Minimal factorization of lapped unimodular transforms

See May Phoong, Yuan-Pei Lin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

The lapped orthogonal transform (LOT) is a popular transform and has found many applications in signal processing. Its extension, the biorthogonal lapped transform (BOLT), has been investigated in detail by Vaidyanathan and Chen (see IEEE Trans. Signal Processing, p.1103-15, 1995). In this paper, we study the lapped unimodular transform (LUT). All of these three transforms are first-order matrices with FIR inverses. We show that like LOT and BOLT, all LUTs can be factorized into degree-one unimodular matrices. The factorization is both minimal and complete. We also show that all first-order systems with FIR inverses can be minimally factorized as a cascade of degree-one LOT, BOLT, and unimodular building blocks. However unlike LOT and BOLT, unimodular filter banks of any order (which include LUTs as a special case) can never have linear phase.

Original languageEnglish
Title of host publicationSignal Processing Theory and Methods I
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages121-124
Number of pages4
ISBN (Electronic)0780362934
DOIs
StatePublished - 1 Jan 2000
Event25th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2000 - Istanbul, Turkey
Duration: 5 Jun 20009 Jun 2000

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume1
ISSN (Print)1520-6149

Conference

Conference25th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2000
CountryTurkey
CityIstanbul
Period5/06/009/06/00

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    Phoong, S. M., & Lin, Y-P. (2000). Minimal factorization of lapped unimodular transforms. In Signal Processing Theory and Methods I (pp. 121-124). [861881] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 1). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2000.861881