Research On Signal Super-Resolution Frequency Estimation Based On IpDFT Transform

Estimation and analysis of signal parameters is an indispensable application requirement in many practical engineering fields,such as radar system,communication system and biomedical system.In addition,sinusoidal signal with additive white noise is often analyzed and studied as a standard signal model in algorithm research.The parameter estimation methods of sinusoidal signals can be divided into time domain methods and frequency domain methods.The parameter estimation method based on discrete Fourier transform(DFT)has become a popular and continuously improved method in frequency domain parameter estimation algorithm because of its intuitive physical meaning and its greatly improved computational efficiency due to the proposal of fast Fourier transform(FFT).However,the algorithm based on DFT transform often has two internal problems: spectrum leakage and fence effect,which will interfere with the estimation accuracy of the algorithm to a certain extent.Therefore,this paper focuses on the sinusoidal signal parameter estimation algorithm based on DFT,and further improves the estimation accuracy and anti noise performance of the algorithm through additional steps on the basis of the classical DFT algorithm.The main research contents include:Firstly,the signal model used in this paper is constructed based on the existing signal parameter estimation theory,and on this basis,the causes of spectrum leakage and fence effect based on DFT transform algorithm are deeply analyzed.Because of this defect,incoherent sampled signals can only realize rough frequency estimation.Then it studies the existing improved algorithms of frequency estimation based on DFT,including interpolated discrete Fourier transform(ipdft)algorithm,which refines the frequency estimation through the relationship between different DFT spectral lines in the same time series,and smart discrete Fourier transform(SDFT)algorithm,which uses the same DFT spectral line at adjacent times to estimate parameters,Both of them can reduce the impact of estimation accuracy caused by spectrum leakage and fence effect to a certain extent,but there is still some room for improvement.Then,aiming at the problem of detecting and separating signals received from multiple directions in array signal processing,a multi-target signal separation algorithm based on ipdft transform is proposed.The algorithm uses the relationship between DFT spectral line and each signal component,and uses the two largest DFT spectral lines near each signal component to construct a system of linear equations to solve the incidence angle of each target signal.The algorithm only uses twice the number of DFT spectral lines of the target signal,which greatly reduces the amount of calculation and has high estimation accuracy.Based on the obtained direction of arrival(DOA)estimation,further according to the linear relationship between DFT spectral line and sampling signal,the amplitude and phase information of each target signal is estimated through simultaneous equations,and the original incident signal is reconstructed,so as to separate the multi-target signals received in multiple directions.Simulation results show that the proposed algorithm can also achieve good separation for two signals with close incident angles.Finally,aiming at the problem of negative frequency component spectrum leakage in the existing ipdft algorithm in real sinusoidal signal estimation,a multi frequency real sinusoidal signal frequency estimation algorithm based on zero filling ipdft is proposed.In the derivation of the algorithm,the negative frequency component is not ignored,but the multi frequency real sinusoidal signal estimation problem is transformed into multiple complex sinusoidal signal estimation problem.The algorithm also uses the relationship between DFT spectral line and each signal component,and in order to reduce the interference of noise and spectrum leakage on DFT spectral line,uses the maximum spectral line corresponding to each signal component and its two adjacent DFT spectral lines to construct a system of linear equations to solve the positive and negative frequencies of multiple signals.At the same time,the algorithm also realizes the frequency domain interpolation after DFT transformation by filling zero in the time domain.Through this strategy of adding speculated spectral lines,the antiinterference ability of the algorithm to noise is improved.Simulation results show that the proposed algorithm can still distinguish different frequencies when the frequency component interval is small,and the proposed algorithm can still accurately estimate the frequency of multiple signals in the scene with serious noise interference.