Narrow band frame multiresolution analysis with perfect reconstruction

We define the notion of a frame multiresolution analysis (FMRA), and analyze its associated subband coding system. An important feature of this 2-band system is that the elements of the filter bank can be narrow band, unlike the half-band nature of a classical 2-band perfect reconstruction filter bank (PRFB). In the class of multiresolution structures, it is unnecessary to introduce FMRAs for perfect reconstruction since this call be achieved by MRAs. However, for FMRAs with narrow band filters, we achieve noise suppression in the subband coding/quantization process simultaneously with reconstruction of a given narrow band signal. As with MRAs, this reconstruction is perfect if channel/quantization noise is discounted and if the signal is in one of the subspaces defining the FMRA