Research On Multi-taper Spectral Estimation Method

The power spectrum density of random signal determines the energy distribution in frequency domain,which is an important representation of random signal.Therefore,it is of great significance in biomedical engineering,natural science,communication,astronomy and other fields.Power spectrum estimation is an important research problem of random signals,which uses limited sample data to estimate the power spectrum density function of random signals.There are many methods for power spectrum estimation,such as multitaper spectrum estimation method proposed by Thomson in 1982,multiple sinusoidal tapers spectrum estimation method proposed by Riedel and Sidorenko in 1995 and jackknifing multitaper spectrum estimates proposed by Thomson in 2007.Based on the research of Thomson,Riedel and Sidorenko and linear process bootstrap(LPB)method,a new LPB multitaper spectrum estimation is proposed in this paper.Firstly,this paper introduces multitaper spectrum estimation,multiple sinusoidal tapers spectrum estimation and jackknifing multitaper spectrum estimates,and expounds the differences between the three methods above.Secondly,the study uses the linear process bootstrap method to improve the multitaper spectrum estimation and calculates the upper bound of MSE of the multitaper spectrum estimation.Then the simulation is carried out in the following three models: the superposition of sine wave functions,the autoregressive process and the moving average process.Simulation analysis shows that the bootstraping multitaper spectrum estimation has a good frequency resolution and variance performance under these three models,which provides the best tradeoff between frequency resolution and variance.Finally,the new estimation method proposed in this paper is evaluated through the empirical analysis of real data.