A Novel Time-Frequency Analysis Approach for Nonstationary Time Series Using Multiresolution Wavelet

Abstract

An efficient time-varying autoregressive (TVAR) modeling scheme using the multiresolution wavelet method is proposed for modeling nonstationary signals and with application to time-frequency analysis (TFA) of time-varying signal. In the new parametric modeling framework, the time-dependent parameters of the TVAR model are locally represented using a novel multiresolution wavelet decomposition scheme. The wavelet coefficients are estimated using an effective orthogonal least squares (OLS) algorithm. The resultant estimation of time-dependent spectral density in the signal can simultaneously achieve high resolution in both time and frequency, which is a powerful TFA technique for nonstationary signals. An artificial EEG signal is included to show the effectiveness of the new proposed approach. The experimental results elucidate that the multiresolution wavelet approach is capable of achieving a more accurate time-frequency representation of nonstationary signals.Index Terms-Chebyshev polynomials, Kalman filter, multiresolution wavelet, orthogonal least squares (OLS), system identification, time-frequency analysis, time-varying models.