Applications of nonmaximally decimated multirate filterbanks in partial response channel ISI cancellation

In this paper, we study applications of nonmaximally decimated multirate filterbanks (NMDMF) in partial response channels, where the partial response transfer functions may not have inverses, such as frequency-selective fading channels. The NMDMF plays the preprocessing (or precoding) role. We present a necessary and sufficient condition on an FIR channel transfer function in terms of its zero set such that an FIR NMDMF with N channels and decimation by K, 0 < K < N, for the encoder exists so that the decoder is able to recover the original signal with an FIR synthesis system, where the integers K and N are arbitrarily fixed. The condition is easy to check and satisfy. In addition to the conditions on the channel transfer functions, the practical design of the FIR NMDMF precoders and their FIR synthesis banks for the reconstruction is also given. An numerical example is presented to illustrate the theory.