This book presents a systematic introduction to time-frequency analysis understood as a central area of applied harmonic analysis, while at the same time honouring its interdisciplinary origins.

Important principles include: classic Fourier analysis as a tool that is central in modern mathematics; the mathematical structures based on the operations of translation and modulations (i.e: the Heisenberg group); the many forms of the uncertainty principle; and the omnipresence of Gaussian functions, both in the methodology of proofs and in important statements.

Contents
Preface
Itinerary
1 Basic Fourier Analysis
2 Time-Frequency Analysis and the Uncertainty Principle
3 The Short-Time Fourier Transferm
4 Quadratic Time-Frequency Representations
5 Discrete Time-Frequency Representations: Gabor Frames
6 Existence of Gabor Frames
7 The Structure of Gabor Systems
8 Zak Transfer m Methods
9 The Heisenberg Group: A Different Point of View
10 Wavelet Transfer ms
11 Modulation Spaces
12 Gabor Analysis of Modulation Spaces
13 Window Design and Wiener's Lemma
14 Pseudodifferential Operators
Appendix
References
Index
Applied and Numerical Harmonie Analysis

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