Shen X., Zayed A.I. (eds.) Multiscale Signal Analysis and Modeling

Springer, 2013. — 385 p.This monograph is a collection of chapters authored or coauthored by friends and colleagues of Professor Gilbert Walter in celebration of his 80th birthday. The authors represent a spectrum of disciplines, mathematics, applied mathematics, electrical engineering, and statistics; yet, the monograph has one common theme: multiscale analysis.
Multiscale analysis has recently become a topic of increasing interest because of its important applications, in particular, in analyzing complex systems in which the data behave differently depending upon which scale the data are looked at. The advent of wavelets has given an impetus to multiscale analysis, but other techniques such as sampling and subsampling have been used successfully as a tool in analyzing multiscale signals. For this reason we have decided to include a variety of chapters covering different aspects and applications of multiscale analysis.Sampling
Convergence of Classical Cardinal Series
Improved Approximation via Use of Transformations
Generalized Sampling in L²(R^d) Shift-Invariant Subspaces with Multiple Stable Generators
Function Spaces for Sampling Expansions
Coprime Sampling and Arrays in One and Multiple Dimensions
Chromatic Expansions and the Bargmann Transform
Representation Formulas for Hardy Space Functions Through the Cuntz Relations and New Interpolation Problems
Constructions and a Generalization of Perfect Autocorrelation Sequences on Z
Multiscale Analysis
On the Application of the SDLE to the Analysis of Complex Time Series
Wavelet Analysis of ECG Signals
Multiscale Signal Processing with Discrete Hermite Functions
Earth Mover’s Distance-Based Local Discriminant Basis
Statistical Analysis
Characterizations of Certain Continuous Distributions
BayesianWavelet Shrinkage Strategies: A Review
Multiparameter Regularization for Construction of Extrapolating Estimators in Statistical Learning Theory