A high-precision frequency estimation method for real sinusoidal signals with immunity to multi-frequency interference

Abstract

The present invention provides a high-precision frequency estimation method for real sinusoidal signals that is resistant to multi-frequency interference and belongs to the field of information technology. The algorithm is mainly aimed at multi-frequency interference real sinusoidal signals with known frequency orders. First, the frequency interference is eliminated step by step through zero-filled FFT spectrum peak search, binary interpolation, zero spectrum line correction and other technologies to obtain rough estimates of signal frequency and complex amplitude; then, based on the existing frequency and complex amplitude estimation results, the multi-frequency interference is eliminated, and the frequency and complex amplitude estimation results are continuously updated using three-point interpolation, zero spectrum line correction and other technologies; finally, a high-precision estimation result of the signal frequency is obtained through step-by-step double-loop iterative operations. The zero spectrum line correction technology innovatively proposed by the present invention and used multiple times in the calculation can efficiently suppress the positive and negative frequency interference under the real sinusoidal signal, so that the method of the present invention can obtain strong anti-interference ability when the frequency interval between the interference signal and the signal to be estimated is extremely small, and achieve high-precision frequency estimation, especially under high signal-to-noise ratio. The performance advantage is obvious.

Description

Technical Field

[0001] The present invention relates to the field of information technology, and in particular to a parameter estimation problem in signal processing technology. Background Art

[0002] Signal processing is a widespread need in the information technology field. As the Fourier series shows, any periodic signal can be composed of a superposition of sine or cosine waves of varying frequencies. Therefore, the problem of estimating sinusoidal signal parameters has become fundamental to the development of various signal processing techniques. Multi-frequency interference real sinusoidal signals, as a specific sinusoidal signal model, are widely used in technical fields such as power systems, instrumentation, device measurement, and nondestructive testing.

[0003] The multi-frequency interference real sinusoidal signal can be regarded as the superposition of multiple single-frequency real sinusoidal signals. Usually, the single-frequency signal with the strongest energy (largest amplitude) is the parameter signal to be estimated. According to the Euler formula, the multi-frequency interference real sinusoidal signal can be further decomposed into the superposition of multiple positive frequency components and negative frequency components. As a result, there will be mutual interference between the positive and negative frequency components in the signal spectrum analysis process, which will seriously reduce the accuracy of spectrum analysis. To this end, many scholars at home and abroad have conducted research on it and proposed many feasible solutions, such as using windowing to reduce the spectrum leakage of the interference signal and reduce the influence of the interference frequency on the signal to be estimated (Zhang Hongbo, Cai Xiaofeng, Lu Gaifeng. Power harmonic analysis based on dual-window full-phase FFT dual-spectral line correction [J]. Instrumentation, 2015, 36, (12): 2835-2841.). However, this method increases the equivalent noise bandwidth. At the same time, due to the widening of the main lobe of the signal after windowing, this method is not suitable for the case where the interference frequency is close to the frequency to be estimated. The paper (DJUKANOVIC S, POPOVIC V. Efficient and accurate detection and frequency estimation of multiple sinusoids [J]. IEEE Access, 2019, 7: 1118-1125.) proposes a method based on the idea of ​​frequency shift and low-pass filtering, which is referred to as the DS method in this paper. This method adopts an iterative interference elimination algorithm structure and achieves high frequency estimation accuracy by repeatedly filtering out negative frequency component interference. However, this method does not completely eliminate negative frequency interference. The literature (Ze-Long Mou, Ya-Qing Tu, Peng Chen, Kui Wang. Accurate frequency estimation of multiple complex and real sinusoids based on iterative interpolation [J]. Digital Signal Processing, 2021, 117: 103173.) proposes a method for reducing negative frequency interference, which is called the MZL method in this invention. This method also adopts the algorithm structure of iterative interference elimination. Although the more accurate three-point interpolation is used in the iteration, the performance of suppressing negative frequency interference is similar to that of the DS method, especially when the interference frequency is close to the frequency to be estimated, the estimation accuracy drops significantly.

[0004] In summary, although there have been many studies on parameter estimation of multi-frequency real sinusoidal signals, due to the influence of negative frequency interference, existing methods perform poorly when the interference frequency is close to the frequency to be estimated, and targeted research and solutions are urgently needed. Summary of the Invention

[0005] To address the difficulty of effectively suppressing adjacent frequency interference in the presence of negative frequency interference, this paper proposes a high-precision frequency estimation method for real sinusoidal signals that is resistant to multi-frequency interference. This method incorporates a novel zero-spectral line correction technique that effectively suppresses the effects of negative frequency interference on real signals. Through a dual-loop computational structure that iterates and eliminates interference on a frequency-by-frequency basis, this method effectively suppresses adjacent frequency interference and achieves high-precision frequency estimation of the signal to be estimated.

[0006] The technical solution of the present invention is a high-precision frequency estimation algorithm for real sinusoidal signals that is resistant to multi-frequency interference. The overall technical solution includes: ① For a multi-frequency interference signal x(n) with a known frequency order L, a step-by-step cycle of coarse frequency estimation is performed. When the frequency order is l, the specific operation is as follows: First, a zero-filled FFT operation is performed to search for spectrum peaks to obtain an initial value of the signal frequency estimation. Secondly, based on Perform zero spectrum line correction to calculate the signal complex amplitude Then, the bisection interpolation method is used to obtain a rough estimate of the signal frequency Again, based on a more precise Perform zero spectrum line calibration update value; finally, based on and Construct the l-th order signal and achieve interference elimination. ② Use the double loop structure of iterative operation and step-by-step interference elimination to achieve high-precision estimation of signal frequency. The specific operation when the number of iterations is i (the maximum number of iterations is Q) and the frequency order is l is: First, based on the known and Eliminate the signals other than the lth order in the signal x(n) to achieve interference elimination; then, use the three-point interpolation method with higher estimation accuracy to obtain the accurate estimation value of the signal frequency Finally, based on a more accurate Perform zero spectrum line correction to update complex amplitude ③ When the number of iterations reaches Q and all frequency orders are traversed, the signal frequency estimation result is returned

[0007] The frequency estimation initial value calculation step based on zero-filled FFT in step ① includes: first, setting s(n)=x(n) and performing signal zero-filling to obtain s E (n) = [s(n), 0, 0, ..., 0], the zero-filling length can be set according to the accuracy and computational complexity. Then, the fast Fourier transform is performed to obtain S(m) = FFT(s E (n)) and perform spectrum peak search to obtain Finally, the initial frequency estimate is

[0008] All calculation steps involving zero spectrum line correction in steps ① and ② are: according to known conditions, or h(n)=s(n) or y(n) is substituted into q=round(Nω * / π) and the following formula:

[0009]

[0010] The steps for calculating the rough estimated value of the signal frequency by using the bisection interpolation method in step ① are as follows: first, negative frequency interference is eliminated, that is, Then, calculate the DTFT transform Finally, we get a rough estimate of the frequency

[0011] The signal interference elimination in step ① is to make

[0012] In step ②, the interference other than the first order is eliminated by setting

[0013] The calculation steps of the three-point interpolation method with higher accuracy adopted in step ② are: first, negative frequency interference is eliminated, that is, Then, calculate and Finally, the precise estimate of the signal frequency is calculated using the following formula:

[0014]

[0015] The frequency estimation method proposed in the present invention can achieve high-precision frequency estimation when the frequency interval between the interference signal and the signal to be estimated is more than 1.5 times the DFT frequency gap, when the amplitude of the interference signal is less than 50% of the amplitude of the signal to be estimated. The estimation performance of the method is significantly higher than that of other similar methods in combating adjacent frequency interference. At the same time, the method of the present invention can also achieve accurate estimation of the frequencies of interference signals of various orders. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] To clearly illustrate the technical solution of the present invention, the following are the drawings and brief descriptions required for describing the embodiments. Obviously, the drawings shown are only some embodiments of the present invention, and those skilled in the art can create other similar drawings based on the drawings without inventive effort. The drawings shown in the present invention are:

[0017] Figure 1 Signal processing flow chart of the present invention;

[0018] Figure 2 Comparison of frequency estimation variance between the present invention and other methods under different signal-to-noise ratio values ​​(L=2);

[0019] Figure 3 Comparison of frequency estimation variance between the present invention and other methods under different signal-to-noise ratio values ​​(L=4);

[0020] Figure 4 Comparison of frequency estimation variance between the present invention and other methods under different signal lengths;

[0021] Figure 5 The frequency estimation variance of the present invention is compared with other methods at different signal frequency intervals. DETAILED DESCRIPTION

[0022] The following is a detailed technical description of the present invention in conjunction with the accompanying drawings and examples. This example provides a detailed implementation method and calculation process based on the technical solution of the present invention. However, the protection scope of the present invention is not limited to the following examples. It should be understood that the examples are only for illustrating the present invention, not for limiting the protection scope of the present invention.

[0023] according to Figure 1 The signal processing flow shown in the figure considers that the input is a multi-frequency interference real sinusoidal signal with a known frequency order L. where a l 、ω l and θ l are the amplitude, frequency and initial phase of the l-th order signal respectively. Assume that the signal order is arranged from strong to weak according to the signal energy, that is, a1≥a2≥,…,≥a L , then usually l = 1 is the signal to be estimated, and the rest are multi-frequency interference; z(n) is the zero mean variance of the superimposed signal σ 2 The total length of the signal is N.

[0024] First, perform coarse frequency estimation of the signal at each order, making full use of technical means such as zero-padding FFT, zero spectrum line correction, and two-point bisection interpolation to obtain as accurate a coarse frequency estimation result as possible. Specifically, repeat the following operations in the order from 1 to L:

[0025] (a) Let s(n) = x(n) and obtain the initial value of the signal frequency estimate by zero-padding FFT spectrum peak search Taking into account the computational complexity and estimation accuracy, preferably, the zero-padding length can be set to N. In this case, the zero-padding signal s 2N (n)=[s(n),0,0,,0] is 2N in length, S(m)=FFT(s 2N (n)), which can be searched

[0026] (b) Perform zero spectrum line correction and calculate Thus, the complex amplitude of the signal is obtained

[0027]

[0028] (c) Use bisection interpolation to obtain the rough frequency estimate of the signal

[0029]

[0030] in

[0031] (d) Perform zero spectrum line correction again with a more accurate signal frequency, that is, calculate and

[0032]

[0033] (e) Gradually eliminate the interference signal, that is,

[0034]

[0035] Then, based on the obtained signal rough frequency estimate The iterative interference elimination method can be used to eliminate the multi-frequency interference outside the signal to be estimated step by step. According to the double-iterative nested operation structure, the high-precision estimation value of the signal frequency is continuously obtained through zero spectrum line correction and three-point interpolation technology. The specific operation is calculated in order of the number of iterations i from 1 to Q (Q is the maximum number of iterations, usually Q=2). In each iterative calculation, the following operations are repeated in order of the frequency order l from 1 to L:

[0036] (a) Based on immediate Eliminate all interference signals except the lth order frequency, that is,

[0037]

[0038] (b) Preferably, the frequency estimate under the i-th iteration is calculated using the three-point interpolation method with higher accuracy.

[0039]

[0040] in

[0041] (c) Perform zero spectrum line correction again with a more accurate signal frequency, that is, calculate and

[0042]

[0043] Finally, after completing the double loop iteration operation, the high-precision estimation result of the signal frequency can be returned.

[0044] To illustrate the estimation performance of the algorithm of the present invention, this embodiment uses numerical simulation experiments to compare the algorithm of the present invention with several other typical algorithms, including DS, MZL and MUSIC methods. Without loss of generality, assume that the signal amplitude a1 = 1 and the initial phase θ l Unless otherwise specified, N = 64, L = 2, Q = 3, a² = 0.5, and ω² = ω₁ + Δω. This means there are only two signals with two frequencies, one of which is an interference signal, separated by a frequency interval of Δω, and the amplitude of the interference signal is half the amplitude of the signal to be estimated. Each numerical simulation result is obtained by averaging 2000 Monte Carlo simulations.

[0045] Figure 2 The relationship between the frequency estimation mean square error (MSE) and the signal-to-noise ratio (SNR) at different frequency intervals is given, where ω1 = 0.3204 rad. Figure 2 In (a), Δω=2π×3 / N, and the corresponding frequency interval is 3 DFT frequency slots. At this time, all estimation methods show good estimation performance, among which MUSIC is always biased, while DS and MZL have slightly degraded performance under high signal-to-noise ratio. As the frequency interval is reduced to 1.5 DFT frequency slots, that is, Δω=2π×1.5N, as shown in Figure 2 As shown in (b), at this time, DS and MZL have significant estimation deviations, MUSIC is still a biased estimate, and the method of the present invention can still achieve a relatively high estimation accuracy.

[0046] Figure 3 The relationship between the frequency estimation mean square error MSE and the signal-to-noise ratio SNR at different frequency intervals is also given. However, when the frequency order is L = 4, the number of interferences increases significantly. At this time, ω1 = 1.5413 rad. For l = 2, 3, 4, ω l =ω1+(l-1)Δω,a l =0.5-0.1(l-2), at this time the multi-frequency interference is still distributed at equal intervals, but the signal amplitude gradually weakens. Figure 3 In (a), Δω = 2π × 2 / N, and the frequency interval is 2 DFT slots. At this point, except for the method of the present invention, which achieves accurate estimation, the estimation performance of the other methods fluctuates to some extent. When the frequency interval is reduced to 1.5 DFT slots, that is, Δω = 2π × 1.5 / N, the performance of the method of the present invention also degrades at high signal-to-noise ratios, but its estimation accuracy is still significantly higher than that of the other methods.

[0047] Figure 4 The relationship between the frequency estimation mean square error MSE and the signal length N is given at different frequency intervals. At this time, ω1=0.9173rad and SNR=30dB. Figure 4As can be seen from (a), when Δω=2π×3 / N, both the method of the present invention and the MZL method can achieve accurate frequency estimation, while the performance of the DS method shows periodic fluctuations. When the frequency interval is reduced to Δω=2π×1.5 / N, as shown in Figure 4 As shown in (b), only the method of the present invention can achieve accurate frequency estimation, while the performance of other estimation methods is significantly reduced.

[0048] Figure 5 The relationship between the frequency estimation mean square error MSE and the frequency interval Δω under different signal lengths is given. At this time, ω1=0.4612rad and SNR=25dB. Figure 4 In (a), N = 64. As the frequency interval Δω increases from 1 DFT frequency slot to 4 DFT frequency slots, the interference gradually weakens. Figure 4 In (b), when N=128, we can see that since the DFT frequency slot interval itself is a function of the signal length N, the change of N does not affect the relative performance of various estimation methods, but only affects the absolute value of the estimation variance. Figure 4 It can be seen from both (a) and (b) that the method of the present invention can achieve accurate frequency estimation when the frequency interval reaches 1.5 times the DFT frequency gap or more, while the other estimation methods have obvious estimation errors.

[0049] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. It is apparent that various modifications and variations may be made by those skilled in the art without departing from the spirit and scope of the present invention. Thus, the present invention is intended to encompass such modifications and variations as long as they fall within the scope of the claims and their equivalents.

Claims

1. A high-precision frequency estimation method for real sinusoidal signals resistant to multi-frequency interference, characterized in that: The method comprises the following steps: ① performing a coarse frequency estimation of a multi-frequency interference signal x(n) with a maximum frequency order of L, and the specific operation at the first order frequency is as follows: first, searching for the spectrum peak by zero-filling FFT to obtain the initial value of the signal frequency estimation; Secondly, based on Perform zero spectrum line correction to calculate the signal complex amplitude Then, the bisection interpolation method is used to obtain a rough estimate of the signal frequency Again, based on Perform zero spectrum line correction update value; finally, based on and Construct the l-th order signal and realize interference elimination; ② Use the double loop structure of iterative operation and step-by-step interference elimination to realize high-precision estimation of signal frequency. The specific operation when the number of iterations is i (the maximum number of iterations is Q) and the frequency order is l is: First, based on and Eliminate signal interference other than the lth-order frequency in the signal x(n); then, use the three-point interpolation method to obtain an accurate estimate of the signal frequency. Finally, based on Perform zero spectrum line correction to update complex amplitude ③ When the number of iterations reaches Q and all frequency orders L are traversed, the signal frequency estimation result is returned All calculation steps involving zero spectrum line correction in steps ① and ② are: According to the known conditions or h(n)=s(n) or y(n) is substituted into q=round(Nω * / π) and the following formula to calculate the complex amplitude of the signal

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