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Design of a Simple Orthogonal Multiwavelet Filter by Matrix Spectral Factorization

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Abstract

We consider the design of an orthogonal symmetric/antisymmetric multiwavelet from its matrix product filter by matrix spectral factorization. As a test problem, we construct a simple matrix product filter with desirable properties and factor it using Bauer’s method, which in this case can be done in closed form. The corresponding orthogonal multiwavelet function is derived using algebraic techniques which allow symmetry to be considered. This leads to the known orthogonal multiwavelet SA1, which can also be derived directly. We also give a lifting scheme for SA1, investigate the influence of the number of significant digits in the calculations, and show some numerical experiments.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their careful reading and helpful suggestions.

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Authors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Bl. 2 Acad. G. Bonchev St., 1113, Sofia, Bulgaria

    Vasil Kolev

  2. Wireless Technology Center, Purdue University, Fort Wayne, IN, 46805, USA

    Todor Cooklev

  3. Department of Mathematics, Iowa State University, Ames, IA, 50011, USA

    Fritz Keinert

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  1. Vasil Kolev
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Kolev, V., Cooklev, T. & Keinert, F. Design of a Simple Orthogonal Multiwavelet Filter by Matrix Spectral Factorization. Circuits Syst Signal Process 39, 2006–2041 (2020). https://doi.org/10.1007/s00034-019-01240-9

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