Download PDF by Hans G. Feichtinger, Thomas Strohmer: Advances in Gabor Analysis

By Hans G. Feichtinger, Thomas Strohmer

ISBN-10: 1461201330

ISBN-13: 9781461201335

ISBN-10: 1461266270

ISBN-13: 9781461266273

The utilized and Numerical Harmonic research (ANHA) e-book sequence goals to supply the engineering, mathematical, and medical groups with major advancements in harmonic research, starting from summary har­ monic research to uncomplicated functions. The identify of the sequence displays the im­ portance of functions and numerical implementation, yet richness and relevance of functions and implementation rely essentially at the constitution and intensity of theoretical underpinnings. hence, from our standpoint, the interleaving of concept and purposes and their inventive symbi­ otic evolution is axiomatic. Harmonic research is a wellspring of principles and applicability that has flour­ ished, built, and deepened over the years inside of many disciplines and by way of inventive cross-fertilization with various parts. The tricky and basic dating among harmonic research and fields similar to sig­ nal processing, partial differential equations (PDEs), and picture processing is mirrored in our cutting-edge ANHA sequence. Our imaginative and prescient of recent harmonic research comprises mathematical components resembling wavelet conception, Banach algebras, classical Fourier research, time­ frequency research, and fractal geometry, in addition to the various themes that impinge on them.

Show description

Read or Download Advances in Gabor Analysis PDF

Similar counting & numeration books

Download e-book for kindle: Introduction to Bayesian Scientific Computing: Ten Lectures by Daniela Calvetti

This publication has been written for undergraduate and graduate scholars in numerous components of arithmetic and its purposes. it truly is for college kids who're prepared to get conversant in Bayesian method of computational technology yet no longer inevitably to head during the complete immersion into the statistical research.

Download e-book for kindle: Modeling and Simulation: An Application-Oriented by Hans-Joachim Bungartz, Stefan Zimmer, Martin Buchholz, Dirk

This e-book presents an advent to mathematical and computer-oriented modeling and to simulation as a common technique. It consequently addresses numerous version periods and their derivations. And it demonstrates the range of methods that may be taken: be it discrete or non-stop, deterministic or stochastic.

Download e-book for kindle: Numerals and Arithmetic in the Middle Ages by Charles Burnett

This quantity, the 3rd via Charles Burnett within the Variorum sequence, brings jointly articles at the diverse numeral types utilized in the center a while, and their use in mathematical and different contexts. a few items examine the creation of Hindu-Arabic numerals into Western Europe, documenting, in additional aspect than at any place else, the several varieties within which they're discovered, sooner than they obtained the normal shapes with which we're commonly used this day.

Extra info for Advances in Gabor Analysis

Sample text

2) expresses indeed that Vgf is essentially supported on U. 2. Uncertainty Principles for Time-Frequency Representations 21 The weak uncertainty principle is a simple consequence of the CauchySchwarz inequality. Therefore, o and so lUI ~ 1 - c. A less trivial and stronger estimate on the size of the essential support can be deduced from Lieb's inequalities. These can also be seen as a version of the uncertainty principle. 2. (Lieb [29)) Assume that f,g E L 2 (Rd ). Then if2 ~ p < 00, if 1 ~ p ~ 2.

1. (Hardy) Let f E L2(JRd ), and assume that and for some a, b> O. Then three cases can occur. (i) If a b = 1, then f(x) (ii) If ab > 1, then f = ce- a7Tx2 . =O. (iii) If a b < 1, then any finite linear combination of Hermite functions satisfies these decay conditions. Once again this uncertainty principle can be rephrased in terms of the Rihaczek distribution: Assume that IRf(x,w)1 = O(e-7T(ax2+bw2)). If ab f(x) = C e- a7TX2 ,. if ab > 1, then f = O. = 1, then According to Metatheorem C we may conjecture a Hardy-like theorem for other time-frequency representations.

This completes the proof. 2 Let N = 2,3, .... 11) . 12) Proof: We have for t E [0,1) that le - tJ + 1 = leJ + 1 or leJ according as t :S e - leJ or t > e - l eJ . Case lcJ = 1. When 1 :S e:S 2 - N-l and t E [0,1), at least one of the numbers e - t - liN, l = 0,1, ... , N - 1, falls in the interval (e, 2](mod 1). 4) ;::: 1. When 2 - N- 1 < e < 2 and t E (1 N-l,e-l), all points e-t-lIN, l = 0, ... ,N -1, fall in the interval [1,e). M. Janssen vanishes at l/ = ~. 4) = O. Case lcJ > 1. 15) ensuring that the series stays away from 0 when l/ E [0,1).

Download PDF sample

Advances in Gabor Analysis by Hans G. Feichtinger, Thomas Strohmer

by Anthony

Rated 4.30 of 5 – based on 12 votes