A generalized multiresolution structure and associated multirate system

Author

Li, Shidong

Author_Institution

Dept. of Math., Maryland Univ., College Park, MD, USA

fYear

1994

fDate

25-28 Oct 1994

Firstpage

40

Lastpage

43

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;

fLanguage

English

Publisher

ieee

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

Type

conf

DOI

10.1109/TFSA.1994.467368

Filename

467368