A generalized multiresolution structure and associated multirate system
Shidong Li · 2002
A notion of generalized multiresolution structure (GMS) is defined and characterized. We consider an increasing sequence of closed subspaces of L/sup 2/(R) generated by affine pseudo frames. We provide a necessary and sufficient condition for constructing pseudo frames formed by translates of a pair of functions for band-limited subspaces. We derive conditions for constructing GMSs, and provide construction examples. We analyze the associated filtering structure as in frame multiresolution analysis (FMRA) and other MRAs. Together with the FMRAs we developed, the results of this study provide part of the theoretical background for multiscale and multirate signal processing methods where redundancy, robustness and noise tolerance play a role.>