Efficient reconstruction of band-limited sequences from nonuniformly decimated versions by use of polyphase filter banks

Based on recent results on the reconstruction of a bandlimited sequence from a nonuniformly decimated version, this paper develops an efficient polyphase structure for such reconstruction. Theoretically, the reconstruction involves the implementation of a bank of multilevel filters, and this paper shows how all these reconstruction filters can be obtained at the cost of one Mth band low-pass filter and a constant matrix multiplier. The resulting structure is therefore more general than the ad hoc scheme reported recently. In addition, the method offers a direct means of controlling the overall reconstruction distortion T ( z ) by appropriate design of a low-pass prototype filter P ( z ) . Extension of these results to multiband band-limited signals and to the case of nonconsecutive nonuniform subsampling are also summarized, along with generalizations to the multidimensional case. Design examples are included to demonstrate the theory, and the complexity of the new method is seen to be much lower than earlier ones.