In this paper we present orthogonal transforms as a signal analysis and processing tool with the capability of variable multiresolution time-spectral decomposition of discrete signals. Our prime interest is in the representation of square summable sequences in terms of wavelet packet matrices used as discrete orthogonal systems, and we concentrate on the fast transform algorithms for such systems. We analyze polyphase and lattice-tree structures which are common for multiple block-size orthogonal transforms, multiresolution multirate filter banks, and wavelet packet transforms. The purpose of this present paper is to compare and contrast the wavelet packet based approach to the traditional techniques for fast orthogonal transform algorithms. We consider results from this technique that influence the design of filter banks and we indicate some results from lattice-structured filter banks which can be useful for the design of fast wavelet packet transform algorithms. A time-varying structure that is based on fast algorithms of orthogonal transforms and their orthogonal sub-transforms is presented. In this case, orthogonal bases consist of a finite collection of wavelet packets which provide a fairly rich family of orthogonal decompositions of the time-scale plane. In particular, the time- sequence plane representation, one of many possible time-spectral and time-scale plane representations is discussed.

Date Published: 1 November 1993
PDF: 10 pages
Proc. SPIE 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing, (1 November 1993); doi: 10.1117/12.162075

Published in SPIE Proceedings Vol. 2034:
Mathematical Imaging: Wavelet Applications in Signal and Image Processing
Andrew F. Laine, Editor(s)