Polynomial Matrix Functions and Compact Wavelets

Author: Nika Salia
Keywords: Wavelet matrices, paraunitary matrix polynomials, Winer-Hopf factorization, Wavelet matrix completion algorithm, spectral factorization, matrix decomposition.
Annotation:

Wavelets have found beneficial applicability in various aspects of wireless communication systems design, including channel modeling, transceiver design, data representation, data compression, source and channel coding, interference mitigation, signal denoising and energy efficient networking. Factorization of compact wavelet matrices into primitive ones has been known for more than 20 years. This method makes it possible to generate wavelet matrix coefficients and also to specify them by their first row. Recently, a new parameterization of compact wavelet matrices of the same order and degree has been introduced by the last author. This method also enables us to fulfill the above mentioned tasks of matrix constructions. In the present paper, we briefly describe the corresponding algorithms based on two different methods, and numerically compare their performance. Keywords: wavelet matrices, paraunitary matrix polynomials, wavelet matrix completion algorithm.

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