CN117347712A - Signal frequency estimation method based on linear frequency modulation Z transformation - Google Patents
Signal frequency estimation method based on linear frequency modulation Z transformation Download PDFInfo
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- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
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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
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Abstract
A signal frequency estimation method based on linear frequency modulation Z transformation comprises the following implementation steps: (1) Sampling the signal x (t) to obtain a sampling sequence x (n); (2) Performing fast Fourier transform on the X (n) to obtain a rough estimated frequency spectrum X (k), taking an amplitude spectrum sequence |X (k) |, and obtaining a smoothed frequency spectrum X through a low-pass filter LP (k) The method comprises the steps of carrying out a first treatment on the surface of the (3) Find X LP (k) The maximum corresponding frequency of (2) is used as a central frequency point of the linear frequency modulation Z transformation; (4) calculating intermediate sequences g (n) and h (n); (5) Calculating output sequence of chirped Z-transform(6) Searching for the maximum value |Y (n) of the Y (n) modulus value m ) I and sequence number n corresponding thereto m The final frequency estimation result isThe invention adopts fast Fourier transform and linear frequency modulation Z transform to carry out coarse estimation and fine estimation of signal frequency, and has low calculation complexity and high estimation precision. The method can be applied to the fields of communication, radar, measurement and control and the like which have requirements on signal frequency estimation.
Description
Technical Field
The invention relates to the field of communication, radar, measurement and control and the like which have demands on signal frequency estimation, in particular to a signal frequency estimation method based on linear frequency modulation Z transformation.
Background
The frequency parameter estimation of the received signal means that the frequency corresponding to the maximum value of the signal amplitude spectrum is estimated, which is the signal processing requirement commonly used in spectrum sensing. Although the frequency estimation algorithm based on discrete fourier transform (Discrete Fourier Transform, DFT) has the advantage of high solving speed, the frequency corresponding to the maximum value of the obtained amplitude spectrum is only a coarse frequency estimation value due to the limited DFT resolution, and further processing is often needed to obtain a frequency refinement estimation result. In the frequency refinement estimation stage, common algorithms include a Jacobsen frequency estimation algorithm, a Candan frequency estimation algorithm, a 2N point DFT frequency estimation algorithm, a refinement frequency estimation method based on an ESPRIT algorithm and the like. The algorithm still has the defects of higher computational complexity, low estimation accuracy and the like.
Disclosure of Invention
The invention aims to solve the problems that: how to reduce the calculation complexity in signal frequency estimation as much as possible and improve the accuracy of the frequency estimation result. The method for solving the technical problem is a signal frequency estimation method based on linear frequency modulation Z transformation, which comprises the following implementation steps:
(1) Sampling the signal x (t) with a sampling frequency f s The number of sampling points is N, and a sampling sequence x (N) is obtained, wherein n=0, 1, … and N-1;
(2) Performing fast Fourier transform on the sampling sequence X (N) to obtain a rough estimated frequency spectrum X (k), and taking an amplitude spectrum sequence |X (k) | of the rough estimated frequency spectrum X (k), wherein k=0, 1, … and N-1; after passing |X (k) | through a low pass filter, a smoothed amplitude spectrum X is obtained LP (k) This is a real sequence;
(3) Finding a smoothed amplitude spectrum X LP (k) X is the maximum value of (2) LP (k m ) Wherein k is m For the sequence number corresponding to the maximum value, k is used m Sampling point number N, sampling frequency f s Calculating the center frequency point of the linear frequency modulation Z transformationDefine the starting frequency point of the chirp-Z-transform +.>Cut-off frequency point->B is the set linear frequency modulation Z transformation analysis frequency band bandwidth;
(4) Calculating intermediate sequences g (n) and h (n), whereinAnd->Wherein n=0, 1, …, N-1, wherein +.>And->
(5) Calculating output sequence of chirped Z-transformWherein n=0,1,…,N-1；
(6) Searching for the maximum value |Y (n) of the Y (n) modulus value m ) I and sequence number n corresponding thereto m The final frequency estimation result is
The invention has the beneficial effects that in various signal processing systems, the signal sampling sequence is subjected to secondary processing by utilizing the linear frequency modulation Z transformation, so that the signal frequency estimation precision is improved. The method can be applied to the fields of communication, radar, measurement and control and the like which have requirements on signal frequency estimation.
Drawings
Fig. 1 is a system block diagram of a signal frequency estimation method based on a chirp-Z-transform.
Detailed Description
For the signal x (t) to be estimated, the frequency estimation method is implemented in the digital domain, so that sampling is required, and then the time domain signal is converted into the frequency domain signal, and two-step estimation is performed. The first step is coarse estimation, through DFT conversion and smoothing treatment, a section where the frequency to be estimated is located is found; the second step is fine estimation by chirping Z-transform in a determined frequency interval. The overall estimation method flow is shown in fig. 1. The specific implementation steps are as follows:
(1) Sampling the signal x (t) with a sampling frequency f s The number of sampling points is N, resulting in a sampling sequence x (N), where n=0, 1, …, N-1. The sampling is to satisfy the Nyquist sampling theorem, ensuring that the signal is not distorted when converted to the digital domain.
(2) The sampling sequence X (N) is subjected to fast fourier transformation to obtain a rough estimated spectrum X (k), and the amplitude spectrum sequence |x (k) | is taken, wherein k=0, 1, …, N-1. Since the amplitude spectrum is usually the amplitude spectrum of a sequence sample and is not smooth, the amplitude spectrum X after the smoothing is obtained by passing the I X (k) I through a low-pass filter LP (k) This is a real sequence. The low pass filter cut-off frequency is determined by the envelope of the spectrum.
(3) Finding a smoothed amplitude spectrum X LP (k) X is the maximum value of (2) LP (k m ) Wherein k is m For the sequence number corresponding to the maximum value, k is used m Sampling point number N, sampling frequency f s Calculating the center frequency point of the linear frequency modulation Z transformationDefine the starting frequency point of the chirp-Z-transform +.>Cut-off frequency point->And B is the set frequency band width of the analysis frequency band of the chirp Z transformation, and the frequency to be estimated is required to be ensured to be positioned in the analysis frequency band determined by the chirp Z transformation.
(4) Calculating intermediate sequences g (n) and h (n), whereinAnd->Wherein n=0, 1, …, N-1, wherein +.>And->
(5) Calculating output sequence of chirped Z-transformWhere n=0, 1, …, N-1.
(6) Searching for the maximum value |Y (n) of the Y (n) modulus value m ) I and sequence number n corresponding thereto m The final frequency estimation result isA signal frequency estimation method based on the linear frequency modulation Z transformation is realized.
Claims (1)
1. A signal frequency estimation method based on linear frequency modulation Z transformation comprises the following implementation steps:
(1) Sampling the signal x (t) with a sampling frequency f s The number of sampling points is N, and a sampling sequence x (N) is obtained, wherein n=0, 1, … and N-1;
(2) Performing fast Fourier transform on the sampling sequence X (N) to obtain a rough estimated frequency spectrum X (k), and taking an amplitude spectrum sequence |X (k) | of the rough estimated frequency spectrum X (k), wherein k=0, 1, … and N-1; after passing |X (k) | through a low pass filter, a smoothed amplitude spectrum X is obtained LP (k) This is a real sequence;
(3) Finding a smoothed amplitude spectrum X LP (k) X is the maximum value of (2) LP (k m ) Wherein k is m For the sequence number corresponding to the maximum value, k is used m Sampling point number N, sampling frequency f s Calculating the center frequency point of the linear frequency modulation Z transformationDefine the starting frequency point of the chirp-Z-transform +.>Cut-off frequency point->B is the set linear frequency modulation Z transformation analysis frequency band bandwidth;
(4) Calculating intermediate sequences g (n) and h (n), whereinAnd->Wherein n=0, 1, …, N-1, wherein +.>And->
(5) Calculating output sequence of chirped Z-transformWherein n=0, 1, …, N-1;
(6) Searching for the maximum value |Y (n) of the Y (n) modulus value m ) I and sequence number n corresponding thereto m The final frequency estimation result is
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