Lapped unimodular transform and its factorization

See May Phoong*, Yuan-Pei Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Two types of lapped transforms have been studied in detail in the literature, namely, the lapped orthogonal transform (LOT) and its extension, the biorthogonal lapped transform (BOLT). In this paper, we will study the lapped unimodular transform (LUT). All three transforms are first-order matrices with finite impulse response (FIR) inverses. We will show that like LOT and BOLT, all LUTs can be factorized into degree-one unimodular matrices. The factorization is both minimal and complete. We will also show that all first-order systems with FIR inverses can be minimally factorized as a cascade of degree-one LOT, BOLT, and LUT building blocks. Two examples will be given to demonstrate that despite having a very small system delay, the LUTs have a satisfactory performance in comparison with LOT and BOLT.

Original languageEnglish
Pages (from-to)2695-2701
Number of pages7
JournalIEEE Transactions on Signal Processing
Volume50
Issue number11
DOIs
StatePublished - 1 Nov 2002

Keywords

  • Filterbank
  • Polynomial matrix
  • Transform
  • Unimodular matrix

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