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 isachieved.
General
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