Optimal FIR inversion filters for an arbitrary subband decomposition of a bandlimited signal

The authors consider the optimal reconstruction of a discrete-time, bandlimited signal from an arbitrary invertible subband decomposition, with decimation in each channel. When this reconstruction is done sequentially using only a finite amount of data at a time, it can be performed with a multirate FIR (finite impulse response) synthesis filter bank. The authors provide a procedure to obtain an optimal set of FIR filters to achieve such a reconstruction. The procedure can incorporate frequency support (bandwidth) a priori information about the input to produce the best possible reconstruction. Examples are provided to illustrate the resulting FIR filters, with and without the use of bandwidth information, for a two-channel system involving IIR (infinite impulse response) analysis filters