The Wigner Distribution: Theory and Applications in Signal Processing - Hardcover

Hardcover

ISBN 10: 044488856X ISBN 13: 9780444888563

Publisher: Elsevier Science, 1997

Synopsis

In the last two decades, the field of time-frequency analysis has evolved into a widely recognized and applied discipline of signal processing. Besides linear time-frequency representations such as the short-time Fourier transform, the Gabor transform, and the wavelet transform, an important contribution to this development has undoubtedly been the Wigner distribution (WD) which holds an exceptional position within the field of bilinear/quadratic time-frequency representations.

The WD was first defined in quantum mechanics as early as 1932 by the later Nobel laureate E. Wigner. In 1948, J. Ville introduced this concept in signal analysis. Based on investigations of its mathematical structure and properties by N.G. de Bruijn in 1967, the WD was brought to the attention of a larger signal processing community in 1980. The WD was soon recognized to be important for two reasons: firstly, it provides a powerful theoretical basis for quadratic time-frequency analysis; secondly, its discrete-time form (supplemented by suitable windowing and smoothing) is an eminently practical signal analysis tool.

The seven chapters of this book cover a wide range of different aspects of the WD and other linear time-frequency distributions: properties such as positivity, spread, and interference term geometry; signal synthesis methods and their application to signal design, time-frequency filtering, and signal separation; WD based analysis of nonstationary random processes; singular value decompositions and their application to WD based detection and classification; and optical applications of the WD. The size of the chapters has been chosen such that an in-depth treatment of the various topics is achieved.

About this title

Review

"An invaluable source if you are involved with functions of both time and frequency, or of course of both space and spatial frequency" --Ultramicroscopy, Vol 75

"...an excellent overview of the theory and applications of the Wigner distribution in signal analysis...written by some of the leading researchers in this area..." --International Journal of Electronics & Communications

"...Thanks to its content, which has now become more or less classical material, this book should be a fine addition to the library of anyone interested in time-frequency signal analysis." --Mathematical Reviews

Synopsis

Within the field of signal processing, this work argues the Wigner distribution (WD) is important for two reasons: firstly, it provides a theoretical basis for quadratic time-frequency analysis; and secondly, its discrete-time form (supplemented by suitable windowing and smoothing) is a practical signal analysis tool. The seven chapters of this book cover a range of different aspects of the WD and other linear time-frequency distributions: properties such as positivity, spread, and interference term geometry; signal synthesis methods and thier application to signal design, time-frequency filtering, and signal separation; WD based analysis of nonstationary random processes; singular value decompositions and their application to WD based detection and classification; and optical applications of the WD.

Edition details

• Publisher: Elsevier Science
• Publication date: 1997
• Language: English
• ISBN 10: 044488856X
• ISBN 13: 9780444888563
• Binding: Hardcover
• Number of pages: 480
• Editor: Hlawatsch Franz, Mecklenbräuker W.