Foundation of time-frequency analysis : with 15 figures /
Gröchenig, Karlheinz.
Foundation of time-frequency analysis : with 15 figures / Karlheinz Gröchenig. - Boston : Birkhäuser, c2001. - xv, 359 p. : ill. ; 25 cm. - Applied and numerical harmonic analysis. .
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.
9780817640224 0817640223
00044508
Signal processing--Mathematics.
Time-series analysis.
Frequency spectra.
TK5102.9 / .G76 2001
621.382 / GRO
Foundation of time-frequency analysis : with 15 figures / Karlheinz Gröchenig. - Boston : Birkhäuser, c2001. - xv, 359 p. : ill. ; 25 cm. - Applied and numerical harmonic analysis. .
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.
9780817640224 0817640223
00044508
Signal processing--Mathematics.
Time-series analysis.
Frequency spectra.
TK5102.9 / .G76 2001
621.382 / GRO