Minimal factorization of lapped unimodular transforms
Journal
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing
Journal Volume
1
Pages
121-124
Date Issued
2000
Author(s)
Lin, Yuan-Pei
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. © 2000 IEEE.
Other Subjects
Bolts; Factorization; FIR filters; Inverse problems; Matrix algebra; FIR filters; Inverse problems; Mathematical transformations; Matrix algebra; Polynomials; Theorem proving; Vectors; Building blockes; First order systems; Lapped orthogonal transform; Lapped Transform; Lapped unimodular transform; Minimal factorization; Unimodular filter banks; Unimodular matrices; Signal processing; Signal processing; Biorthogonal lapped transform; Lapped orthogonal transform; Lapped unimodular transform
Type
conference paper
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