Wavelet filters and infinite-dimensional unitary groups

By O. Bratteli, Palle E. T. Jorgensen. 2000

54 citations recorded by the source corpus.

In this paper, we study wavelet filters and their dependence on two numbers, the scale N and the genus g. We show that the wavelet filters, in the quadrature mirror case, have a harmonic analysis which is based on representations of the C � -algebra ON. A main tool in our analysis is the infinite-dimensional group of all maps T ! U(N) (where U(N) is the group of all unitary N-by-N matrices), and we study the extension problem from low-pass filter to multiresolution filter using this group.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8c0e9be6120c1434956206611a00157d395b641e

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Wavelets on Fractals (2003, methodology): “for some N ∈ Z+, N ≥ 2 we showed in [ 5 ] that there are functions m1, . . . , mN −1 on T such that”