Journal ArticleDOI
The aliasing problem in discrete-time Wigner distributions
T. Claasen,W. Mecklenbrauker +1 more
TLDR
In this paper, the authors compare different definitions of the Wigner distribution with respect to aliasing and computational complexity and conclude that no definition leads to a function that is optimum in all respects.Abstract:
There is no straightforward way to proceed from the continuous-time Wigner distribution to a discrete-time version of this time-frequency signal representation. A previously given definition of such a function turned out to yield a distribution that was periodic with period π instead of 2π and this caused aliasing to occur. Various alternative definitions are considered and compared with respect to aliasing and computational complexity. From this comparison it appears that no definition leads to a function that is optimum in all respects. This is illustrated by an example.read more
Citations
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Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Journal ArticleDOI
Time-frequency distributions-a review
TL;DR: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented with emphasis on the diversity of concepts and motivations that have gone into the formation of the field.
Journal ArticleDOI
Linear and quadratic time-frequency signal representations
TL;DR: A tutorial review of both linear and quadratic representations is given, and examples of the application of these representations to typical problems encountered in time-varying signal processing are provided.
Journal ArticleDOI
A method for time-frequency analysis
TL;DR: This method provides some substantial advantages over the Wigner distribution, including the fact that the well-known cross term effects are reduced or completely removed, and the computation time can be significantly shorter.
Journal ArticleDOI
An efficient real-time implementation of the Wigner-Ville distribution
Boualem Boashash,P. Black +1 more
TL;DR: To evaluate the analytic signal required by the WVD analysis system, it is shown that the time domain definition implemented as a finite impulse response (FIR) filter is practical and more efficient than the frequency domain definition of the analytical signal.
References
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Journal ArticleDOI
On the Quantum Correction For Thermodynamic Equilibrium
TL;DR: In this article, the Boltzmann formula for the probability of a configuration is given in classical theory by means of a probability function, and the result discussed is developed for the correction term.
Book ChapterDOI
On the quantum correction for thermodynamic equilibrium
TL;DR: In this article, the Boltzmann formula for lower temperatures has been developed for a correction term, which can be developed into a power series of h. The formula is developed for this correction by means of a probability function and the result discussed.
The wigner distribution - a tool for time-frequency signal analysis
T. Claasen,W. Mecklenbrauker +1 more
TL;DR: In this paper, the Wigner distribution is adapted to the case of discrete-time signals and it is shown that most of the properties of this time-frequency signal representation carry over directly to the discrete time case, but some other problems are associated with the fact that in general, these aliasing contributions will not be present if the signal is either oversampled by a factor of at least two, or is analytic.
The wigner distribution - a tool for time-frequency signal analysis part ii: discrete-time signals
T. Claasen,W. Mecklenbrauker +1 more
TL;DR: In this second part of the paper the Wigner distribution is adapted to the case of discrete-time signals, and it is shown that most of the properties of this time-frequency signal representation carry over directly to the discrete- time case, but some cause problems.
Journal ArticleDOI
The Wigner distribution function applied to optical signals and systems
TL;DR: In this article, the Wigner distribution function of an optical signal appears to be in close resemblance to the ray concept in geometrical optics, and this resemblance reaches even farther: although derived from Fourier optics, the WIGNer distribution functions of some elementary optical systems can directly be interpreted in terms of geometry.
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The wigner distribution - a tool for time-frequency signal analysis part ii: discrete-time signals
T. Claasen,W. Mecklenbrauker +1 more