Research On Frequency Estimation Method Based On Iterative Interpolation

FFT is one of the principal methods for signal spectrum analyzing due to its definite physical meaning and easily been implemented on computer,however,in spectrum analysis,as the leakage effect and picket fence effect in the discrete,which leads to the errors in parameters estimation.Spectrum leakage effect and spectral parameter estimation errors caused by picket fence effect can be effectively suppressed and improved by time-domain windowing and frequency-domain interpolating.Interpolation FFT is the widely studied spectrum parameter estimation method.Among the existing spectrum parameter estimation methods,the interpolated FFT method is a more widely studied method.However,the existing FFT method has the shortcomings of frequency calculation formula is limited by window function,spectral line selection is fixed,and the anti-noise performance of the algorithm is not ideal.Therefore,its application in practical engineering is limited to a certain extent.In this paper,based on the summary of the existing FFT interpolation method,the main research work is as follows:Firstly,the iterative interpolation FFT method based on multiple-term MSD windows is proposed by using the windows main-lobe fitting and MSD window interpolation formula,the general calculation formula for all classical windows is given.Then,the problem of correlation coefficients of two spectral lines at random intervals in the discrete spectrum of all classical window Gaussian white noise sequences is studied,and the calculation formula is given.This improved algorithm has faster computation speed and higher accuracy for the windows with fast side lobe attenuation,which is often used in harmonics analysis and such windows have low scalloping loss,therefore,this improved method is very suitable for the harmonic analysis or signal with low disturbed by noise.Secondly,the iterative interpolation FFT method based on Zero padding is proposed for the purpose of enhancing the anti noise of interpolation FFT,and it can be extended to all classical windows by the windows main-lobe fitting,besides,The statistical characteristics of the frequency estimator of this method are analyzed in detail based on the study of the correlation coefficients of two spectral lines at random intervals in the discrete spectrum of the Gaussian white noise sequence of the classic window in Chapter 2,the estimated variance of commonly used window functions is given.This method has excellent anti noise performance and it can reach CRLB only through one or two iterations.It has good robustness in the environment of strong noise interference and is suitable for engineering signal analysis with large noise interference.Finally,according to the different characteristics of the three engineering signals,the iterative interpolation FFT based on Rectangle window and the generalized iterative interpolation DFT are applied to the characteristic defect frequencies(CDF)estimation of rolling bearings,the oil well dynamic fluid level detection and error curve compensation of linear displacement sensor,respectively.The results show that these two improved discrete spectrum parameter estimation methods can effectively improve the depth detection precision of oil well dynamic fluid,the effect of error curve compensation and the identification accuracy of CDF,which indicate that the proposed methods have good performance and practical engineering value.