Theory and Implementation of Wavelet Analyses in Rational Resolution Decompositions
Bruce P. Anderson · Defense Technical Information Center (DTIC) · 1992
The multiresolution analysis (MRA) developed by Mallat and Meyer and further discussed by Daubechies is a useful tool in the analysis of sampled signals such as images and speech. This thesis develops the theory and implementation of a rational-resolution analysis (RRA) as an extension of the dyadic MRA for arbitrary rational dilation factors. We present a method to calculate families of compactly-supported scaling functions and wavelets based on arbitrary integer dilation factors and provide examples. The perfect- reconstruction properties of the RRA are discussed and it is demonstrated that the compactly-supported scaling functions and wavelets do not yield perfect- reconstruction. However, the approximation-reconstruction is demonstrated and families of basis function which do lead to perfect reconstruction are characterized. Finally, comparisons are made between RRAs and conventional MRAs and illustrated with speech signals.