Research And Application On Frequency Estimation Algorithms Of Real Sinusoidal Signals On DFT

Frequency estimation of real sinusoidal signals is widely used in various technical areas,This technology can not only be applied to radar detection and sonar systems which can be used in the military but also plays a key role in the production and life of people and their important power systems,communication systems which have developed rapidly in recent years.But Discrete Fourier Transform(DFT) which has been widely used in frequency estimation,has many restrictions and disadvantages,such as picket fence effect,leakage effect and so on.DFT-based frequency estimation algorithms of real sinusoidal signals are studied in this desertation aiming at suppressing spectrum leakage and improving accuracy and anti-noise ability of frequency estimation,and the specific research work completed includes:Firstly,the basic characteristic of real sinusoidal signals and theories of frequency estimation are introduced.The spectrum of the signals is analyzed,and frequency leakage and fence effect of DFT-based estimators are explained based on this.The defect of DFT and noise result in deviation,which is also the breakthrough to improve the performance of algorithms in this dersertation.Besides,the randomicity of Gaussian white noise(AWGN)and some parameters applied to analyze performances of frequency estimators are introduced.Then the theoretical lower bound CRLB(Cramer Rao Lower Bound,CRLB)of frequency estimation mean square error is derived from the perspective of probability theory,which is an essential parameter of frequency estimation algorithms.The CRLB for single parameter and multiple parameters is also derived and studied.Secondly,existing DFT-based frequency estimation algorithms are introduced and studied.The frequency estimator based on frequency domain transformation can be classified into two types: Interpolated DFT(Interpolated Discrete Fourier Transform,Ip DFT)and Smart DFT(Smart Discrete Fourier Transform,SDFT).The Ip DFT algorithm performs by the differences between the adjacent frequency components at the same time instant.And iterative calculation and windowing usually applied to improve the performace of Ip DFT algorithms by supressing spectrum leakage further.Furthermore,SDFT-based algorithms extracts frequency based on the same DFT component of the signal sequences at different times.Classical least squares(CLS)can improve estimation accuracy of SDFT algorithm.Two types of estimators are both able to solve the problem of long-range leakage in DFT effectively,but still have some room for improvement under serious spectrum leakage.In addition,the characteristic of additive white Gaussian noise(AWGN)in frequency domain is analyzed for subsequent analysis of theoretical variances of algorithms.The relationship between noise and its real and imaginary components after DFT is derived by using mathematical expectation,and the final relationship between variance and noise is obtained,which simplifies the estimation of theoretical value,which is conductive to the following comparative experiments.Finally,a new and high-precision algorithm based on three-point interpolated Fourier transform is studied.This algorithm can eliminate the negative frequency interference by establishing interpolated relation of three adjacent DFT frequency components.It takes both positive and negative frequencies into account instead of ignoring the negative component.The frequency is estimated by the same frequency component in the adjacent time instants in order to completely eliminate interference of the negative frequency spectrum.The simulation results show that the proposed algorithm improves the stability,anti-noise performance and estimation accuracy compared with other algorithms.Meanwhile,accuracy of the proposed estimator when there is harmonics interference is analyzed by simulations.Computer simulations demonstrate that the proposed algorithm provides high accuracy and good noise suppression capability when applied for unbalanced three-phase power system.In addition,we derive the estimator by extending the frequency estimator above that relies on interpolation on Fourier coefficients to two-dimension signals.And compared with other classical two-dimensional estimation algorithms,simulations reveals that the proposed algorithm provides high estimation accuracy and good noise suppression capability.It means the interference of negative frequency can be eliminated by Ip DFT even when a signal has two sepctral lines.