Time-Varying Spectral Analysis with Gabor Frames

Abstract

The purpose of this study is a better understanding of time-varying frequency information of nonstationary time series. Previous studies have mainly focused on displaying the frequency pattern across time, but the statistical modeling and inference on time-varying frequencies have been neglected. It has been investigated a sparse Bayesian approach for time-varying frequency analysis and a parametric estimation of the instantaneous frequency (IF) in this thesis. We propose to impose a novel prior on time-frequency coefficients of Gabor frames using the finite version of Indian buffet process (IBP) to create dependency structures coupled with the stochastic search variable selection (SSVS) to achieve sparsity in Bayesian framework. For a parametric estimation of time-varying frequency, we suggest a likelihood-based estimation method which is a new statistical model efficiently integrating the random phase shifting and time-varying patterns of frequencies.