Subband decomposition of signals with generalized sampling

The authors generalize down and up-sampling operations by proposing block sampling. Perfect reconstruction conditions for two-band subband coding with block sampling are derived. By generalizing the sampling operation, new degrees of freedom are introduced and as a result, filter banks which were not previously possible become possible. Generalized down-sampler introduces different aliasing components than that of the traditional down-sampler. This can be used to ease some the requirements of the filter bank design problem. A constructive sampling method is proposed so that coprimeness of the transfer functions of the analysis filter banks is not only a necessary but also sufficient condition for perfect reconstruction. The results are extended to the case where the filter banks are linear periodically time-varying. The multichannel case is analyzed and the relation between unimodular matrices and perfect reconstruction filter banks is discussed