In this paper we summarize the basic formulas of wavelet analysis
with the help of Poisson wavelets on the sphere. These wavelets have the nice property that all basic formulas of wavelet analysis as reproducing kernels, etc. may be expressed simply with the help of higher degree Poisson wavelets. This makes them numerically attractive for applications in geophysical modeling. We do not give any proofs and we refer to "M. Holschneider, I. Iglewska-Nowak, JFAA, 2007", where all proofs are published.
An impressive variety of multirate filter banks evolved during the past twenty years. We presents an algebraic approach that subsumes many concepts developed so far (e.g. multifilters, nonseparable multidimensional filter banks, cyclic filter banks, filter banks with values in finite fields, etc.). In our approach the signals and filters are viewed as elements of a group ring. We give necessary and sufficient conditions for perfect reconstruction and derive complete parameterization in terms of ladder (or lifting) structures.
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