The Design And Research On Application Of Time-varying Filter Banks And Time-varying Wavelets

In the field of signal and image processing, time-varying filter banks and time-varying wavelet transforms have attracted considerable attention as powerful tools to exploit the non-stationary of signals. This paper, we study time-varying filter banks and time-varying wavelets in the following three aspects.Firstly, we discuss the perfect reconstruction problem of time-varying filter banks. In this paper, the case in which the system filters change with time is mainly considered, and two design methods to implement these time-varying systems are also given.Secondly, a simple method is proposed to construct time-varying orthogonal wavelets based on the lattice structure of two-channel paraunitary filter banks, in which both the perfect reconstruction and orthogonality properties are well preserved. The regularity conditions imposed on the lattice structure are expressed in terms of the lattice coefficients and the wavelet filter banks are obtained by using an optimization technique. Then the time-varying orthogonal wavelets can be constructed by the lattice structure formulation for time-varying filter banks. Design examples show that this method is of great flexibility and effectiveness.Thirdly, we also study the application of time-varying wavelets for denoising time-varying signals. Compared to time-invariant wavelets, design examples demonstrate that time-varying wavelets are superior to time-invariant wavelets in the time-varying signal processing.