Wavelets, Sampling and Synchronization

TL;DR: The theory of communication is extended to include a number of new factors, in particular the effect of noise in the channel, and the savings possible due to the statistical structure of the original message anddue to the nature of the final destination of the information.

TL;DR: This paper lists and interprets the numerous properties of the Zak transform and the relation with other time-frequency representations such as the Wigner distribution and the radar ambiguity function is given, and the Gabor representation problem is tackled.

TL;DR: The classical Shannon sampling theorem is extended to the subspaces used in the multiresolution analysis in wavelet theory, and is first shown to have a Riesz basis formed from the reproducing kernels.

TL;DR: The authors study the properties of cardinal orthogonal scaling functions (COSF), which provide the standard sampling theorem in multiresolution spaces with scaling functions as interpolants, and present a family of COSF with exponential decay, which are generalizations of the Haar function.