CN109581052A - A kind of reality of iterated interpolation answers conversion frequency estimation method - Google Patents
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- G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
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Abstract
The present invention relates to field of signal processing, the frequency estimating methods of especially noisy sinusoidal signal.Applicable object of the invention is the Frequency Estimation of noisy sinusoidal signal, comprising the following steps: firstly, using the multiple amplitude of Fast Fourier Transform (FFT) (FFT) algorithm pre-estimation sampled signal, and construct the reference signal for containing only negative frequency component；Secondly, sampled signal and reference signal are subtracted each other the real multiple conversion of realization, to inhibit the influence of negative frequency component；Then, two point interpolations are carried out to the frequency spectrum of complex signal, to estimate its frequency residual error and multiple amplitude, and reconfigures reference signal and complex signal；Finally, obtaining accurate frequency estimation by iterative calculation.The frequency estimating methods of noisy sinusoidal signal of the present invention realize that simple, noise immunity is good, strong real-time, dramatically reduce the influence of negative frequency component, improve the frequency estimation accuracy of signal.
Description
Technical field
The present invention relates to field of signal processing, the frequency estimating methods of especially noisy sinusoidal signal.
Background technique
The Frequency Estimation of sinusoidal signal is the frequency values that signal is detected from noise-containing sampled signal, is widely applied
In fields such as radar, communication, voice, biomedicine and metering devices, there is important theory significance and application value.
Frequency estimating methods can be mainly divided into two major classes: time domain method and frequency domain method.Time domain method is carried out to sampled signal
Time domain converts to obtain the method for frequency estimation, such method is simple, but vulnerable to the non-integer-period sampled influence of signal, anti-noise
Property it is poor, calculation amount is larger, is unfavorable for practical application, and main includes extension correlation method, phase frequency matching method etc..Frequency domain method is pair
Sampled signal carries out method of the spectrum analysis to obtain phase difference estimation value, is easy by hardware realization, and calculating speed is fast, real
When property is good, and has stronger noise immunity, thus has obtained more researchs, mainly includes windowed interpolation method, frequency spectrum shift method
Deng.
(1) correlation method (bibliography [1]: Cao Y, Wei G, Chen F J.A closed-form is extended
expanded autocorrelation method for frequency estimation of a sinusoid[J]
.Signal Processing, 2012,92 (4): 885-892.), this method is obtained by carrying out autocorrelation calculation to sampled signal
To autocorrelation signal and reference signal is generated, using least square method instrument error function, is obtained by minimizing error function
Frequency estimation.This method is simple, but vulnerable to the non-integer-period sampled influence of signal, and the estimated accuracy under low signal-to-noise ratio is not
It is high.
(2) phase frequency matching method (bibliography [2]: Tu Y Q, Shen Y L.Phase correction
autocorrelation-based frequency estimation method for sinusoidal signal[J]
.Signal Processing, 2017,130:183-189.), this method has redefined auto-correlation function, and it is non-to eliminate signal
Integer-period sampled influence improves frequency estimation accuracy, but calculates complexity, and real-time is poor.
(3) windowed interpolation method (bibliography [3]: K.Duda, S.Barczentewicz, Interpolated DFT for
sinα(x) windows [J], IEEE Transaction on Instrumentation&Measurement, 2014,63 (4):
754-760.), this method inhibits the influence of negative frequency component in signal by adding window, and the frequency spectrum of signal is reduced by interpolation
Leakage, but there are deviations for Frequency Estimation result, and precision is lower, and especially when signal frequency is lower, estimated accuracy is poor.
(4) frequency spectrum shift method (bibliography [4]:S.An Accurate Method for
Frequency Estimation of a Real Sinusoid [J] .IEEE Signal Processing Letters,
2016,23 (7): 915-918.), this method generates reference signal by rough estimate signal frequency, and is multiplied in fact with sampled signal
Existing frequency spectrum shift reduces the influence of negative frequency in the form of filtering out DC component, and uses high-precision complex signal Frequency Estimation
Algorithm realizes Frequency Estimation.The algorithm calculation amount is low, and precision is preferable, but signal frequency it is lower with high s/n ratio when, due to filter
Except negative frequency component is not thorough, cause frequency estimation accuracy lower.
Summary of the invention
The present invention is directed to propose a kind of estimated accuracy height, strong real-time, noise immunity is good, the Frequency Estimation side that has a wide range of application
Method is suitable for noisy sinusoidal signal frequency and estimates, solve the problems, such as that existing frequency-domain frequency estimation method is influenced by negative frequency, expands
Its application range.
The noisy sinusoidal signal frequency estimation method of the present invention is described as follows:
The basic thought of method: being converted into complex signal for real signal, then carry out spectrum analysis to complex signal, to reduce negative frequency
The influence of rate, while the influence by iterating to calculate elimination negative frequency as much as possible, further increase low frequency, middle high s/n ratio
Under the conditions of Frequency Estimation precision.
Firstly, pre-processing using Fast Fourier Transform (FFT) (fft algorithm) to sampled signal, the rough estimate that signal answers amplitude is obtained
Evaluation.Secondly, generating the reference signal for containing only negative frequency component according to the rough estimate evaluation of multiple amplitude.Then, by sampled signal
Subtract each other to obtain complex signal with reference signal, real multiple conversion is realized, to reduce negative frequency component in real signal.Finally, to complex signal
Frequency spectrum carries out interpolation, seeks more accurate frequency residual sum and answers amplitude, and regenerates reference signal and complex signal, then to multiple
Signal is handled, further to eliminate the influence of negative frequency component.Via iterating to calculate several times, obtain not influenced by negative frequency
Precise frequency estimated value.
If shown in sampled signal model such as formula (1).
X (n)=a cos (ω n+ θ)+z (n) (1)
In formula: ω, a, θ respectively indicate the frequency, amplitude and initial phase of signal, and n=0,1 ..., N-1, N is signal length；
Z (n) is that mean value is 0 respectively, variance σ2White Gaussian noise, the two is irrelevant.The signal-to-noise ratio of sampled signal is defined as:
SNR=a2/2σ2。
Signal amplitude and initial phase can be calculated according to frequency values, and therefore, frequency is the most important ginseng of sampled signal
Number can be indicated with formula (2):
ω=(k0+δ)ωs (2)
In formula: ωsFor frequency resolution, ωs=2 π/N；k0For the index value of Energy maximum value point in signal spectrum, k0=
[ω N/2 π], [] indicate take closest to integer；δ is frequency residual error, -0.5≤δ≤0.5.
Utilize Euler's formula:
A cos (ω n+ θ)=Aeiωn+A*e-iωn (3)
In formula: A is multiple amplitude, A=0.5aeiθ, A*=0.5ae-iθ, A and A*It is conjugated each other.
From formula (3) it can be seen that containing two kinds of frequency contents of positive frequency and negative frequency in sampled signal, in spectrum analysis
When, since the two is overlapped mutually influence, so that there are deviations for Frequency Estimation.
To eliminate influence of the negative frequency component to Frequency Estimation in signal, propose that a kind of reality of iterated interpolation answers conversion frequency
Estimation method.
Firstly, setpoint frequency Initial residuls:The number of iterations is i:1≤i≤I.
Step 1: estimation signal answers amplitude.
For sampled signal x0(n), fast Fourier (FFT) calculating is carried out to it, and it is maximum to obtain energy in signal spectrum
It is worth the index value of point.
The multiple amplitude of sampled signal is found out using formula (5):
Step 2: generating reference signal.
The estimated value that amplitude is answered according to signal contains only the reference signal of negative frequency component using formula (6) construction.
Step 3: realizing real multiple conversion.
Sampled signal and reference signal are subtracted each other using formula (7), real signal is converted into complex signal, realizes real multiple conversion,
The negative frequency component in signal is reduced, to inhibit the influence of negative frequency component.
xi(n)=x0(n)-ri(n) (7)
Step 4: interpolation calculation frequency residual error.
Two point interpolations are carried out to the signal spectrum after real multiple conversion using formula (8) and (9), it is residual to seek more accurate frequency
Difference.
Step 5: iterative calculation precise frequency.
After obtaining accurate frequency residual error, formula (5)-(9) are iterated to calculate, accurate frequency residual error is obtained, utilizes formula
(2) the frequency essence estimated value not influenced by negative frequency component is calculated.
Detailed description of the invention
The present invention is further described below according to the drawings and specific embodiments.
Fig. 1 is that the reality of iterated interpolation answers the basic thought of conversion frequency estimation method.
In figure: 1 indicates sampled signal；2 indicate Amplitude Estimation value；3 indicate the reference signal containing only negative frequency component；4 tables
Signal after showing real multiple conversion；5 indicate frequency residual error；6 indicate that FFT is calculated；7 and 10 indicate to generate reference signal；8 indicate real multiple
Conversion；9 indicate that iterated interpolation calculates.
Fig. 2 is sampled signal time domain schematic diagram.
Fig. 3 is the spectrogram of sampled signal and complex signal.
In figure: the frequency spectrum of the expression sampled signal of solid line 1；Dotted line 2 indicates the real frequency spectrum for answering converted signals.
Specific embodiment
A specific embodiment of the invention is as follows:
Firstly, setting setpoint frequency Initial residuls:The number of iterations is i:1≤i≤I.
Step 1: utilizing formulaTo sampled signal x0(n) it is pre-processed, and utilizes formulaEstimation signal answers amplitude.
Step 2: utilizing formulaConstruction contains only the reference signal of negative frequency component.
Step 3: utilizing formula xi(n)=x0(n)-ri(n) real multiple conversion is realized.
Step 4: utilizing formulaSignal after p=± 0.5 pair reality is converted again carries out frequency spectrum
Interpolation utilizes formulaSeek more accurate frequency residual error.
Step 5: iterative calculation signal, which answers amplitude and second step, obtains accurate frequency residual error to the 4th step, and utilize formulaCalculate frequency essence estimated value.
Claims (1)
1. a kind of reality of iterated interpolation answers conversion frequency estimation method, it is characterised in that: applicable object is noisy sinusoidal signal
Frequency Estimation；
Method includes the following steps:
Firstly, setpoint frequency Initial residuls:The number of iterations: I；
Step 1: to sampled signal x0(n) Fast Fourier Transform (FFT) is carried out, X (k)=FFT (x is obtained0(n)), 0≤k≤N/2-1,
ByObtain k0, and utilize formulaEstimation signal answers amplitude；
In formula: n indicates sampled signal x0(n) moment point, n=0,1 ..., N-1, N indicate signal length, and arg max X (k) is indicated
The value of k, ω when X (k) is maximizeds=2 π/N expression frequency resolution, subscript i expression i-th iteration, 1≤i≤I,Table
Show the estimated value of parameter；
Step 2: utilizing formulaConstruct reference signal；
In formula:It indicatesConjugate function；
Step 3: utilizing formula xi(n)=x0(n)-ri(n) real multiple conversion is realized；
Step 4: utilizing formulaTwo o'clock is carried out to the real frequency spectrum for answering converted signals
Interpolation, and utilize formulaSeek more accurate frequency residual error；
In formula: XpIndicate signal spectrum value, subscript p indicates interpolation interval；
Step 5: iterative calculation signal answer amplitude and second step to the 4th step, and utilize formulaCalculate frequency essence
Estimated value.
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| CN110808929A (en) * | 2019-10-23 | 2020-02-18 | 中国人民解放军陆军勤务学院 | Real-complex conversion type signal-to-noise ratio estimation algorithm of subtraction strategy |
| CN112307907A (en) * | 2020-10-09 | 2021-02-02 | 中国人民解放军陆军勤务学院 | Unbiased frequency estimation method for adaptive notch filter deviation compensation |
| CN112816779A (en) * | 2021-01-23 | 2021-05-18 | 中国人民解放军陆军勤务学院 | Harmonic real signal parameter estimation method for analytic signal generation |
| CN112883787A (en) * | 2021-01-14 | 2021-06-01 | 中国人民解放军陆军勤务学院 | Short sample low-frequency sinusoidal signal parameter estimation method based on spectrum matching |
| CN112964929A (en) * | 2021-01-14 | 2021-06-15 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | New algorithm for estimating parameters of noise-containing multi-frequency attenuation signals |
| CN113156206A (en) * | 2020-12-07 | 2021-07-23 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | Time-frequency combined noise-containing signal parameter estimation new algorithm |
| CN113341220A (en) * | 2021-08-05 | 2021-09-03 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | Method for estimating frequency of noise-containing multi-frequency attenuation real signal |
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Cited By (10)
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| CN110808929A (en) * | 2019-10-23 | 2020-02-18 | 中国人民解放军陆军勤务学院 | Real-complex conversion type signal-to-noise ratio estimation algorithm of subtraction strategy |
| CN112307907A (en) * | 2020-10-09 | 2021-02-02 | 中国人民解放军陆军勤务学院 | Unbiased frequency estimation method for adaptive notch filter deviation compensation |
| CN112307907B (en) * | 2020-10-09 | 2023-09-19 | 中国人民解放军陆军勤务学院 | Unbiased frequency estimation method for deviation compensation of self-adaptive wave trap |
| CN113156206A (en) * | 2020-12-07 | 2021-07-23 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | Time-frequency combined noise-containing signal parameter estimation new algorithm |
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| CN112883787A (en) * | 2021-01-14 | 2021-06-01 | 中国人民解放军陆军勤务学院 | Short sample low-frequency sinusoidal signal parameter estimation method based on spectrum matching |
| CN112964929A (en) * | 2021-01-14 | 2021-06-15 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | New algorithm for estimating parameters of noise-containing multi-frequency attenuation signals |
| CN112816779A (en) * | 2021-01-23 | 2021-05-18 | 中国人民解放军陆军勤务学院 | Harmonic real signal parameter estimation method for analytic signal generation |
| CN112816779B (en) * | 2021-01-23 | 2023-08-18 | 中国人民解放军陆军勤务学院 | Harmonic real signal parameter estimation method for analytic signal generation |
| CN113341220A (en) * | 2021-08-05 | 2021-09-03 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | Method for estimating frequency of noise-containing multi-frequency attenuation real signal |
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