Research On Frequency Estimation Algorithm Of Sinusoidal Signal Based On DFT Interpolation

With the rapid development of signal processing technology,frequency estimation has been widely used in many engineering fields such as mobile communications and power monitoring.Therefore,it is of great significance to estimate the frequency of sinusoidal signals submerged in noise.In recent years,the Discrete Fourier Transform(DFT)implemented by Fast Fourier Transform has been widely used in signal frequency estimation.However,DFT has many shortcomings and limitations,such as spectrum leakage and fence effect.The spectrum leakage of DFT is divided into short-range spectrum leakage caused by positive frequencies and long-range spectrum leakage caused by negative frequencies.These problems seriously affect the accuracy of frequency estimation.Therefore,this article focuses on the frequency estimation of sinusoidal signals.The specific research contents include:Firstly,the basic theoretical knowledge related to frequency estimation is studied,the complex sinusoidal signal model and the real sinusoidal signal model used for frequency estimation are discussed separately,and the difference between them in the time domain and the frequency domain is compared.In real life,signals are often accompanied by noise.Therefore,this article introduces the most common Gaussian white noise in communication systems and the probability density function of noisy signals.Then the problems of spectrum leakage and fence effect in DFT frequency estimation are analyzed.In order to measure the pros and cons of the algorithm,the commonly used parameters such as deviation and variance to measure the accuracy of frequency estimation are introduced in detail,and the lower limit of the mean square error-Cramer-Rao Lower Bound(CRLB)is derived.Secondly,,the frequency estimation algorithm based on DFT is studied,and several frequency estimation algorithms based on Interpolated Discrete Fourier Transform(Ip DFT)and Smart Discrete Fourier Transform(Smart Discrete Fourier Transform,SDFT)frequency estimation algorithm,and compare the performance of each algorithm through experimental simulation.The algorithm based on Ip DFT estimates the frequency through different spectral line values at the same time,while the algorithm based on SDFT estimates the frequency through the same spectral line value at different times.Both of these two types of algorithms can compensate for spectrum leakage and the error between the roughly estimated frequency and the true frequency of the signal,and further improve the accuracy of frequency estimation,but most algorithms do not completely eliminate the effect of spectrum leakage.Thirdly,in view of the problems of the existing Ip DFT algorithm,this paper proposes a precise three-point interpolation DFT frequency estimation method based on rectangular windows,and derives the theoretical variance of the algorithm in detail.By comparing the theoretical variance with the true variance,It can be seen that the algorithm has good performance.The algorithm minimizes the interference of white noise by using rectangular windows.Due to the spectrum superposition of positive and negative frequencies,the use of three-point interpolation DFT can eliminate short-range and long-range spectrum leakage.The simulation experiment results show that even when the number of sine wave cycles is small,the frequency estimation performance of this algorithm is better than the existing Ip DFT algorithm.Finally,in order to eliminate the impact of imbalance in the three-phase power system,this paper proposes a two-point iterative Ip DFT algorithm.First,the unbalanced system model is described,and the unbalanced signal is converted into a real-valued sinusoidal signal through a simple signal decomposition strategy,and then the system frequency is iteratively searched for with the smallest error by the bisection method.This algorithm has two characteristics: First,when the cost function is established,the amplitude and phase as reference elements are removed.Therefore,in the iterative process,there is no need to consider the influence of signal amplitude and phase values.Second,use the long-range and short-range spectral leakage caused by the negative and positive frequencies to design a cost function to compensate for the spectral leakage.The simulation results show that compared with other algorithms,this algorithm has higher frequency estimation accuracy,more stable frequency tracking ability and faster convergence speed.