Numerical comparison of different algorithms for construction of wavelet matrices

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 parametrization 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.

[1]  Edem Lagvilava,et al.  On Compact Wavelet Matrices of Rank $$m$$m and of Order and Degree $$N$$N , 2011, 1109.3809.

[2]  Peter Niels Heller,et al.  Rank M Wavelets with N Vanishing Moments , 1995, SIAM J. Matrix Anal. Appl..

[3]  Hualou Liang,et al.  Wavelet Analysis , 2014, Encyclopedia of Computational Neuroscience.

[4]  H. M. Newlin.  Developments in the use of wavelets in communication systems , 1998, IEEE Military Communications Conference. Proceedings. MILCOM 98 (Cat. No.98CH36201).

[5]  Robert Bregovic,et al.  Multirate Systems and Filter Banks , 2002 .

[6]  Homayoun Nikookar,et al.  A Review of Wavelets for Digital Wireless Communication , 2006, Wirel. Pers. Commun..

[7]  Gigla Janashia,et al.  A New Method of Matrix Spectral Factorization , 2009, IEEE Transactions on Information Theory.

[8]  Dario Bini,et al.  Parallel Solution of Certain Toeplitz Linear Systems , 1984, SIAM J. Comput..

[9]  Jaroslav Kautsky,et al.  Pollen product factorization and construction of higher multiplicity wavelets , 1995 .