Wavelets and perfect reconstruction subband coding with causal stable IIR filters

We show for the first time that it is possible to have a large family of perfect reconstruction subband coding filter banks, which are causal and IIR both at the analysis and at the synthesis ends. Complete parametrization of such classes of filters leading to design methods are given. Parametrizations in frequency domain terms as well as in terms of state space descriptions of filters are provided for better numerical implementation of design methods. The development is valid for two-band as well as for multiband subband coding schemes. The iterated filter banks are shown to give rise to a new family of biorthogonal version of continuous wavelets, the scaled and dilated version of which represents arbitrary square integrable signals. Dilation factors larger than two are implicit in the development resulting from the fact that we consider multiband subband coding schemes