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Author: Karlheinz Gröchenig
Publisher: Springer Science & Business Media
ISBN: 1461200032
Category : Technology & Engineering
Languages : en
Pages : 367
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Book Description
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.
Author: Karlheinz Gröchenig
Publisher: Springer Science & Business Media
ISBN: 1461200032
Category : Technology & Engineering
Languages : en
Pages : 367
Get Book Here
Book Description
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.
Author: G. Longo
Publisher: Springer
ISBN: 3709126207
Category : Technology & Engineering
Languages : en
Pages : 180
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Book Description
The concept of time and frequency representation of signals dates back to the first notation for music. From a mathematical viewpoint we can associate the time function to its Fourier transform. This book introduces a useful representation of signals simultaneously in time and frequency.
Author: Ronald L. Allen
Publisher: John Wiley & Sons
ISBN: 0471660361
Category : Technology & Engineering
Languages : en
Pages : 961
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Book Description
Offers a well-rounded, mathematical approach to problems in signal interpretation using the latest time, frequency, and mixed-domain methods Equally useful as a reference, an up-to-date review, a learning tool, and a resource for signal analysis techniques Provides a gradual introduction to the mathematics so that the less mathematically adept reader will not be overwhelmed with instant hard analysis Covers Hilbert spaces, complex analysis, distributions, random signals, analog Fourier transforms, and more
Author: Franz Hlawatsch
Publisher: John Wiley & Sons
ISBN: 1118623835
Category : Technology & Engineering
Languages : en
Pages : 377
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Book Description
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.
Author: Jeffrey A. Hogan
Publisher: Springer Science & Business Media
ISBN: 0817644318
Category : Mathematics
Languages : en
Pages : 403
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Book Description
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.
Author: Boualem Boashash
Publisher: Academic Press
ISBN: 0123985250
Category : Technology & Engineering
Languages : en
Pages : 1070
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Book Description
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
Author: B. E. Blair
Publisher:
ISBN:
Category : Frequency standards
Languages : en
Pages : 576
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Book Description
Author: Leon Cohen
Publisher: Prentice Hall
ISBN: 9780135945322
Category : Technology & Engineering
Languages : en
Pages : 299
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Book Description
Featuring traditional coverage as well as new research results that, until now, have been scattered throughout the professional literature, this book brings together—in simple language—the basic ideas and methods that have been developed to study natural and man-made signals whose frequency content changes with time—e.g., speech, sonar and radar, optical images, mechanical vibrations, acoustic signals, biological/biomedical and geophysical signals. Covers time analysis, frequency analysis, and scale analysis; time-bandwidth relations; instantaneous frequency; densities and local quantities; the short time Fourier Transform; time-frequency analysis; the Wigner representation; time-frequency representations; computation methods; the synthesis problem; spatial-spatial/frequency representations; time-scale representations; operators; general joint representations; stochastic signals; and higher order time-frequency distributions. Illustrates each concept with examples and shows how the methods have been extended to other variables, such as scale. For engineers, acoustic scientists, medical scientists and developers, mathematicians, physicists, and mangers working in the fields of acoustics, sonar, radar, image processing, biomedical devices, communication.
Author: Antonia Papandreou-Suppappola
Publisher: CRC Press
ISBN: 1420042467
Category : Technology & Engineering
Languages : en
Pages : 433
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Book Description
Because most real-world signals, including speech, sonar, communication, and biological signals, are non-stationary, traditional signal analysis tools such as Fourier transforms are of limited use because they do not provide easily accessible information about the localization of a given frequency component. A more suitable approach for those studying non-stationary signals is the use of time frequency representations that are functions of both time and frequency. Applications in Time-Frequency Signal Processing investigates the use of various time-frequency representations, such as the Wigner distribution and the spectrogram, in diverse application areas. Other books tend to focus on theoretical development. This book differs by highlighting particular applications of time-frequency representations and demonstrating how to use them. It also provides pseudo-code of the computational algorithms for these representations so that you can apply them to your own specific problems. Written by leaders in the field, this book offers the opportunity to learn from experts. Time-Frequency Representation (TFR) algorithms are simplified, enabling you to understand the complex theories behind TFRs and easily implement them. The numerous examples and figures, review of concepts, and extensive references allow for easy learning and application of the various time-frequency representations.
Author: Franz Hlawatsch
Publisher: Springer Science & Business Media
ISBN: 9780792381310
Category : Technology & Engineering
Languages : en
Pages : 240
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Book Description
Linear signal spaces are of fundamental importance in signal and system theory, communication theory, and modern signal processing. This book proposes a time-frequency analysis of linear signal spaces that is based on two novel time-frequency representations called the `Wigner distribution of a linear signal space' and the `ambiguity function of a linear signal space'. Besides being a useful display and analysis tool, the Wigner distribution of a linear signal space allows the design of high-resolution time-frequency filtering methods. This book develops such methods and applies them to the enhancement, decomposition, estimation, and detection of noisy deterministic and stochastic signals. Formulation of the filtering (estimation, detection) methods in the time-frequency plane yields a direct interpretation of the effect of adding or deleting information, changing parameters, etc. In a sense, the prior information and the signal processing tasks are brought to life in the time-frequency plane. The ambiguity function of a linear signal space, on the other hand, is closely related to a novel maximum-likelihood multipulse estimator of the range and Doppler shift of a slowly fluctuating point target - an estimation problem that is important in radar and sonar. Specifically, the ambiguity function of a linear signal space is relevant to the problem of optimally designing a set of radar pulses. The concepts and methods presented are amply illustrated by examples and pictures. Time-Frequency Analysis and Synthesis of Linear Signal Spaces: Time-Frequency Filters, Signal Detection and Estimation, and Range-Doppler Estimation is an excellent reference and may be used as a text for advanced courses covering the subject.
