Theory of optimal orthonormal subband coders

Author

Vaidyanathan, P.P.

Author_Institution

Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA

Volume

46

Issue

6

fYear

1998

fDate

6/1/1998 12:00:00 AM

Firstpage

1528

Lastpage

1543

Abstract

The theory of the orthogonal transform coder and methods for its optimal design have been known for a long time. We derive a set of necessary and sufficient conditions for the coding-gain optimality of an orthonormal subband coder for given input statistics. We also show how these conditions can be satisfied by the construction of a sequence of optimal compaction filters one at a time. Several theoretical properties of optimal compaction filters and optimal subband coders are then derived, especially pertaining to behavior as the number of subbands increases. Significant theoretical differences between optimum subband coders, transform coders, and predictive coders are summarized. Finally, conditions are presented under which optimal orthonormal subband coders yield as much coding gain as biorthogonal ones for a fixed number of subbands

Keywords

band-pass filters; data compression; filtering theory; optimisation; prediction theory; transform coding; biorthogonal coders; coding gain; coding-gain optimality; data compression; filter banks; input statistics; necessary conditions; optimal compaction filters; optimal design; optimal orthonormal subband coders; orthogonal transform coder; predictive coders; sufficient conditions; transform coders; Compaction; Data compression; Decorrelation; Filter bank; Filtering theory; Helium; Karhunen-Loeve transforms; Quantization; Statistics; Sufficient conditions;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.678466

Filename

678466