Discrete wavelet transforms for Toeplitz matrices

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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. © 2003 Elsevier Science Inc. All rights reserved.

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Lin, F. R., Ching, W. K., & Ng, M. K. (2003). Discrete wavelet transforms for Toeplitz matrices. Linear Algebra and Its Applications, 370, 269–285. https://doi.org/10.1016/S0024-3795(03)00415-4

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