Theory and design of shift-invariant filter banks and wavelets

A drawback of the critical-sampling multirate system is its shift-variant property at the subband output. This prevents wavelets from many applications where shift-invariance is required. For a given set of filter coefficients and cost function, all of the existing methods solve the problem by finding the path in the decomposition tree that minimizes shift-variance with respect to a given cost function. This procedure is signal dependent and is inefficient, especially for long data sets and images, since the subband decomposition has to be performed for all shifts of input signal during the processing time. In this paper, we establish a framework for a shift-invariant filter bank by connecting the relation between the polyphase representation and shift-invariant property of filter banks. Theory, analysis, and design are presented, and comparison to the existing systems is discussed. Design examples and simulations on image coding are presented.