Discrete wavelet transforms for Toeplitz matrices

Fu Rong Lin; Wai Ki Ching; Michael K. Ng

doi:10.1016/S0024-3795(03)00415-4

Discrete wavelet transforms for Toeplitz matrices

Fu Rong Lin
, Wai Ki Ching
, Michael K. Ng^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we discuss discrete wavelet transforms for Toeplitz matrices and block–Toeplitz–Toeplitz–block matrices. The main contribution of this paper is to give the Toeplitz-like structure of the wavelet transformed Toeplitz matrices, and show that the computational cost for such structure is O(k³ln) where n is the size of the Toeplitz matrix, k is the order of the wavelet and l is the level used in the wavelet transform. The comparison between the wavelet transformed Toeplitz matrices and the Fourier transformed Toeplitz matrices is also given.

Original language	English
Pages (from-to)	269-285
Number of pages	17
Journal	Linear Algebra and Its Applications
Volume	370
DOIs	https://doi.org/10.1016/S0024-3795(03)00415-4
Publication status	Published - 1 Sept 2003

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 9 Industry, Innovation, and Infrastructure

User-Defined Keywords

Toeplitz matrix
Circulant matrix
Discrete wavelet transforms
Discrete Fourier transform
Toeplitz-like structure

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10.1016/S0024-3795(03)00415-4

Cite this

@article{7b6f3f494d7e4dfcaf4b3467166d2ada,

title = "Discrete wavelet transforms for Toeplitz matrices",

abstract = "In this paper, we discuss discrete wavelet transforms for Toeplitz matrices and block–Toeplitz–Toeplitz–block matrices. The main contribution of this paper is to give the Toeplitz-like structure of the wavelet transformed Toeplitz matrices, and show that the computational cost for such structure is O(k3ln) where n is the size of the Toeplitz matrix, k is the order of the wavelet and l is the level used in the wavelet transform. The comparison between the wavelet transformed Toeplitz matrices and the Fourier transformed Toeplitz matrices is also given.",

keywords = "Toeplitz matrix, Circulant matrix, Discrete wavelet transforms, Discrete Fourier transform, Toeplitz-like structure",

author = "Lin, \{Fu Rong\} and Ching, \{Wai Ki\} and Ng, \{Michael K.\}",

note = "Publisher Copyright: {\textcopyright} 2003 Elsevier Inc. All rights reserved. Funding Information: Supported in part by the Guangdong Provincial Natural Science Foundation of China No. 021244. Research supported in part by RGC grant no. HKU 7126/02P and HKU CRCG grant nos. 10203919, 10204436 and 10204488. Research supported in part by Hong Kong Research Grants Council grant nos. HKU 7132/00P and 7130/02P, and HKU CRCG grant nos. 10203501, 10203907 and 10204437.",

year = "2003",

month = sep,

day = "1",

doi = "10.1016/S0024-3795(03)00415-4",

language = "English",

volume = "370",

pages = "269--285",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

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TY - JOUR

T1 - Discrete wavelet transforms for Toeplitz matrices

AU - Lin, Fu Rong

AU - Ching, Wai Ki

AU - Ng, Michael K.

N1 - Publisher Copyright: © 2003 Elsevier Inc. All rights reserved. Funding Information: Supported in part by the Guangdong Provincial Natural Science Foundation of China No. 021244. Research supported in part by RGC grant no. HKU 7126/02P and HKU CRCG grant nos. 10203919, 10204436 and 10204488. Research supported in part by Hong Kong Research Grants Council grant nos. HKU 7132/00P and 7130/02P, and HKU CRCG grant nos. 10203501, 10203907 and 10204437.

PY - 2003/9/1

Y1 - 2003/9/1

N2 - In this paper, we discuss discrete wavelet transforms for Toeplitz matrices and block–Toeplitz–Toeplitz–block matrices. The main contribution of this paper is to give the Toeplitz-like structure of the wavelet transformed Toeplitz matrices, and show that the computational cost for such structure is O(k3ln) where n is the size of the Toeplitz matrix, k is the order of the wavelet and l is the level used in the wavelet transform. The comparison between the wavelet transformed Toeplitz matrices and the Fourier transformed Toeplitz matrices is also given.

AB - In this paper, we discuss discrete wavelet transforms for Toeplitz matrices and block–Toeplitz–Toeplitz–block matrices. The main contribution of this paper is to give the Toeplitz-like structure of the wavelet transformed Toeplitz matrices, and show that the computational cost for such structure is O(k3ln) where n is the size of the Toeplitz matrix, k is the order of the wavelet and l is the level used in the wavelet transform. The comparison between the wavelet transformed Toeplitz matrices and the Fourier transformed Toeplitz matrices is also given.

KW - Toeplitz matrix

KW - Circulant matrix

KW - Discrete wavelet transforms

KW - Discrete Fourier transform

KW - Toeplitz-like structure

UR - https://www.scopus.com/pages/publications/0037962250

U2 - 10.1016/S0024-3795(03)00415-4

DO - 10.1016/S0024-3795(03)00415-4

M3 - Journal article

AN - SCOPUS:0037962250

SN - 0024-3795

VL - 370

SP - 269

EP - 285

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Discrete wavelet transforms for Toeplitz matrices

Abstract

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