Discrete Periodic Multiresolution Analysis

Periodic and Spline Multiresolution Analysis and the Lifting Scheme

The lifting scheme is a well-known general framework for the construction of wavelets, especially in finitedimensional settings. After a short introduction about the basics of lifting, it is discussed how wavelet constructions in two specific finite settings can be related to the lifting approach. These examples concern on one hand polynomial splines and on the other the Fourier approach for tr...

A discrete-time multiresolution theory

Multiresolution analysis and synthesis for discretetime signals is described in this paper. Concepts of scale and resolution are first reviewed in discrete time. The resulting framework allows one to treat the discrete wavelet transform, octave-band perfect reconstruction filter banks, and pyramid transforms from a unified standpoint. This approach is very close to previous work on multiresolut...

On discrete multiresolution analytic signals

WSI GRIS Compression of Discrete Multiresolution Models

Periodic orbits in periodic discrete dynamics

5 We study the combinatorial structure of periodic orbits of nonautonomous difference 6 equations xn+1 = fn(xn) in a periodically fluctuating environment. We define the 7 Γ-set to be the set of minimal periods that are not multiples of the phase period. We 8 show that when the functions fn are rational functions, the Γ-set is a finite set. In 9 particular, we investigate several mathematical mo...