Research And Application Of DFT In Frequency Estimation

Sinusoidal signal frequency estimation is a fundamental problem in the field of signal processing.The Fourier analysis method is the most basic method of signal analysis.Discrete Fourier Transform is the core of Fourier analysis.It transforms the signal from the time domain to the frequency domain,and then studies the spectrum structure and changing laws of the signal.In this paper,the research and application of DFT in frequency estimation are carried out as follows.Firstly,the basic theory of frequency estimation is studied.The mathematical model used in the frequency estimation problem of this paper—the sinusoidal signal model is introduced.The discrete-time Fourier transform of the sinusoidal signal model is discussed.Then,the basic parameter estimation theory is expounded,including some definitions of parameter estimation.In addition,the methods of parameter estimation are introduced,including least squares estimation,linear minimum mean square error estimation and maximum likelihood estimation.Then,using the sinusoidal signal as the mathematical model,the commonly used efficient frequency estimation algorithms for two-point DFT and three-point DFT are reviewed.The two-point DFT frequency estimation algorithm includes a triangular self-convolution window interpolation DFT algorithm,an extra-chord window-based IpDFT algorithm,and an MSD windowed IpDFT algorithm.The three-point DFT frequency estimation algorithm includes a least squares combined with the SDFT algorithm and an MDW windowed IpDFT algorithm.Both types of algorithms can effectively improve the spectrum leakage and fence effect in DFT transform.Then,the DFT-based two-point frequency estimation algorithm is studied,and the frequency is estimated by the unary quadratic equation and the unary cubic equation,respectively.Consider and calculate spectral superposition of positive and negative frequencies to improve estimation performance.We analyze the theoretical properties of the algorithm in the case of additive white Gaussian noise.The simulation results agree well with the theoretical values.In addition,we also compared with other algorithms,including CLS-SDFT algorithm,TSCW algorithm,IpDFT algorithm with redundant string windowing,IpDFT algorithm based on MSD windowing,IpDFT algorithm based on MDW windowing,etc.Finally,a new frequency estimation algorithm based on different frequencies at different times is proposed.The signal model to be estimated is introduced.Through the formula derivation,a method based on the unary cubic equation is introduced to estimate the frequency.Secondly,we carried out simulation analysis based on unary cubic equation and compared with other algorithms,including CLS-SDFT algorithm,TSCW algorithm,IpDFT algorithm with redundant string windowing,IpDFT algorithm based on MSD windowing and based on The MDW windowed IpDFT algorithm verifies that the proposed algorithm has excellent simulation performance.