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Joint spatial-frequency
distribution of Gaussian signals and prospects of its applications for
description of optical systems
Kozlovskii Yu.M.
Institute for Condensed Matter Physics, 1 Sventsitski,
79011 Lviv, Ukraine
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We consider a joint spatial-frequency distribution as a result of superposition
of two known Wigner and Ville distributions. The joint distribution is
characterized by a certain parameter t that plays a part of
measure of superposition: the joint frequency-spatial distribution passes
into the Ville one at t=0 and coincides with the Wigner
distribution at t=1 . For the values 0< t<1
there exists a row of ‘mixed’ distributions, which represent superposition
of the Wigner and Ville distributions. Explicit expression for the joint
distribution of Gaussian signal is obtained by means of analytical calculations.
We present graphic illustrations for the shape of joint distribution of
Gaussian signal at different values of the joint parameter t. It
is demonstrated that the Wigner distribution is formed as a rotation of
Ville distribution on the information diagram by the angle proportional
to the joint parameter t .
Keywords: photonic crystal, Si - liquid crystal
system, admixture layer, bandgap width.
PACS: 05.60.+w, 05.70.Ln, 05.20.Dd, 52.25.Dg,
52.25.Fi
UDC:
Ukr. J. Phys. Opt.
9 105-119
doi: 10.3116/16091833/9/2/105/2008
Received: 17.01.2008
In final form: 01.04.2008 |
|
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