This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications.
Author: Karlheinz Gröchenig
Publisher: Springer Science & Business Media
Category: Technology & Engineering
Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.
[CAR 98] CARMONA R., HWANG H. L., TORRESANI B., Practical Time-
Frequency Analysis, Academic Press, 1998. [COA 99] COATEs ... [GRO 01]
GROCHENIG K., Foundations of Time-Frequency Analysis, Birkhauser, Boston,
2001. [HIL 84] ...
Author: Franz Hlawatsch
Publisher: John Wiley & Sons
Category: Technology & Engineering
Covering a period of about 25 years, during which time-frequency has undergone significant developments, this book is principally addressed to researchers and engineers interested in non-stationary signal analysis and processing. It is written by recognized experts in the field.
Time - frequency analysis originates in the early development of quantum me
chanics by H . Weyl , E . Wigner and J . v . Neumann around 1930 , and in the
theoretical foundation of information theory and signal analysis by D . Gabor in
This book gives the university researcher and R&D engineer insights into how to use TFSAP methods to develop and implement the engineering application systems they require.
Author: Boualem Boashash
Publisher: Academic Press
Time-Frequency Signal Analysis and Processing (TFSAP) is a collection of theory, techniques and algorithms used for the analysis and processing of non-stationary signals, as found in a wide range of applications including telecommunications, radar, and biomedical engineering. This book gives the university researcher and R&D engineer insights into how to use TFSAP methods to develop and implement the engineering application systems they require. New to this edition: New sections on Efficient and Fast Algorithms; a "Getting Started" chapter enabling readers to start using the algorithms on simulated and real examples with the TFSAP toolbox, compare the results with the ones presented in the book and then insert the algorithms in their own applications and adapt them as needed. Two new chapters and twenty three new sections, including updated references. New topics including: efficient algorithms for optimal TFDs (with source code), the enhanced spectrogram, time-frequency modelling, more mathematical foundations, the relationships between QTFDs and Wavelet Transforms, new advanced applications such as cognitive radio, watermarking, noise reduction in the time-frequency domain, algorithms for Time-Frequency Image Processing, and Time-Frequency applications in neuroscience (new chapter). A comprehensive tutorial introduction to Time-Frequency Signal Analysis and Processing (TFSAP), accessible to anyone who has taken a first course in signals Key advances in theory, methodology and algorithms, are concisely presented by some of the leading authorities on the respective topics Applications written by leading researchers showing how to use TFSAP methods
Describing functions: atomic decompositions versus frames. Monatshefte Math.,
112(1):1–42, 1991.  K. Gröchenig. Foundations of Time-Frequency Analysis,
Applied and Numerical Harmonic Analysis. Birkhäuser Boston, Inc., Boston, MA,
Author: Elena Cordero
Publisher: Walter de Gruyter GmbH & Co KG
This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to study dispersive equations such as the Schrödinger, wave, and heat equations and related Strichartz problems. The first part of the book is addressed to non-experts, presenting the basics of time-frequency analysis: short time Fourier transform, Wigner distribution and other representations, function spaces and frames theory, and it can be read independently as a short text-book on this topic from graduate and under-graduate students, or scholars in other disciplines.
Preface By time–frequency (TF) analysis we mean, loosely, techniques and
principles used in signal analysis, PDE and ... and Karlheinz Gröchenig's Foundations of Time–Frequency Analysis  are two excellent texts in this
Author: Jeffrey A. Hogan
Publisher: Springer Science & Business Media
Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of these areas are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book fills that gap by presenting the interface of time-frequency and time-scale methods as a rich area of work. "Foundations of Time-Frequency and Time-Scale Methods" will be suitable for applied mathematicians and engineers in signal/image processing and communication theory, as well as researchers and students in mathematical analysis, signal analysis, and mathematical physics.
( 11 ) CORDERO , E . AND GRÖCHENIG , K . : Time - frequency analysis of
localization operators . J . Funct . Anal . 205 ( 2003 ) , no . 1 , 107 ... [ 21 ]
GRÖCHENIG , K . : Foundations of time - frequency analysis . Applied and
Numerical Harmonic ...
... Debnath : Wavelet Transforms and Time - Frequency Signal Analysis ( ISBN 0 -
8176 - 4104 - 1 ) K . Gröchenig : Foundations of Time - Frequency Analysis (
ISBN 0 - 8176 - 4022 - 3 ) D . F . Walnut : An Introduction to Wavelet Analysis (
Author: John Benedetto
Category: Analyse harmonique
Sampling, wavelets, and tomography are three active areas of contemporary mathematics sharing common roots that lie at the heart of harmonic and Fourier analysis. The advent of new techniques in mathematical analysis has strengthened their interdependence and led to some new and interesting results in the field. This state-of-the-art book not only presents new results in these research areas, but it also demonstrates the role of sampling in both wavelet theory and tomography. Specific topics covered include: * Robustness of Regular Sampling in Sobolev Algebras * Irregular and Semi-Irregular Weyl-Heisenberg Frames * Adaptive Irregular Sampling in Meshfree Flow Simulation * Sampling Theorems for Non-Bandlimited Signals * Polynomial Matrix Factorization, Multidimensional Filter Banks, and Wavelets * Generalized Frame Multiresolution Analysis of Abstract Hilbert Spaces * Sampling Theory and Parallel-Beam Tomography * Thin-Plate Spline Interpolation in Medical Imaging * Filtered Back-Projection Algorithms for Spiral Cone Computed Tomography Aimed at mathematicians, scientists, and engineers working in signal and image processing and medical imaging, the work is designed to be accessible to an audience with diverse mathematical backgrounds. Although the volume reflects the contributions of renowned mathematicians and engineers, each chapter has an expository introduction written for the non-specialist. One of the key features of the book is an introductory chapter stressing the interdependence of the three main areas covered. A comprehensive index completes the work.
Applied and Numerical Harmonic Analysis Published titles J . M . Cooper :
Introduction to Partial Differential Equations with ... and Time - Frequency Signal Analysis ( ISBN 0 - 8176 - 4104 - 1 ) K . Gröchenig : Foundations of Time - Frequency ...
Author: Jon H. Davis
Methods of Applied Mathematics with a MATLAB Overview is devoted to the applications of Fourier analysis, topics encompass the classical applications in partial differential equations and boundary value problems as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are covered, along with the necessary background in complex variables and Sturm-Liouville theory. The final chapter provides an examination of wavelets, short-time Fourier analysis, and geometrically-based transforms. The use of the computer program MATLAB has been integrated throughout the text, with particular emphasis on the program's numerical and graphing capabilities. Requiring only familiarity with calculus and linear algebra and some introductory acquaintance with differential equations and vector calculus, this work can be used flexibly, either for a one-semester survey or an in-depth, year-long course. With its broad scope and careful pedagogy, this treatment will serve students in pure and applied mathematics, physical sciences, and engineering. Book jacket.
5.7 SUMMARY In this chapter , we have reviewed the basic concepts underlying time - frequency analysis . A time - frequency ... Williams , W.J. Recent advances
in time - frequency representations : Some theoretical foundations . In Time ...
Author: Gail D. Baura
Publisher: Wiley-IEEE Press
System theory is becoming increasingly important to medical applications. Yet, biomedical and digital signal processing researchers rarely have expertise in practical medical applications, and medical instrumentation designers usually are unfamiliar with system theory. System Theory and Practical Applications for Biomedical Signals bridges those gaps in a practical manner, showing how various aspects of system theory are put into practice by industry. The chapters are intentionally organized in groups of two chapters, with the first chapter describing a system theory technology, and the second chapter describing an industrial application of this technology. Each theory chapter contains a general overview of a system theory technology, which is intended as background material for the application chapter. Each application chapter contains a history of a highlighted medical instrument, summary of appropriate physiology, discussion of the problem of interest and previous empirical solutions, and review of a solution that utilizes the theory in the previous chapter. Biomedical and DSP academic researchers pursuing grants and industry funding will find its real-world approach extremely valuable. Its in-depth discussion of the theoretical issues will clarify for medical instrumentation managers how system theory can compensate for less-than-ideal sensors. With application MATLABÂ® exercises and suggestions for system theory course work included, the text also fills the need for detailed information for students or practicing engineers interested in instrument design. An Instructor Support FTP site is available from the Wiley editorial department: ftp://ftp.ieee.org/uploads/press/baura
It gives the reader a good idea of the essence of harmonic analysis . H. G.
Feichtinger ( Wien ) K. Gröchenig : Foundations of Time - Frequency Analysis .
With 15 Figures . ( Applied and Numerical Harmonic Analysis . ) Birkhäuser ,
Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.
[ 16 ] Gröchenig , K. , Foundations of Time - Frequency Analysis , Birkhäuser ,
Boston , Basel , Berlin , 2000 . [ 17 ] Gröchenig , K. , Heil , C. , Modulation Spaces
and Pseudo differential Operators , Integral Equations Operator Theory , 34 (
1999 ) ...
This book is an ideal source for teachers and students who wish to understand the mechanisms of the auditory system.
Author: Jerry Tobias
Foundations of Modern Auditory Theory, Volume I is an 11-chapter text that covers the basic auditory processes. This volume deals first with the electrophysiological and conditioning data that reflect periodicity perception, the analysis of high-frequency tones, and the mechanisms and effects of auditory masking. These topics are followed by discussions on the poststimulatory auditory fatigue and adaptation; the theoretical bases necessary for an understanding of the critical band’s ubiquity; and the mechanical events in transformation process occurring in cochlea. This volume describes the anatomical structure and electrophysiological action of the cochlea and further explores ear models to study the mechanical properties of the auditory system and the basic neural transmission processes and their properties. The concluding chapters look into the distinct patterns of disorder in psychoacoustic function and the perception of musical stimuli. This book is an ideal source for teachers and students who wish to understand the mechanisms of the auditory system.
8 , 3362-3378 . ( 15 ) K. Gröchenig , An uncertainty principle related to the
Poisson summation formula , Studia Math . 121 ( 1996 ) 87-104 . [ 16 ] Foundations of time - frequency analysis , Applied and numerical harmonic
analysis , Birkhäuser ...
[ 7 ] K. Gröchenig , Foundations of Time - Frequency Analysis , Birkhäuser , 2001
. ( 8 ) K. Kato , M. Kobayashi and S. Ito , Representation of Schrödinger operator
of a free particle via short time Fourier transform and its applications , to appear in
Ramirez R.W. , The FFT fundamentals and concepts , Prentice Hall PTR ,
Englewood Cliffs , New Jersey 1985 , p . 124 . 11. Gröchening K. , Foundations of time - frequency analysis , Birkhäuser , Boston 2001 , p . 23 . 12. Poularikas , The
With respect to the contents of the author ' s book ( Foundations 35S
Pseudodifferential operators and other of time - frequency analysis , Birkhäuser
Boston , Boston , MA , 2001 ; MR1843717 ( 2002h : 42001 ) ] , recent deep
contributions are ...
[ 22 ] K. Gröchenig , Foundations of Time - Frequency Analysis , Applied and
Numerical Harmonic Analysis . Birkhäuser Boston Inc. , Boston , 2001 . [ 23 ] K.
Gröchenig and M. Leinert , “ Symmetry of matrix algebras and symbolic calculus
[ 3 ] K . Gröchenig , Foundations of Time - Frequency Analysis , Applied and
Numerical Harmonic Analysis . Birkhäuser , Boston , 2001 . [ 4 ] H . G .
Feichtinger and G . Zimmermann , " A Banach space of test functions for Gabor
analysis , " In ...
The aim of this book is to serve as a graduate text and reference in time series analysis and signal processing, two closely related subjects that are the concern of a wide range of disciplines, such as statistics, electrical engineering, ...
Author: D. S. G. Pollock
Publisher: Academic Press
Category: Technology & Engineering
The aim of this book is to serve as a graduate text and reference in time series analysis and signal processing, two closely related subjects that are the concern of a wide range of disciplines, such as statistics, electrical engineering, mechanical engineering and physics. The book provides a CD-ROM containing codes in PASCAL and C for the computer procedures printed in the book. It also furnishes a complete program devoted to the statistical analysis of time series, which will be attractive to a wide range of academics working in diverse mathematical disciplines.