A study on construction of time-varying orthogonal wavelets

Time-varying wavelets are highly desired in exploiting the nonstationarity of signals. However, it is difficult to hold the perfect reconstruction (PR) and regularity properties simultaneously in the construction of time-varying wavelets. This paper proposes a simple method to construct time-varying orthogonal wavelets based on the lattice structure of two-channel paraunitary (PU) filter banks, in which both the PR 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.