CN111562438B - Sinusoidal signal frequency estimation method and device based on FFT and phase difference - Google Patents
Sinusoidal signal frequency estimation method and device based on FFT and phase difference Download PDFInfo
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Abstract
The invention discloses a sinusoidal signal frequency estimation method and device based on FFT and phase difference, and designs a frequency domain and time domain combined estimation method. Under the condition that the calculation resources and the calculation time are limited, the method has the advantages that the estimation precision and the estimation range are obviously improved compared with the traditional method, the realization is simple, and the effect is good. The method not only solves the problem of insufficient estimation precision of the FFT algorithm, but also solves the problems of small estimation range and large noise influence based on the time domain phase.
Description
Technical Field
The invention relates to the technical field of sinusoidal signal frequency estimation, in particular to a sinusoidal signal frequency estimation method and device based on FFT and phase difference.
Background
The frequency estimation of the sinusoidal signal is a classic subject of signal processing and is widely applied to the fields of radar, sonar, communication, electronic countermeasure and the like, so that the research on the frequency estimation has important theoretical significance and application value. For many years, researchers have studied many frequency estimation algorithms, focusing on two aspects, estimation accuracy and algorithm complexity.
The direct spectrum estimation method adopting the discrete Fourier transform of the FFT has the advantages of clear physical significance, high calculation speed, high real-time performance, contribution to hardware realization, higher signal-to-noise ratio gain, insensitivity to algorithm parameters and the like, is a method with better comprehensive performance, and is widely applied. But energy leakage and barrier effect exist in FFT, even under the condition of no noise influence, the frequency estimation of the method can not meet the precision requirement, and the algorithm precision depends on the length of the sampling data to a great extent. Aiming at the problem, many scholars successively provide a plurality of interpolation algorithms on the basis of FFT (fast Fourier transform), so that the frequency estimation precision is improved, but the precision is still difficult to guarantee under the condition of low signal-to-noise ratio.
Therefore, how to provide a sinusoidal signal frequency estimation method with higher accuracy is a problem that needs to be solved urgently by those skilled in the art.
Disclosure of Invention
In view of this, the invention provides a sinusoidal signal frequency estimation method and device based on FFT and phase difference, which adopts a method of combining frequency domain and time domain to achieve the improvement of sinusoidal signal frequency estimation effect, and has the advantages of simple principle, high precision, fast operation speed, and easy engineering implementation.
In order to achieve the purpose, the invention adopts the following technical scheme:
a sinusoidal signal frequency estimation method based on FFT and phase difference, comprising:
step 1: the detected signal S0 is subjected to CIC extraction filtering after front-end filtering, out-of-band noise is removed, the sampling rate is reduced, the extraction factor is R1, and an extracted signal S1 is obtained;
step 2: FFT conversion is carried out on the extracted signal S1 to obtain the frequency domain rough estimation frequency f of the signal S1c1；
And step 3: coarse estimation of frequency f from frequency domainc1Carry out digital frequency conversionShifting the frequency spectrum of the signal S1 to a zero frequency position to obtain a signal S2;
and 4, step 4: performing CIC extraction filtering on the signal S2, wherein the extraction factor is R2, and then performing low-pass filtering and denoising to obtain a signal S3;
and 5: calculating the phase of each sample point of the signal S3, and calculating the phase difference of adjacent sample points
And according to
Estimating the time domain fine estimation frequency fc2；
Wherein f isc2For the frequency of the signal after the low-pass filter, i.e. the frequency is estimated accurately in time domain, fsFor the sampling frequency of the incoming detected signal S0,
is the phase difference between two adjacent sampling points of the signal S3;
step 6: coarse estimation of frequency f based on frequency domainc1Sum time domain fine estimation frequency fc2Obtaining the estimated frequency f of the sinusoidal signalsig＝fc1+fc2。
Preferably, after step 6, the method further comprises: sinusoidal signal frequency f based on radio frequency down-conversion factor and estimationsigAnd obtaining the frequency of the radio frequency sinusoidal signal.
An FFT and phase difference based sinusoidal signal frequency estimation apparatus, comprising:
the first decimation filtering module is used for performing CIC decimation filtering on the detected signal S0 after front-end filtering, removing out-of-band noise and reducing the sampling rate, wherein the decimation factor is R1, and obtaining a decimated signal S1;
a frequency domain rough estimation module, configured to perform FFT on the extracted signal S1 to obtain a frequency domain rough estimation frequency f of the signal S1c1；
A frequency spectrum shifting module for roughly estimating the frequency f according to the frequency domainc1Carrying out digital frequency conversion on the obtained productShifting the frequency spectrum of the signal S1 to a zero frequency position to obtain a signal S2;
the second decimation filtering module is used for performing CIC decimation filtering on the signal S2, wherein the decimation factor is R2, and then performing low-pass filtering and denoising to obtain a signal S3;
a time domain fine estimation module for calculating the phase of each sampling point of the signal S3 and calculating the phase difference of adjacent sampling points
And according to
Estimating the time domain fine estimation frequency fc2；
Wherein f isc2For the frequency of the signal after the low-pass filter, i.e. the frequency is estimated accurately in time domain, fsFor the sampling frequency of the incoming detected signal S0,
is the phase difference between two adjacent sampling points of the signal S3;
a first calculation module for roughly estimating the frequency f based on the frequency domainc1Sum time domain fine estimation frequency fc2Obtaining the estimated frequency f of the sinusoidal signalsig＝fc1+fc2。
Preferably, the method further comprises the following steps: a second calculation module for calculating the frequency f of the sinusoidal signal according to the RF down-conversion factorsigAnd obtaining the frequency of the radio frequency sinusoidal signal.
According to the technical scheme, compared with the prior art, the invention discloses a sinusoidal signal frequency estimation method and device based on FFT and phase difference, a frequency domain and time domain combined estimation method is designed, the rough estimation frequency of a signal is estimated through an FFT algorithm, the frequency spectrum of the signal is down-converted to zero frequency according to the rough estimation frequency, then a uniform extraction low-pass filter is adopted to filter noise, phase information is extracted, phase difference information of front and rear sampling points is utilized to obtain the fine estimation frequency, the rough estimation frequency and the fine estimation frequency are added to obtain the estimation frequency of an input digital sinusoidal signal, and the frequency of a radio frequency sinusoidal signal is obtained by combining radio frequency down-conversion factors. Under the condition that the calculation resources and the calculation time are limited, the method has the advantages that the estimation precision and the estimation range are obviously improved compared with the traditional method, the realization is simple, and the effect is good. The method not only solves the problem of insufficient estimation precision of the FFT algorithm, but also solves the problems of small estimation range and large noise influence based on the time domain phase.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a flow chart of a sinusoidal signal frequency estimation method based on FFT and phase difference of the present invention;
FIG. 2 is a waveform diagram of the real part of the sinusoidal signal before and after passing through the Gaussian channel according to the present invention;
FIG. 3 is a diagram of the amplitude-frequency characteristic of a 36-fold CIC decimation filter provided by the present invention;
FIG. 4 is a diagram of the amplitude-frequency characteristic of a CIC decimation filter of 50 times provided by the present invention;
FIG. 5 is a graph of the amplitude-frequency characteristic of the low-pass filter provided by the present invention;
FIG. 6 shows frequency estimation errors corresponding to different signal frequencies when the number of FFT points is 512 and the normalized bandwidth of the low-pass filter is 0.1 according to the present invention;
FIG. 7 shows frequency estimation errors corresponding to different signal frequencies when the number of FFT points is 1024 and the normalized bandwidth of the low-pass filter is 0.05;
FIG. 8 is a diagram illustrating mean square error of frequency estimation for different SNR provided by the present invention;
fig. 9 is a schematic diagram of calculating a phase according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, an embodiment of the present invention discloses a sinusoidal signal frequency estimation method based on FFT and phase difference, including:
step 1: the detected signal S0 is subjected to CIC extraction filtering after front-end filtering, out-of-band noise is removed, the sampling rate is reduced, the extraction factor is R1, and an extracted signal S1 is obtained;
step 2: FFT conversion is carried out on the extracted signal S1 to obtain the frequency domain rough estimation frequency f of the signal S1c1；
And step 3: coarse estimation of frequency f from frequency domainc1Carrying out digital frequency conversion, and moving the frequency spectrum of the signal S1 to a zero frequency position to obtain a signal S2;
in order to simplify the denoising filter, the signal is moved to zero frequency, and a uniform low-pass filter can be adopted in a larger estimation range, so that the design of the low-pass filter is irrelevant to the frequency range of the sinusoidal signal to be analyzed, the design of the filter is simplified, and the analysis effect is improved.
And 4, step 4: performing CIC extraction filtering on the signal S2, wherein the extraction factor is R2, and then performing low-pass filtering and denoising to obtain a signal S3;
and 5: calculating the phase of each sample point of the signal S3, and calculating the phase difference of adjacent sample points
And according to
Estimating the time domain fine estimation frequency fc2；
In particular, the signal S3 is a series of digital signals consisting of a real part and an imaginary part, such as: s31、S32、S33、S34……S3k……S3N；
S3k＝Ik+iQk k＝1,2,3……,N；
θk＝arctan(Qk/Ik)
Take FIG. 9 as an example, θk＝arctan(Qk/Ik)＝arctan(-2/3)。
Wherein f isc2For the frequency of the signal after the low-pass filter, i.e. the frequency is estimated accurately in time domain, fsFor the sampling frequency of the incoming detected signal S0,
is the phase difference between two adjacent sampling points of the signal S3;
step 6: coarse estimation of frequency f based on frequency domainc1Sum time domain fine estimation frequency fc2Obtaining the estimated frequency f of the sinusoidal signalsig＝fc1+fc2。
The invention discloses a sinusoidal signal frequency estimation method based on FFT and phase difference, which is a method capable of quickly and accurately estimating the frequency of a sinusoidal signal, and is a new method combining a frequency domain and a time domain to improve the frequency estimation effect of the sinusoidal signal.
The technical scheme provided by the invention has the main idea that frequency domain frequency estimation is carried out based on FFT to obtain a coarse estimation value, and the signal is moved to zero frequency according to the coarse estimation value, so that an extraction filter and a low-pass filter can be uniformly designed to realize low-pass filtering and de-noising of sinusoidal signals in a wide frequency range, and then time domain frequency estimation is carried out on the de-noised low-pass signals based on phase difference to obtain a frequency precise estimation value. And finally, obtaining an actual frequency value by combining the rough estimation value and the fine estimation value. The method has the advantages of simple principle, high accuracy, high operation speed and easy engineering realization.
In order to further optimize the above technical solution, after step 6, the method further includes: sinusoidal signal frequency f based on radio frequency down-conversion factor and estimationsigAnd obtaining the frequency of the radio frequency sinusoidal signal.
In addition, the embodiment of the invention also discloses a sinusoidal signal frequency estimation device based on FFT and phase difference, which comprises:
the first decimation filtering module is used for performing CIC decimation filtering on the detected signal S0 after front-end filtering, removing out-of-band noise and reducing the sampling rate, wherein the decimation factor is R1, and obtaining a decimated signal S1;
a frequency domain rough estimation module, configured to perform FFT on the extracted signal S1 to obtain a frequency domain rough estimation frequency f of the signal S1c1；
A frequency spectrum shifting module for roughly estimating the frequency f according to the frequency domainc1Carrying out digital frequency conversion, and moving the frequency spectrum of the signal S1 to a zero frequency position to obtain a signal S2;
the second decimation filtering module is used for performing CIC decimation filtering on the signal S2, wherein the decimation factor is R2, and then performing low-pass filtering and denoising to obtain a signal S3;
a time domain fine estimation module for calculating the phase of each sampling point of the signal S3 and calculating the phase difference of adjacent sampling points
And according to
Estimating the time domain fine estimation frequency fc2；
Wherein f isc2For the frequency of the signal after the low-pass filter, i.e. the frequency is estimated accurately in time domain, fsFor the sampling frequency of the incoming detected signal S0,
is the phase difference between two adjacent sampling points of the signal S3;
a first calculation module for roughly estimating the frequency f based on the frequency domainc1Sum time domain fine estimation frequency fc2Obtaining the estimated frequency f of the sinusoidal signalsig＝fc1+fc2。
In order to further optimize the above technical solution, the method further comprises: second calculation modelA block for estimating the sinusoidal signal frequency f from the radio frequency down-conversion factorsigAnd obtaining the frequency of the radio frequency sinusoidal signal.
The method for estimating the frequency of the sinusoidal signal based on the FFT and the phase difference according to the present invention will be further described with reference to the following embodiments.
Sine signal x (t) ═ exp (j × 2 × pi × f to be measuredcT), wherein the sampling frequency fsIs 90MHz, fcIs [ -500:1:500 [)]kHz, FFT point number of 512, Gaussian white noise test algorithm performance, input signal-to-noise ratio of-10 dB, fcAt-500 kHz, the waveform of the real part of the sinusoidal signal before and after passing through the Gaussian channel is as shown in FIG. 2.
(1) Extracting and filtering a signal to be detected, and extracting and filtering data by adopting a Cascade Integrator Comb (CIC) filter, wherein a Z-domain transfer function is as follows:
where R is the decimation factor, D is the number of filter delays, and S is the filter order. Specifically, the filter R is 36, D is 1, S is 4, the amplitude-frequency characteristic is as shown in fig. 3, and the frequency after decimation is 2.5 MHz;
(2) performing FFT (fast Fourier transform) on the extracted signal, finding out a maximum amplitude point n of the signal, and calculating the rough estimation frequency of the signal, wherein the FFT estimation precision is 4.8828 kHz;
specifically, the extracted signal is divided into 16 segments of data with length of 512 points, each segment of data is subjected to FFT transformation, a point n corresponding to the maximum amplitude is obtained, and the point n is converted into a rough estimated frequency:
averaging 16 coarse estimation frequencies to obtain fc1；
(3) From the coarse estimated frequency fc1Carrying out digital down-conversion, and moving the signal to zero frequency;
(4) extracting and filtering the signal by adopting a Cascade Integration Comb (CIC) filter, wherein R is 50, D is 1, S is 4, the amplitude-frequency characteristic is shown in figure 4, and the sampling rate after extraction is 50 kHz; the signal passes through a low-pass filter with the normalized bandwidth of 0.1 and the normalized cutoff frequency of 0.15 to remove noise, and the amplitude-frequency characteristic of the low-pass filter is shown in figure 5;
(5) calculating the phase of each sampling point through an arctan function, performing phase differentiation (subtracting a phase value of a previous point from an angle value of a next point), and performing 100-point averaging to obtain the phase of each sampling point
(6) Will be provided with
Substituting into formula
Calculating the time domain fine estimation frequency fc2；
(7) The final estimated frequency is f ═ fc1+fc2。
The frequency estimation error curves corresponding to different signal frequencies are shown in fig. 6, and it can be seen that the estimation accuracy of the algorithm is independent of the frequency of the sinusoidal signal itself within the whole analysis bandwidth, and the error is small and is in the range of [ -0.280.31] Hz.
The number of FFT points is changed to 1024, the low pass filter normalized bandwidth is 0.05, the cutoff normalized bandwidth is 0.1, and the frequency estimation error curve is shown in fig. 7. The filter bandwidth is narrower, noise filtering is cleaner, estimation precision is higher, and estimation error is in the range of-0.0830.074 Hz.
Fixing the sine signal to 400kHz, adding Gaussian white noise under the sampling rate of 90MHz, setting the signal-to-noise ratio to be-20-30 dB, setting the number of FFT points to be 512, and keeping the parameters of the step (1) … and the step (7) unchanged. Calculating the mean square error of frequency estimation, wherein the estimated value is f, and the true value is fcMean square error δ ═ E ((f-f) is definedc)2) The average is calculated 1000 times, and the mean square error curve of the frequency estimation under different signal-to-noise ratios is shown in fig. 8.
It can be seen from the above example that, the sinusoidal signal frequency estimation method based on FFT and phase difference provided by the present invention fully utilizes the large range of frequency domain estimation and the high accuracy of time domain estimation by combining the frequency domain rough estimation and the time domain fine estimation, and has the advantages of simple principle, uncomplicated operation, high estimation accuracy and high speed, and has strong practical value.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (4)
1. A sinusoidal signal frequency estimation method based on FFT and phase difference is characterized by comprising the following steps:
step 1: the detected signal S0 is subjected to CIC extraction filtering after front-end filtering, out-of-band noise is removed, the sampling rate is reduced, the extraction factor is R1, and an extracted signal S1 is obtained;
step 2: FFT conversion is carried out on the extracted signal S1 to obtain the frequency domain rough estimation frequency f of the signal S1c1；
And step 3: coarse estimation of frequency f from frequency domainc1Carrying out digital frequency conversion, and moving the frequency spectrum of the signal S1 to a zero frequency position to obtain a signal S2;
and 4, step 4: performing CIC extraction filtering on the signal S2, wherein the extraction factor is R2, and then performing low-pass filtering and denoising to obtain a signal S3;
and 5: calculating the phase of each sample point of the signal S3, and calculating the phase difference of adjacent sample points
And according to
Estimating the time domain fine estimation frequency fc2(ii) a Calculating the phase of each sampling point through an arctan function, performing phase differentiation, subtracting the phase value of the previous point from the angle value of the next point, and performing 100-point averaging to obtain the phase of each sampling point
Wherein f isc2For the frequency of the signal after the low-pass filter, i.e. the frequency is estimated accurately in time domain, fsFor the sampling frequency of the incoming detected signal S0,
is the phase difference between two adjacent sampling points of the signal S3;
step 6: coarse estimation of frequency f based on frequency domainc1Sum time domain fine estimation frequency fc2Obtaining the estimated frequency f of the sinusoidal signalsig＝fc1+fc2。
2. The FFT and phase difference based sinusoidal signal frequency estimation method of claim 1, further comprising, after step 6: sinusoidal signal frequency f based on radio frequency down-conversion factor and estimationsigAnd obtaining the frequency of the radio frequency sinusoidal signal.
3. An apparatus for sinusoidal signal frequency estimation based on FFT and phase difference, comprising:
the first decimation filtering module is used for performing CIC decimation filtering on the detected signal S0 after front-end filtering, removing out-of-band noise and reducing the sampling rate, wherein the decimation factor is R1, and obtaining a decimated signal S1;
a frequency domain rough estimation module, configured to perform FFT on the extracted signal S1 to obtain a frequency domain rough estimation frequency f of the signal S1c1；
A frequency spectrum shifting module for roughly estimating the frequency f according to the frequency domainc1Carrying out digital frequency conversion, and moving the frequency spectrum of the signal S1 to a zero frequency position to obtain a signal S2;
the second decimation filtering module is used for performing CIC decimation filtering on the signal S2, wherein the decimation factor is R2, and then performing low-pass filtering and denoising to obtain a signal S3;
a time domain fine estimation module for calculating the phase of each sampling point of the signal S3 and calculating the phase difference of adjacent sampling points
And according to
Estimating the time domain fine estimation frequency fc2(ii) a Calculating the phase of each sampling point through an arctan function, performing phase differentiation, subtracting the phase value of the previous point from the angle value of the next point, and performing 100-point averaging to obtain the phase of each sampling point
Wherein f isc2For the frequency of the signal after the low-pass filter, i.e. the frequency is estimated accurately in time domain, fsFor the sampling frequency of the incoming detected signal S0,
is the phase difference between two adjacent sampling points of the signal S3;
a first calculation module for roughly estimating the frequency f based on the frequency domainc1Sum time domain fine estimation frequency fc2Obtaining the estimated frequency f of the sinusoidal signalsig＝fc1+fc2。
4. The FFT and phase difference based sinusoidal signal frequency estimation device of claim 3, further comprising: a second calculation module for calculating the frequency f of the sinusoidal signal according to the RF down-conversion factorsigAnd obtaining the frequency of the radio frequency sinusoidal signal.
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