ac or of pulses
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/16—Spectrum analysis; Fourier analysis
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/16—Spectrum analysis; Fourier analysis
- G01R23/165—Spectrum analysis; Fourier analysis using filters
- G01R23/167—Spectrum analysis; Fourier analysis using filters with digital filters
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/16—Spectrum analysis; Fourier analysis
- G01R23/177—Analysis of very low frequencies
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
- G01S15/02—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems using reflection of acoustic waves
- G01S15/50—Systems of measurement, based on relative movement of the target
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/35—Details of non-pulse systems
- G01S7/352—Receivers
- G01S7/356—Receivers involving particularities of FFT processing
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
- G01S7/523—Details of pulse systems
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- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
- G06F17/141—Discrete Fourier transforms
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10G—REPRESENTATION OF MUSIC; RECORDING MUSIC IN NOTATION FORM; ACCESSORIES FOR MUSIC OR MUSICAL INSTRUMENTS NOT OTHERWISE PROVIDED FOR, e.g. SUPPORTS
- G10G7/00—Other auxiliary devices or accessories, e.g. conductors' batons or separate holders for resin or strings
- G10G7/02—Tuning forks or like devices
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
- G10L25/00—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00
- G10L25/90—Pitch determination of speech signals
Definitions
- the present invention relates to an apparatus, a method, and a program for detecting a peak frequency that maximizes the power spectrum.
- the time window length is the time length of the signal wave to be subjected to FFT, and the frequency resolution is the minimum resolution of the signal wave frequency, that is, the frequency detection accuracy.
- this time window length is also referred to as “a time to cut out a signal wave to be applied to FFT”, “a time of a signal wave to be applied to FFT”, and the like.
- the meaning of the equation (2) is that the FFT time window length and the frequency resolution are in a reciprocal relationship. This reciprocal relationship has a significant effect at frequencies where the frequency resolution is small. For example, if a frequency resolution of 0.01 (Hz) is required, a signal wave having a reciprocal number of 100 (s) must be applied to the FFT. Further, if the time of the signal wave applied to the FFT is 0.01 (s), only the reciprocal frequency resolution of 100 (Hz) can be obtained.
- This reciprocal relationship may be a constraint when using FFT, and various devices have been made to avoid the reciprocal relationship.
- the time window length T 0 is fixed to a predetermined value, and the received signal wave is mutually exchanged at intervals of T 0.
- FFT is applied to each of a plurality of periods cut out while shifting so as not to overlap (that is, FFT is applied multiple times), and the obtained plurality of peak frequencies are averaged.
- the peak frequency may be calculated with a resolution (fine frequency interval) higher than the frequency resolution f 0 obtained by one FFT.
- the number of FFT operations is increased, there is a problem that the signal wave cut-out time applied to the FFT becomes longer by that number.
- the value of amplitude at a constant frequency interval (equal to frequency resolution (f 0 )) from 0 to N ⁇ 1 is given to the number of samples N subjected to FFT.
- a power spectrum is obtained.
- the frequency corresponding to the maximum power spectrum is called a peak frequency.
- zero value data is added to the portion between the data, and the data sequence obtained by adding the zero value data (time length 102.4 (ms)) is subjected to FFT to obtain the peak frequency (the same document). [0103].
- the effective data string included in the data string to be subjected to FFT is only about 1/10 of the whole (about 1/20 according to the document [0103]).
- a digital band-pass filter digital BPF 62 in FIG. 7
- a / D conversion that is generally applied when the wave is an analog signal wave
- the filter characteristics of the digital bandpass filter must be made gentle.
- this document does not recognize any potential problem that makes it difficult to avoid the negative effects of disturbance noise in the case of short-time input signal waves. There is no suggestion or teaching of a means for solving a general problem.
- the digital signal wave (digital data string) to be subjected to FFT has a length of about 1/10 (or about 1/20) of the time window length required when applying FFT. Since actual data exists only in this part, many power spectra must be generated. When disturbance noise is included in an actual signal wave to which FFT is applied, an extra spectrum appears around the peak frequency, which may make it difficult to specify the peak frequency. .
- a peak frequency detection device for achieving the above object is a peak frequency detection device for detecting a peak frequency at which a power spectrum is maximum in a predetermined frequency band (f cl to f ch ), and a digital data sequence N elements (n is an integer equal to or greater than 2), and N (N is an integer that is a power of 2) determined according to the sampling frequency f s , frequency resolution f tg, and time window length T tg
- a 1 / n multiplication unit that outputs a value multiplied by / n as the peak frequency of the digital data string, n ⁇ 1 / (f tg ⁇ T tg ) f s / (n ⁇ f tg ) ⁇ N
- y sin (2 ⁇ ft) is raised to the nth power, and a signal wave having a frequency component (n ⁇ f) is extracted from the signal wave obtained by raising the nth power, and the peak frequency of the signal wave is obtained. If possible, it can be understood that if the frequency obtained there is multiplied by 1 / n, it corresponds to the frequency f of the original signal wave.
- FIG. 1 schematically shows this relationship.
- the sampling frequency of FFT used for frequency analysis is f s , and the number of samples is N.
- the peak frequency is obtained by applying an FFT having the same values of f s and N as when the peak frequency of y is obtained.
- the frequency f n ′ of y n is a calculated value of (n ⁇ f).
- the frequency f n of the y n ' is determined under the same frequency resolution f 0 and the frequency resolution for y, is that. That is, the frequency resolution of f n ′ is also f 0 .
- the frequency resolution f tg is the frequency resolution of the peak frequency desired by the user when obtaining the peak frequency of the original signal wave.
- the time window length T tg is the FFT time window length desired by the user. f tg and T tg can be determined independently.
- the present invention is a method for calculating the peak frequency of the original signal wave while satisfying the following conditions. -Frequency resolution of peak frequency f n ⁇ f tg FFT time window length T n ⁇ T tg
- the multiplier n is Must be met.
- the peak frequency of the signal wave can be detected with a desired frequency resolution and a desired time window length. Specifically, the peak frequency of the signal wave can be detected with a desired frequency resolution and a desired time window length even in the range of f tg ⁇ T tg ⁇ 1.
- N In the case of FFT, N must be a power of 2, so the possible range of N is f s / (n ⁇ f tg ) ⁇ N ⁇ f s ⁇ T tg (N is a power of 2) It becomes.
- the desired frequency resolution f tg and the desired time window length T tg are satisfied no matter which N is adopted.
- the amount of calculation of FFT is smaller when N is smaller, It is better to adopt N closest to.
- the desired frequency resolution f tg a multiplier n capable of detecting the peak frequency with the time window length T tg , the FFT sampling frequency f s , and the FFT sample number N I can decide.
- the method of determining the multipliers n, f s , and N does not have to follow the above procedure. Any method may be used, such as repeating trial and error until a condition is satisfied by appropriately applying numerical values, or by creating a simple program.
- a peak frequency detection apparatus for achieving the above object includes a first digital bandpass filter that extracts a digital data string of frequencies included in the predetermined frequency band, and the nth power unit includes the first digital bandpass filter.
- the output of one digital bandpass filter may be input.
- the analog filter in the previous stage can be simplified or omitted in order to extract a signal in a predetermined frequency band from a signal including various frequency components, so that the circuit scale can be reduced.
- the sampling frequency f 1 / r a digital data sequence IS (r is an integer of 2 or more) with a thinning unit for the sampling frequency by thinning out the to f s
- the output of the decimation unit may be input to the first digital bandpass filter.
- the peak frequency can be detected with a desired frequency resolution f tg and time window length T tg even when the sampling frequency of the digital data string input to the peak frequency detection device is larger than f s .
- a peak frequency detection apparatus for achieving the above object includes an interpolating unit that interpolates a received digital data string by g times (g is an integer of 2 or more) and sets a sampling frequency to f s ,
- the output of the interpolation unit may be input to the digital bandpass filter.
- the peak frequency can be detected with the desired frequency resolution f tg and time window length T tg even when the sampling frequency of the digital data string input to the peak frequency detection device is smaller than f s .
- a peak frequency detector for achieving the above object includes a second digital bandpass filter for extracting a digital data sequence included in a second frequency band from N digital data sequences raised to the nth power.
- the FFT unit may receive the digital data string extracted by the second digital bandpass filter, and the second frequency band may be approximately n ⁇ f cl to n ⁇ f ch .
- a digital data string has only a single frequency component, it has a plurality of frequency components when it is raised to the nth power, so that a plurality of peaks appear in the power spectrum. It appears in n ⁇ f cl to n ⁇ f ch corresponding to cl to f ch . Therefore, by extracting the components of n ⁇ f cl to n ⁇ f ch , it is possible to detect the peak frequency at which the power spectrum becomes maximum in a predetermined frequency band (f cl to f ch ). If the peak frequency to be detected can be specified and selected from a plurality of peak frequencies, the second digital bandpass filter need not be used.
- the peak frequency detection apparatus for achieving the above object thins out the digital data sequence extracted by the second digital bandpass filter to 1 / r (r is an integer of 2 or more) and sets the sampling frequency to f s.
- the output of the thinning unit may be input to the FFT unit.
- the peak frequency can be detected with a desired frequency resolution f tg and time window length T tg even when the sampling frequency of the digital data string input to the peak frequency detection device is larger than f s .
- a first digital bandpass filter for extracting a digital data sequence of frequencies included in the specific frequency band, and a second digital frequency filter from an output of the n-th power unit
- a second digital bandpass filter that extracts a digital data sequence included in the frequency band, the output of the first digital bandpass filter is input to the nth power unit, and the second digital bandpass filter is input to the FFT unit.
- the output of the digital bandpass filter may be input, and the second frequency band may be approximately n ⁇ f cl to n ⁇ f ch .
- the lower the multiplier the less the extra frequency components generated by the power.
- the fewer the extra frequency components the easier it is to remove the extra frequency components with the digital bandpass filter.
- the upper limit of the multiplier n that can be handled in a multistage configuration by unitizing the power part and the digital bandpass filter is larger than the upper limit of the multiplier n that can be handled by the power stage of the first stage and the second digital bandpass filter. Therefore, by adopting this configuration, the range of n that can be set as a multiplier can be widened.
- a peak frequency detection device for achieving the above object includes an operation unit that receives a user instruction, and a parameter setting unit that sets at least one of n, f s , and N according to the instruction. May be.
- the functions of the respective means described in the claims are realized by hardware resources whose functions are specified by the configuration itself, hardware resources whose functions are specified by a program, or a combination thereof.
- the functions of these means are not limited to those realized by hardware resources that are physically independent of each other.
- the present invention can be realized as a method, a computer program, and a computer program recording medium.
- the recording medium for the computer program may be a magnetic recording medium, a magneto-optical recording medium, or any recording medium that will be developed in the future.
- the peak frequency f in the frequency band f cl to f ch defined by the lower limit value f cl and the upper limit value f ch of the received digital data sequence sampled at the sampling frequency f s is calculated.
- a peak frequency detection device that detects a desired frequency resolution f tg and a desired time window length T tg and a Doppler measuring instrument using the same will be described.
- the peak frequency detection apparatus 1 includes a first digital bandpass filter (BPF) unit 11, an n-th power unit 12, and a second digital bandpass filter (BPF). ) Part 13, FFT part 14, and 1 / n multiplication part 15.
- BPF digital bandpass filter
- BPF second digital bandpass filter
- Step 1. Determine multiplier n
- n (n is an integer of 2 or more) that satisfies the condition of n ⁇ 1 / (f tg ⁇ T tg ) is determined.
- n may be a minimum integer satisfying n ⁇ 1 / (f tg ⁇ T tg ), and if N does not exist in step 3 described later, n may be incremented by 1 and recalculation may be performed. You can make it larger from the beginning.
- Step 2. Select FFT sampling frequency f s )
- the sampling frequency of the digital data string input to the peak frequency detection device 1 is the FFT sampling frequency f s .
- f s cannot satisfy the above expression due to circuit restrictions or the like, another embodiment is used.
- N that satisfies f s / (n ⁇ f tg ) ⁇ N ⁇ f s ⁇ T tg (N is a power of 2) is selected. If, when the N is not present, either by increasing n to N are present, either by increasing f s, or both. However, from the FFT sampling theorem, f s > 2 ⁇ n ⁇ f ch Must be met.
- the multipliers n, f s and N selected by the method described above are set in the n-th power unit 12 and the FFT unit 14. Further, the lower limit value f cl and the upper limit value f ch of the band in which the peak frequency is to be detected are set as the cutoff frequency of the first digital BPF 11.
- the cut-off frequency of the second digital BPF 13 is set to a value that is n times the lower limit value f cl and the upper limit value f ch of the band in which the peak frequency is to be detected.
- the first digital BPF 11 selects an extra DC component, a low frequency component, a high frequency out of a set band from a wide range of frequency components of the digital data sequence.
- the frequency components close to the single frequency f are extracted by eliminating the components.
- f cl -f ch is set narrowly, and as shown in FIG. It is better to obtain the peak frequency separately.
- f cl to f ch are initial frequency bands
- f 1 and f 2 are two frequencies having a large power spectrum
- f cl ′ to f ch ′ are narrow frequency bands. Note that the interval between f cl ′ to f ch ′ need not be constant, and as shown in FIG. 5, the interval between f cl ′ to f ch ′ may be increased as the frequency increases.
- a (1) includes some extra frequency components having a small power spectrum in addition to the frequency f.
- this A (1) is input to the nth power unit 12.
- B (n) includes frequency components, n ⁇ f, (n ⁇ 2) ⁇ f, (n ⁇ 4) ⁇ f,..., Extra low-frequency components and high-frequency components having a small power spectrum.
- B (n) is input to the second digital BPF 13 and frequency components in the band of n ⁇ f cl to n ⁇ f ch are extracted.
- the frequency band of the second digital BPF 13 is preferably n ⁇ f cl to n ⁇ f ch , which is n times the frequency band of the first digital BPF 11, but may be slightly changed depending on the application.
- C (n) includes some extra frequency components in addition to the frequency n ⁇ f.
- the reason why the sampling frequency f s of the digital data string input to the peak frequency detection device 1 is set to f s > 2 ⁇ n ⁇ f ch is that the upper limit of the frequency band of C (n) is n ⁇ f ch That's why.
- the sampling frequency f s of the received digital data string is required to satisfy the FFT sampling theorem.
- C (n) is input to the FFT unit 14 to calculate the peak frequency.
- the FFT unit 14 performs FFT on C (n) with the set sampling frequency f s and the number of samples N, and calculates a peak frequency. Let the peak frequency output from the FFT unit 14 be (n ⁇ f ′).
- the peak frequency (n ⁇ f ′) output from the FFT unit 14 is passed through the 1 / n multiplication unit 15 to obtain f ′.
- the obtained f ′ is a calculated value of the peak frequency f of the digital data string input to the peak frequency detection device 1. This f ′ is calculated by satisfying f tg and T tg .
- the peak frequency detection device 1 can detect the peak frequency from the received digital data sequence with the desired frequency resolution f tg and the desired time window length T tg . And since the peak frequency detection apparatus 1 does not perform approximate calculation, there is no deterioration in accuracy of the calculated peak frequency. Therefore, the peak frequency can be detected with high accuracy.
- FIG. 6 is a block diagram showing a Doppler measuring instrument 2 incorporating the peak frequency detection device 1.
- the Doppler measuring instrument 2 includes a transmitter / receiver 21 having both a function of transmitting a signal wave into the medium and a function of receiving a reflected wave from an object in the medium.
- the transceiver 21 is connected to the output of the transmission circuit 23 and the input of the reception amplifier 24 via the transmission / reception switching circuit 22.
- the transmission circuit 23 generates a signal having a transmission frequency f tx .
- the output of the receiving amplifier 24 is provided with a modulator 25 that converts the received signal into an intermediate frequency signal.
- a signal having a local oscillation frequency f loc is supplied from the local oscillation circuit 26 to the modulator 25. .
- the output of the modulator 25, that is, the intermediate frequency signal is input to an analog / digital converter (A / D) 28 via an analog filter 27 and converted into a digital signal at a sampling frequency required for FFT. Next, it is input to the peak frequency detection device 1 and subjected to frequency analysis by FFT, and the peak frequency is output from the peak frequency detection device 1.
- a / D analog / digital converter
- the characteristics are set such that aliasing does not occur in the A / D converter 28 in the next stage.
- the frequency resolution f 0 is 12 Hz.
- the sampling frequency f s of the A / D converter 28 is determined.
- the frequency band f cl to f ch of the first digital BPF 11 is adjusted to 17000 ⁇ 1200 Hz
- f cl 15800 Hz
- N 4096 It becomes.
- sampling frequency fs and the number of samples N are determined, and the digital data string output from the analog / digital converter (A / D) 28 is input to the peak frequency detection device 1.
- a Butterworth type IIR filter having an 8th order and a cutoff frequency set to 189.6 kHz (12 ⁇ f cl ) and 218.4 kHz (12 ⁇ f ch ) is preferably used. Can be used.
- the Doppler frequency fdop of the received signal wave is It becomes.
- Sin ⁇ 2 ⁇ (17000 + 800) t ⁇ Sin (2 ⁇ 17800t) is assumed to be an input signal to the A / D converter 28 with a sampling frequency of 510 kHz, a pseudo digital data string is created, and the peak frequency is set according to the above setting.
- f ′ is calculated so as to satisfy f tg .
- T 1 is a section subjected to FFT.
- the reason why the first digital BPF 11 which is a band pass filter is provided will be described.
- [Expression 4] and [Expression 5] it is necessary to remove the extra DC component, low frequency component, and high frequency component other than the frequency bands f cl to f ch before raising to the power of n. There is. If this can be realized by the analog filter 27, the first digital BPF 11 can be dispensed with.
- such an analog filter is high-order, high-precision, large in circuit scale, and expensive.
- the analog filter 27 is designed so that aliasing does not occur in the A / D converter 28, and the extraction of the components of the frequency bands f cl to f ch can be easily designed with high order and high accuracy, and does not cost. It is best to use a digital bandpass filter.
- FIG. 8 is a block diagram showing a configuration of a peak frequency detection device 3 as a second embodiment of the present invention.
- the peak frequency detection device 3 has a configuration in which a thinning unit 16 is added before the first digital BPF 11 of the peak frequency detection device 1. This is because the sampling frequency is lowered by thinning out and reducing the digital data string after A / D conversion.
- Second implementation when the sampling frequency f s of the digital data string input to the peak frequency detection device 3 is high and the cutoff frequency f ch of the multiplier n and the first digital BPF 11 satisfies f s > 4 ⁇ n ⁇ f ch It is preferable to apply the form.
- the digital data string is thinned to 1 / r (r is an integer of 2 or more), and the digital data string after thinning is f s > 2 ⁇ n ⁇ f ch To be.
- f s is the sampling frequency after thinning.
- the peak frequency detector 3 of the present embodiment is applied to the Doppler measuring instrument 2 shown in FIG. 6 .
- necessary numerical data other than the following numerical data are the same as those in the first embodiment.
- the received digital data input to the thinning unit 16 column of the sampling frequency f is is a 10.2MHz.
- y sin (2 ⁇ 17800t) is assumed to be an input signal to the A / D converter 28 with a sampling frequency of 10.2 MHz, and a pseudo data string is created.
- the result of the actual frequency analysis with the setting is the same as the numerical example of the first embodiment, and satisfies f tg and T tg .
- FIG. 9 is a block diagram showing a configuration of a peak frequency detection device 4 showing a third embodiment of the present invention.
- the peak frequency detection device 4 has a configuration in which a thinning unit 17 is added after the second digital BPF 13 of the first embodiment.
- First digital BPF section 11, n th power unit 12, the second digital BPF13, the sampling frequency of the input digital data is, just what was f s in the first embodiment, becomes f IS, operation The same.
- the sampling frequency f s of the received digital data string is high, and f s > 4 ⁇ n ⁇ f ch with respect to the multiplier n and the cut-off frequency f ch of the first digital BPF 11, it is common to reduce the amount of calculation. It is preferable to apply the second embodiment. However, even in the present embodiment, processing satisfying the desired time window length f tg and the desired time window length T tg is possible.
- the thinning unit 17 when the received digital data sequence is thinned to 1 / r (r is an integer of 2 or more) and the sampling frequency of the thinned digital data sequence is f s , f s > 2 ⁇ n ⁇ f ch To be.
- the thinned digital data string is input to the FFT unit 14, and the subsequent processing is the same as in the first embodiment.
- this embodiment cannot be applied when r ⁇ 2 and f s / (n ⁇ f tg ) ⁇ N ⁇ f s ⁇ T tg (N is a power of 2) cannot be satisfied. In this case, the first embodiment is applied.
- the peak frequency detector 4 of the present embodiment is applied to the Doppler measuring instrument 2 shown in FIG. 6 .
- necessary numerical data other than the following numerical data are the same as those in the first embodiment.
- the sampling frequency of the A / D converter 28 is 10.2 MHz
- the sampling frequency f IS the received digital data sequence input to the thinning unit 17, the 10.2 MHz.
- y sin (2 ⁇ 17800t) is assumed to be an input signal to the A / D converter 28 with a sampling frequency of 10.2 MHz, and a pseudo digital data string is created.
- the result of actually performing the frequency analysis with the setting of the example is the same as the numerical example of the first embodiment, and satisfies f tg and T tg .
- FIG. 10 is a block diagram showing a configuration of a peak frequency detection device 5 as a fourth embodiment of the present invention.
- the peak frequency detection device 5 has a configuration in which an interpolation unit 18 is added before the digital BPF 11 of the first embodiment.
- the sampling frequency can be increased by interpolating and increasing the digital data string after A / D conversion.
- the sampling frequency of the digital data sequence input to the peak frequency detection device 5 has a low f s , and 2 ⁇ f ch ⁇ f s ⁇ 2 with respect to the higher cutoff frequency f ch of the multiplier n and the first digital BPF 11. In the case of ⁇ n ⁇ f ch , this embodiment is applied.
- the interpolation unit 18 interpolates the received digital data sequence by g times (g is an integer of 2 or more), and the sampling frequency f s of the digital data sequence after the interpolation is f s > 2 ⁇ n ⁇ f ch.
- the digital data sequence before interpolation is U (1): u 0 , u 1 , u 2 ,...
- the digital data sequence after interpolation is V (1): v 0 , v 1 , v 2 ,.
- the sampling frequency f IS reception digital data string input to the interpolation section 18 is a 42.5KHz.
- the digital data sequence before interpolation is U (1): u 0 , u 1 , u 2 ,..., And the digital data sequence after interpolation is V (1): v 0 , v 1 , v 2 ,.
- the sampling frequency f s of V (1) is 510 kHz. Therefore, the subsequent processing, as in the case of the configuration of FIG. 10, the V (1), is regarded as the reception digital data string of the sampling frequency f s to be input to the first digital BPF 11, frequency analysis in the same manner Just do it.
- y sin (2 ⁇ 17800t) is assumed to be an input signal to the A / D converter 28 with a sampling frequency of 42.5 kHz, and a pseudo digital data sequence is created.
- the result of actually performing the frequency analysis with the setting of the example is the same as the numerical example of the first embodiment, and satisfies f tg and T tg .
- FIG. 12A shows an input signal to the A / D converter 28.
- y sin (2 ⁇ 17000t) +2
- a sin waveform having an amplitude of 1 and a frequency of 17 kHz, in which the DC component 2 that cannot be removed by the analog filter remains is used.
- a signal obtained by A / D converting the input signal at 42.5 kHz, which is 2.5 times the sampling frequency of 17 kHz, corresponds to a digital data string input to the peak frequency detection device 1.
- the digital data string is expanded 12 times by the interpolation unit 18.
- FIG. 12B is an example of a digital data string output from the interpolation unit 18.
- the output of the first digital BPF unit 11 is such that the extra DC component, extra low frequency component, and extra high frequency component output from the interpolation unit 18 are deleted, and the converged waveform is a waveform close to a sin waveform.
- the frequency band is limited by the first digital BPF unit 11 in this way, generation of frequency components other than the formulas [4] and [5] is suppressed when the next n-th power unit 12 is raised to the nth power. Is done. That is, by providing a digital band-pass filter in the previous stage of the nth power unit 12, even if an extra frequency component is included in the digital data string, it can be handled. Accordingly, the performance of the analog filter 27 in the previous stage can be reduced to the extent that aliasing does not occur in the A / D converter 28 in the next stage, and the sampling frequency of the A / D converter 28 can also be reduced. And cost can be reduced.
- the cut-off frequency f cl, a digital band pass filter f ch, a digital high-pass filter cut-off frequency f cl may be formed by combining a digital low-pass filter cut-off frequency f ch.
- FIG. 13 is a block diagram showing a configuration of a peak frequency detection device 6 as a fifth embodiment of the present invention.
- the peak frequency detection device 6 is obtained by replacing the n-th power unit 12 and the second digital BPF 13 of the first embodiment with a multiple power unit 19.
- Blocks (j) are cascade-connected in the order of k stages (k is an integer of 2 or more).
- the direct current component is generated when y is raised to the power m j according to the equation [5]. Therefore, the digital BPF (j) needs to be able to delete the direct current component.
- the desired frequency resolution f tg and the desired time window length T tg are satisfied. Also in this embodiment, since approximate calculation is not performed, there is no deterioration in accuracy of the peak frequency to be calculated.
- the exponentiation unit and the second digital BPF unit are configured in multiple stages, the amount of calculation is increased as compared with the first embodiment.
- the advantage that the peak frequency can be calculated without deterioration in accuracy by satisfying the desired frequency resolution f tg and the desired time window length T tg up to a higher multiplier n is more than compensated for these negative aspects.
- This B (4) is passed through the digital BPF (1), and the digital data string after passing through the digital BPF (1) is C (4): c 0 , c 1 , c 2 ,.
- the digital BPF (1) is a Butterworth type IIR filter having an order of 8, an cutoff frequency of 63.2 kHz (4 ⁇ f cl ), and 72.8 kHz (4 ⁇ f ch ).
- each element of C (4) is cubed in the power part (2), and the digital data string after passing through the power part (2) is expressed as D (12): d 0 , d 1 , d 2 ,.
- D (12) the digital data string after passing through the power part (2) is expressed as D (12): d 0 , d 1 , d 2 ,.
- This D (12) is passed through the digital BPF (2), and the digital data string after passing through the digital BPF (2) is assumed to be E (12): e 0 , e 1 , e 2 ,.
- the digital BPF (2) is a Butterworth type IIR filter having an order of 8, a cut-off frequency of 189.6 kHz (4 ⁇ 3 ⁇ f cl ), and 218.4 kHz (4 ⁇ 3 ⁇ f ch ).
- FIG. 15 is a block diagram showing a configuration in which a parameter setting unit 20 is added to the peak frequency detection device 1 of the first embodiment.
- the parameter setting unit 20 is a computer including a processor, a memory, and an input / output mechanism, and the peak frequency detection devices 1 and 3 according to a user input using an operation unit (not shown) such as a keyboard, a mouse, or a touch panel display (not shown).
- an operation unit such as a keyboard, a mouse, or a touch panel display (not shown).
- the parameters are as follows as described above.
- Sampling frequency f is of received digital data string Sampling frequency f s of digital data string Desired frequency resolution f tg Desired time window length T tg n multiplier (n is an integer of 2 or more) Frequency band of the first digital BPF, approximately f cl to f ch (f cl ⁇ f ch ) Frequency band of second digital BPF Almost n ⁇ f cl to n ⁇ f ch FFT sampling frequency f s FFT sampling number N
- the parameter setting unit 20 may store the numerical values of all the parameters in advance in the memory in association with the input values that can be selected by the user, and may set the values according to the input values of the user.
- a numerical value may be stored in advance in a memory in association with an input value that can be selected by the user, set according to the user's input, and the remaining parameters may be calculated by the processor according to the input numerical value. .
- a peak frequency detection device used as a tuning assist device that allows a user to input only the scale number corresponding to the frequency and obtains and sets numerical values of all parameters from the memory according to the input scale number.
- the parameter setting unit 20 acquires and sets the numerical value of the parameter corresponding to any one of the scale numbers 1 to 88 from the memory.
- FIG. 16 is an example of a screen configuration diagram of the touch panel display in a state where a scale number is input.
- the numerical values of all parameters are determined in advance according to the scale number P and stored in the nonvolatile memory.
- the scale number corresponds to the key of the equal temperament piano
- scale number 1 corresponds to the frequency of the lowest note
- scale number 88 corresponds to the frequency of the highest note. That is, the frequency f p corresponding to musical scale number P is a value determined by the following equation [Expression 21] is stored in advance in the nonvolatile memory.
- f tg is a frequency corresponding to 2 cents worth of f p.
- the cent value is a value representing the frequency ratio between two sounds in a logarithmic expression, and 100 cents corresponds to a semitone having an average temperament of 12 scales.
- T tg is 1/10 of the time window length (1 / f tg ).
- f cl is a frequency of 50 under cents f p.
- f ch is the frequency of the 50 cents f p.
- the parameter setting unit 20 can set the numerical values of all the parameters according to the input of the scale number P. By using the parameters set in this way, the peak frequency of the received digital data sequence can be calculated.
- the digital data string input to the peak frequency detection device 1 may be sequentially input to the peak frequency detection device 1 in real time through a microphone and an A / D converter (not shown), or may be stored in a memory.
- the peak frequency can be calculated without any problem. Therefore, it is possible to lower the required specifications of the hardware in the previous stage of the peak frequency detection device, and to reduce the size and cost.
- the peak frequency can be calculated if the sampling frequency of the input signal is 2 ⁇ f ch or more with respect to the cut-off frequency f ch of the first digital BPF, so that the analog filter or A / D converter in the previous stage can be calculated. It is possible to lower the required hardware specifications.
- the multiplier n set to the power part is set to be large, the order of the digital bandpass filter can be increased and sharpened to be strong against external noise.
- the first digital BPF may be a low-pass filter.
- the present invention has been described with reference to detection of Doppler frequency in reflected echo and application to a tuning assist device as an example, the scope of application of the present invention is not limited to this.
- the present invention can be widely and generally applied to applications in which the peak frequency of a signal wave is detected by FFT.
- each functional unit according to the above embodiment may be realized by one or a plurality of LSIs (Large Scale Integration), and the plurality of functional units may be realized by a single LSI.
- the integration method is not limited to LSI, and may be realized by a dedicated circuit or a general-purpose processor.
- an FPGA Field Programmable Gate Array
- a reconfigurable processor Reconfigurable Processor
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Abstract
Description
n≧1/(ftg×Ttg)
fs/(n×ftg)≦N≦fs×Ttg
fs>2×n×fch
を満たす。なお本明細書において、fcl~fchはfcl以上fch以下を意味するものとする。
・ピーク周波数の周波数分解能fn≦ftg
・FFTの時間窓長Tn≦Ttg
fs/(n×ftg)≦N≦fs×Ttg(Nは2のべき乗)
となる。
n=m1×m2×…×mk
fcl(j)≒(m1×m2×…×mj)×fcl
fch(j)≒m1×m2×…×mj)×fch
であってもよい。
n≧1/(ftg×Ttg)
fs/(n×ftg)≦N≦fs×Ttg
fs>2×n×fch
1.第一実施形態
第一実施形態では、サンプリング周波数fsでサンプリングされた受信デジタルデータ列の、下限値fclと上限値fchとで定められた周波数帯域fcl~fchにおけるピーク周波数fを、所望の周波数分解能ftgと所望の時間窓長Ttgを満たして検出するピーク周波数検出装置とこれを用いたドップラー計測器について説明する。
(ステップ1.乗数nを定める)
まず、n≧1/(ftg×Ttg)の条件を満たすn(nは、2以上の整数)を定める。例えば、nを、n≧1/(ftg×Ttg)を満たす最小の整数とし、後述するステップ3でNが存在しなければ、nを1増加させて再計算をしても良いし、最初から大きめにしておいても良い。
(ステップ2.FFTのサンプリング周波数fsを選択する)
fs>2×n×fch
となるように選択する。なお、本実施形態では、ピーク周波数検出装置1に入力されるデジタルデータ列のサンプリング周波数がFFTのサンプリング周波数fsとなる。fsが回路上の制約等で上式を満たせない場合は、他の実施形態を使用する。
(ステップ3.FFTのサンプル数Nを定める)
次に、fs/(n×ftg)≦N≦fs×Ttg(Nは2のべき乗)を満たすNを選択する。もし、Nが存在しない場合は、Nが存在するまでnを大きくするか、fsを大きくするか、もしくはその両方を行う。ただし、FFTのサンプリング定理から、
fs>2×n×fch
を満たしていなければならない。
乗数n、fs、Nが設定されたピーク周波数検出装置1に対象とするデジタルデータ列を入力すると、以下のように、所望の周波数分解能ftgと所望の時間窓長Ttgを満たしてピーク周波数が検出される。
送信周波数ftx:120kHz
局部発信周波数floc:137kHz
検出最大速度(水平方向)V:15m/s
検出速度精度(水平方向)V0:0.15m/s
検出対象物の位置の精度(位置分解能)D0:7.5m
Δfp=2×1200Hz=2400Hz
となる。
fmid±(△fp/2)=17000±1200Hz
の信号を通し、次段のA/D変換器28でエイリアシングが発生しないような特性とする。
n≧1/(ftg×Ttg)=1/(12×0.01)=8.3
となる。ここでは、n=12とする。
fs>2×n×fch=2×12×18200=436800Hz
となるため、fs=510kHzとする。
N=4096
となる。
図8は、本発明の第二実施形態としてのピーク周波数検出装置3の構成を示すブロック図である。ピーク周波数検出装置3は、ピーク周波数検出装置1の第一デジタルBPF11の前に、間引き部16が追加された構成となっている。これは、A/D変換後のデジタルデータ列を間引いて減らすことによりサンプリング周波数を下げるためである。ピーク周波数検出装置3に入力されるデジタルデータ列のサンプリング周波数fsが高く、乗数nと第一デジタルBPF11のカットオフ周波数fchがfs>4×n×fchを満たす場合、第二実施形態を適用することが好ましい。
fs>2×n×fch
となるようにする。fsは間引き後のサンプリング周波数である。
P(1):p0,p1,p2,…とし、間引いた後のデジタルデータ列を、Q(1):q0,q1,q2,…としたとき、qi=p(r×i)(i=0,1,2,3,4,・・・)を行う。r=2のときは、q0=p0、q1=p2、q2=p4、q3=p6となる。
間引く方法はこれ以外であっても良い。例えば、r=2のときに、q0=(p0+p1)/2、q1=(p2+p3)/2、q2=(p4+p5)/2、…などとしても良い。
fs/(n×ftg)≦N≦fs×Ttg (Nは2のべき乗)
を満たすNが存在せず、nを大きくすることもできない場合、本実施例は適用できない。この場合は第一実施形態を適用する。
fs=fis/r=10.2MHz/20=510kHz>436.8kHz
となる。
図9は、本発明の第三実施形態を示すピーク周波数検出装置4の構成を示すブロック図である。ピーク周波数検出装置4は、第一実施形態の第二デジタルBPF13の後に間引き部17が追加された構成となっている。第一デジタルBPF部11、n乗部12、第二デジタルBPF13は、入力されるデジタルデータのサンプリング周波数が、第一実施形態ではfsだったものが、fisとなっただけで、動作は同じである。受信デジタルデータ列のサンプリング周波数fsが高く、乗数nと第一デジタルBPF11のカットオフ周波数fchに対して、fs>4×n×fchの場合、計算量を削減するため、一般的には第二実施形態を適用するのが良い。しかし、本実施形態であっても、所望の時間窓長ftg、所望の時間窓長Ttgを満たした処理が可能である。
fs>2×n×fch
となるようにする。間引いた後のデジタルデータ列は、FFT部14に入力され、その後の処置は、第一実施形態と同一である。
fs=fis/r=10.2MHz/20=510kHz>436.8kHz
となる。FFTのサンプリング周波数fsは、fs=510kHzとなる。
(以下、出願時に段落番号を繰り上げます) 図10は、本発明の第四実施形態としてのピーク周波数検出装置5の構成を示すブロック図である。ピーク周波数検出装置5は、第一実施形態のデジタルBPF11の前に、補間部18が追加された構成となっている。補間部18を追加することにより、A/D変換後のデジタルデータ列を補間して増やすことによりサンプリング周波数を上げることができる。ピーク周波数検出装置5に入力されるデジタルデータ列のサンプリング周波数がfsが低く、乗数nと第一デジタルBPF11の高いほうのカットオフ周波数fchに対して、2×fch<fs<2×n×fchの場合、本実施形態を適用する。
vi=u0 (i=0,1,2,3,・・・,(g-1))
vi=u1 (i=g,g+1,g+2,g+3,・・・,(2g-1))
vi=u2 (i=2g,2g+1,2g+2,2g+3,・・・,(3g-1))
・・・
となるように補間する。g=2のときは、v0=u0、v1=u0、v2=u1、v3=u1、v4=u2、v5=u2、…となる。補間する方法はこれ以外であっても良い。例えば、g=2のときに、
v0=u0
v1=(u0+u1)/2
v2=u1
v3=(u1+u2)/2
v4=u2
v5=(u2+u3)/2
・・・
となるように補間しても良い。
2×fch=2×18.2kHz=36.4kHz
2×n×fch=2×12×18.2kHz=436.8kHz
2×fch<fis<2×n×fch
であるから、本実施形態が適用される。
fs=fis×g=42.5kHz×12=510kHz>436.8kHz
となる。
v0~v11=u0
v12~v23=u1
v24~v35=u2
v36~v47=u3
・・・
となるように補間を行う。
図12Aは、A/D変換器28への入力信号で、
y=sin(2π17000t)+2
とする。つまり、アナログフィルタで取りきれなかった直流分2が残っている、振幅1、周波数17kHzのsin波形とする。この入力信号を、サンプリング周波数が17kHzの2.5倍である42.5kHzでA/D変換したものが、ピーク周波数検出装置1に入力されるデジタルデータ列に相当する。
図13は、本発明の第五実施形態としてのピーク周波数検出装置6の構成を示すブロック図である。ピーク周波数検出装置6は、第一実施形態のn乗部12と第二デジタルBPF13を多重べき乗部19に置き換えたものである。
n=m1×m2×・・・×mk
が成立するように選択される。
また、
fcl(j)≒(m1×m2×…×mj)×fcl
fch(j)≒(m1×m2×…×mj)×fch
と設定する。
とする。すなわち、bi= (ai)4 (i=0,1,2,3,4,…)となる。
ここまで説明したピーク周波数検出装置1、3-6に、パラメータ設定部を追加してもよい。図15は、第一実施形態のピーク周波数検出装置1にパラメータ設定部20を追加した構成を示すブロック図である。パラメータ設定部20は、プロセッサ、メモリ、入出力機構を備えるコンピュータであって、図示しないキーボードやマウスやタッチパネルディスプレイ等の図示しない操作部を用いたユーザの入力に応じてピーク周波数検出装置1、3-6にパラメータの値を設定する。パラメータは、これまで説明したとおり、次のようなものである。
受信デジタルデータ列のサンプリング周波数fis
デジタルデータ列のサンプリング周波数fs
所望の周波数分解能ftg
所望の時間窓長Ttg
n乗部の乗数n(nは2以上の整数)
第一デジタルBPFの周波数帯域 ほぼfcl~fch(fcl<fch)
第二デジタルBPFの周波数帯域 ほぼn×fcl~n×fch
FFTのサンプリング周波数fs
FFTのサンプリング数N
以上説明した本発明の実施形態によると、FFTによる周波数解析の際に制約となる周波数分解能(f0)と時間窓長(T0)との間にあるf0=1/T0と言う相反関係の問題を回避し、前記所望の周波数分解能ftgと前記所望の時間窓長Ttgでもって、信号波のピーク周波数の検出を可能にすることができる。受信デジタルデータ列のサンプリング周波数は、2×fch以上であればピーク周波数計算が可能となる。そして、近似計算やカーブフィッティング、平均化などの処理を必要としないため、ピーク周波数の計算精度の劣化は無い。
尚、本発明の技術的範囲は、上述した実施例に限定されるものではなく、本発明の要旨を逸脱しない範囲内において種々変更を加え得ることは勿論である。
Claims (11)
- 所定の周波数帯域(fcl~fch)においてパワースペクトルが最大となるピーク周波数を検出するピーク周波数検出装置であって、
デジタルデータ列の各要素をn乗(nは2以上の整数)するn乗部と、
サンプリング周波数fsと周波数分解能ftgと時間窓長Ttgに応じて決まるN(Nは2のべき乗の整数)個のn乗されたサンプリング周波数fsのデジタルデータ列に対して高速フーリエ変換を行って得られるパワースペクトルの最大値に対応する周波数を仮想ピーク周波数として導出するFFT部と、
前記仮想ピーク周波数を1/n倍した値をデジタルデータ列のピーク周波数として出力する1/n倍部と、
を備え、
n≧1/(ftg×Ttg)
fs/(n×ftg)≦N≦fs×Ttg
fs>2×n×fch
を満たすピーク周波数検出装置。 - 前記所定の周波数帯域に含まれる周波数のデジタルデータ列を抽出する第一デジタルバンドパスフィルタを備え、
前記n乗部には、前記第一デジタルバンドパスフィルタの出力が入力される、
請求項1に記載のピーク周波数検出装置。 - サンプリング周波数fisのデジタルデータ列を1/r(rは2以上の整数)に間引いてサンプリング周波数をfsにする間引き部を備え、
前記第一デジタルバンドパスフィルタには前記間引き部の出力が入力される、
ことを特徴とする請求項2に記載のピーク周波数検出装置。 - 前記デジタルデータ列をg倍(gは2以上の整数)に補間してサンプリング周波数をfsにする補間部を備え、
前記第一デジタルバンドパスフィルタには前記補間部の出力が入力される、
ことを特徴とする請求項2記載のピーク周波数検出装置。 - n乗されたN個の前記デジタルデータ列から第二の周波数帯域に含まれるデジタルデータ列を抽出する第二デジタルバンドパスフィルタを備え、
前記FFT部には、前記第二デジタルバンドパスフィルタによって抽出されたデジタルデータ列が入力され、
前記第二の周波数帯域は、ほぼn×fcl~n×fchである、
請求項1に記載のピーク周波数検出装置。 - 前記第二デジタルバンドパスフィルタで抽出されたデジタルデータ列を1/r(rは2以上の整数)に間引いてサンプリング周波数をfsとする間引き部を備え、
前記FFT部には、前記間引き部の出力が入力される、
請求項5に記載のピーク周波数検出装置。 - 前記特定の周波数帯域に含まれる周波数のデジタルデータ列を抽出する第一デジタルバンドパスフィルタと、
前記n乗部の出力から第二の周波数帯域に含まれるデジタルデータ列を抽出する第二デジタルバンドパスフィルタとを備え、
前記n乗部には、前記第一デジタルバンドパスフィルタの出力が入力され、
前記FFT部には、前記第二デジタルバンドパスフィルタの出力が入力され、
前記第二の周波数帯域は、ほぼn×fcl~n×fchである、
請求項1記載のピーク周波数検出装置。 - 前記n乗部に代えて、入力されるデジタルデータ列をmj乗(mjは2以上の整数)するべき乗部(j)(j=1,2,…,k)と前記べき乗部(j)の出力から特定の周波数帯域fcl(j)~fch(j)の信号を抽出するデジタルバンドパスフィルタ(j)とを備えるべき乗ブロック(j)をk(kは2以上の整数)段備える多重べき乗部を備え、
n=m1×m2×…×mk
fcl(j)≒(m1×m2×…×mj)×fcl
fch(j)≒m1×m2×…×mj)×fch
である請求項1~4のいずれか一項に記載のピーク周波数検出装置。 - ユーザの指示を受け付ける操作部と、
前記指示に応じたn、fs、Nの少なくともいずれかを設定するパラメータ設定部と、
を備える請求項1から8のいずれか一項に記載のピーク周波数検出装置。 - 所定の周波数帯域(fcl~fch)においてパワースペクトルが最大となるピーク周波数を検出するピーク周波数検出方法であって、
デジタルデータ列の各要素をn乗(nは2以上の整数)し、
サンプリング周波数fsと周波数分解能ftgと時間窓長Ttgに応じて決まるN(Nは2のべき乗の整数)個のn乗されたサンプリング周波数fsのデジタルデータ列に対して高速フーリエ変換を行って得られるパワースペクトルの最大値に対応する周波数を仮想ピーク周波数として導出し、
前記仮想ピーク周波数を1/n倍した値をデジタルデータ列のピーク周波数として出力する、
ことを含み、
n≧1/(ftg×Ttg)
fs/(n×ftg)≦N≦fs×Ttg
fs>2×n×fch
を満たすピーク周波数検出方法。 - 所定の周波数帯域(fcl~fch)においてパワースペクトルが最大となるピーク周波数を検出するピーク周波数検出プログラムであって、
デジタルデータ列の各要素をn乗(nは2以上の整数)するn乗部と、
サンプリング周波数fsと周波数分解能ftgと時間窓長Ttgに応じて決まるN(Nは2のべき乗の整数)個のn乗されたサンプリング周波数fsのデジタルデータ列に対して高速フーリエ変換を行って得られるパワースペクトルの最大値に対応する周波数を仮想ピーク周波数として導出するFFT部と、
前記仮想ピーク周波数を1/n倍した値をデジタルデータ列のピーク周波数として出力する1/n倍部と、
してコンピュータを機能させ、
n≧1/(ftg×Ttg)
fs/(n×ftg)≦N≦fs×Ttg
fs>2×n×fch
を満たすピーク周波数検出プログラム。
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