Title :
A generalized multiresolution structure and associated multirate system
Author_Institution :
Dept. of Math., Maryland Univ., College Park, MD, USA
Abstract :
A notion of generalized multiresolution structure (GMS) is defined and characterized. We consider an increasing sequence of closed subspaces of L2(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
Keywords :
filtering theory; quantisation (signal); signal resolution; signal sampling; FMRA; affine pseudo frames; band-limited subspaces; filtering structure; frame multiresolution analysis; generalized multiresolution structure; multirate signal processing; multirate system; multiscale signal processing; necessary and sufficient condition; noise tolerance; pseudo frames construction; quantisation noise reduction; redundancy; robustness; sampling theory; Convergence; Educational institutions; Finite impulse response filter; Mathematics; Multiresolution analysis; Narrowband; Noise robustness; Redundancy; Signal processing; Signal resolution;
Conference_Titel :
Time-Frequency and Time-Scale Analysis, 1994., Proceedings of the IEEE-SP International Symposium on
Conference_Location :
Philadelphia, PA
Print_ISBN :
0-7803-2127-8
DOI :
10.1109/TFSA.1994.467368
