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Foundation of time-frequency analysis : with 15 figures / Karlheinz Gröchenig.

By: Material type: TextTextSeries: Applied and numerical harmonic analysisPublication details: Boston : Birkhäuser, c2001.Description: xv, 359 p. : ill. ; 25 cmISBN:
  • 9780817640224
  • 0817640223
Subject(s): DDC classification:
  • 621.382 GRO
LOC classification:
  • TK5102.9 .G76 2001
Contents:
Itinerary Karlheinz Gröchenig Pages 1-2 Basic Fourier Analysis Karlheinz Gröchenig Pages 3-20 Time-Frequency Analysis and the Uncertainty Principle Karlheinz Gröchenig Pages 21-36 The Short-Time Fourier Transform Karlheinz Gröchenig Pages 37-58 Quadratic Time-Frequency Representations Karlheinz Gröchenig Pages 59-82 Discrete Time-Frequency Representations: Gabor Frames Karlheinz Gröchenig Pages 83-101 Existence of Gabor Frames Karlheinz Gröchenig Pages 103-126 The Structure of Gabor Systems Karlheinz Gröchenig Pages 127-146 Zak Transform Methods Karlheinz Gröchenig Pages 147-174 The Heisenberg Group: A Different Point of View Karlheinz Gröchenig Pages 175-201 Wavelet Transforms Karlheinz Gröchenig Pages 203-214 Modulation Spaces Karlheinz Gröchenig Pages 215-244 Gabor Analysis of Modulation Spaces Karlheinz Gröchenig Pages 245-275 Window Design and Wiener’s Lemma Karlheinz Gröchenig Pages 277-299 Pseudodifferential Operators Karlheinz Gröchenig Pages 301-327 Back Matter Pages 329-360
Review: "Time-frequency analysis is a source of ideas and applications in modern harmonic analysis. The history of time-frequency analysis dates back to von Neumann, Wigner, and Gabor, who considered the problems in quantum mechanics and in information theory. For many years time-frequency analysis has been pursued mainly in engineering, but recently - with the development of wavelet theory - it has emerged as a thriving field of applied mathematics." "This book presents the first systematic introduction to time-frequency analysis understood as a central area of applied harmonic analysis, while at the same time honoring its interdisciplinary origins. Important principles are (a) classical Fourier analysis as a tool that is central in modern mathematics, (b) the mathematical structures based on the operations of translation and modulations (i.e., the Heisenberg group), (c) the many forms of the uncertainty principle, and (d) the omnipresence of Gaussian functions, both in the methodology of proofs and in important statements."--BOOK JACKET.
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Item type Current library Collection Call number Status Date due Barcode
Project book Project book CUTN Central Library Medicine, Technology & Management Non-fiction 621.382 GRO (Browse shelf(Opens below)) Checked out to Renuka Devi V (20019T) 31/01/2024 48828

Includes bibliographical references (p. 335-353) and index.

Itinerary
Karlheinz Gröchenig
Pages 1-2
Basic Fourier Analysis
Karlheinz Gröchenig
Pages 3-20
Time-Frequency Analysis and the Uncertainty Principle
Karlheinz Gröchenig
Pages 21-36
The Short-Time Fourier Transform
Karlheinz Gröchenig
Pages 37-58
Quadratic Time-Frequency Representations
Karlheinz Gröchenig
Pages 59-82
Discrete Time-Frequency Representations: Gabor Frames
Karlheinz Gröchenig
Pages 83-101
Existence of Gabor Frames
Karlheinz Gröchenig
Pages 103-126
The Structure of Gabor Systems
Karlheinz Gröchenig
Pages 127-146
Zak Transform Methods
Karlheinz Gröchenig
Pages 147-174
The Heisenberg Group: A Different Point of View
Karlheinz Gröchenig
Pages 175-201
Wavelet Transforms
Karlheinz Gröchenig
Pages 203-214
Modulation Spaces
Karlheinz Gröchenig
Pages 215-244
Gabor Analysis of Modulation Spaces
Karlheinz Gröchenig
Pages 245-275
Window Design and Wiener’s Lemma
Karlheinz Gröchenig
Pages 277-299
Pseudodifferential Operators
Karlheinz Gröchenig
Pages 301-327
Back Matter
Pages 329-360

"Time-frequency analysis is a source of ideas and applications in modern harmonic analysis. The history of time-frequency analysis dates back to von Neumann, Wigner, and Gabor, who considered the problems in quantum mechanics and in information theory. For many years time-frequency analysis has been pursued mainly in engineering, but recently - with the development of wavelet theory - it has emerged as a thriving field of applied mathematics." "This book presents the first systematic introduction to time-frequency analysis understood as a central area of applied harmonic analysis, while at the same time honoring its interdisciplinary origins. Important principles are (a) classical Fourier analysis as a tool that is central in modern mathematics, (b) the mathematical structures based on the operations of translation and modulations (i.e., the Heisenberg group), (c) the many forms of the uncertainty principle, and (d) the omnipresence of Gaussian functions, both in the methodology of proofs and in important statements."--BOOK JACKET.

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