Research On Windowed Algorithm For Frequency Estimation Of Real Sinusoidal Signal Based On DFT

Estimating the frequency of real-valued sinusoidal signals embedded in Gaussian white noise has been an important research topic in modern digital signal processing for many years.With the rapid development of information technology in recent years,the frequency estimation of real sinusoidal signals have been widely used both in military and civilian engineering fields.This paper focuses on the frequency estimation problem of real sinusoid signal based on windowed DFT.The topic selection has certain theoretical significance and practical value.The specific research work includes:Firstly,the basic theory of frequency estimation is studied,the mathematical model of the real sinusoidal signal used in this paper is constructed,the frequency domain function of the sinusoid signal model is deeply studied,and the inherent shortcomings of DFT such as spectrum leakage and fence effect are explained.Besides,the existing frequency estimation algorithms based on DFT are introduced and studied.The frequency estimator based on frequency domain transformation can be classified into two types based on Interpolated DFT(IpDFT)and Smart DFT(SDFT).The IpDFT algorithm performs frequency estimation by the differences between the adjacent frequency components at the same time instant,while SDFT-based algorithm extracts frequency based on the same DFT component of the signal sequences at different times.According to formula derivation and simulation results,both types of DFT estimators and their improvement schemes can effectively improve the spectrum leakage problem of DFT-based estimators,but there is still room for improvement.Next,a new type of real-valued sinusoidal signal frequency estimation algorithm based on windowed interpolated discrete Fourier transform(Interpolated DFT,IpDFT)is proposed to solve the nagetive spectrum leakage problem in the existing DFT frequency estimators.The main idea of the proposed algorithm is comparing the absolute value of the peak spectral line and the spectral lines on both sides,and then use the interpolation relationship between the three spectral lines to establish a quadratic equation of one element about the frequency.The proposed IpDFT algorithm completely takes into account the long-range leakage of negative frequency components,so it can minimize the impact of spectrum leakage.The simulation experiment results prove that compared with other IpDFT algorithms,the new proposed algorithm has extremely high estimation accuracy and ability to resist the interference of mirror components,especially when the positive and negative frequency distributions are close.Then,for the situation where the positive and negative frequency distribution of the real sine signal are close,a new two-point real sinusoid signal frequency estimation algorithm based on windowed IpDFT is proposed.According to the relationship between the real and imaginary parts of the peak spectrum,the algorithm superimposes the proportional relationship between the real and imaginary parts to form the final interpolation scale factor for frequency calculation.Simulations verify the advantages of the proposed algorithm in terms of anti-spectrum leakage and anti-noise.Compared with the traditional two-point algorithm,the new algorithm effectively improves the estimation accuracy of the two-point algorithm,especially in the case of small frequency signals.The performance of the algorithm can even surpass some threepoint windowed IpDFT algorithms,which proves that the algorithm effectively considers the inter-spectral interference caused by negative frequency components.Finally,the differences between the same DFT frequency components at different times is studied.Aiming at the interference caused by the negative frequency components of the real sinusoidal signal,a new frequency estimation algorithm based on the two-point sliding window DFT is proposed,and the delay sliding window is adopted to solve the problem of estimated distortion at certain frequency points.The simulation results prove that the algorithm can greatly reduce the impact of spectrum leakage.Compared with the classic SDFT estimation scheme with similar principles,the performance of the proposed algorithm is better,especially for sinusoidal signals with close positive and negative frequency intervals.The advantages of the proposed algorithm are more obvious than other estimation algorithms based on the frequency domain.In the presence of higher harmonic interference,the algorithm can still maintain the leading estimation accuracy.