Balancing order and some other discrete-time properties of multiwavelets

Jerome Lebrun; Martin Vetterli

doi:10.1117/12.366764

26 October 1999 Balancing order and some other discrete-time properties of multiwavelets

Jerome Lebrun, Martin Vetterli

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366764
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

This paper deals with multiwavelets and the different properties of approximation and smoothness that are associated with them. In particular, we focus on the important issue of the preservation of discrete time polynomial signals by multiwavelet based filter banks. We give here a precise definition of balancing for higher degree discrete time polynomial signals and link it to a very natural factorization of the lowpass refinement mask that is the counterpart of the well-known zeros at (pi) condition on the scaling function in the usual wavelet framework. This property of balancing proves them to be central to the issues of the preservation of smooth signals by the filter bank, the approximation power of the multiresolution analysis and the smoothness of the scaling functions and wavelets. Using these new results, we are able to construct a family of orthogonal multiwavelets with symmetries and compact support that is indexed by the order of balancing. We also give the minimum length orthogonal multiwavelets for any balancing order.

Citation Download Citation

Jerome Lebrun and Martin Vetterli "Balancing order and some other discrete-time properties of multiwavelets", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366764

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