9,965 research outputs found
Uncertainty Principles for Wigner-Ville Distribution Associated with the Linear Canonical Transforms
The Heisenberg uncertainty principle of harmonic analysis plays an important role in modern applied mathematical applications, signal processing and physics community. The generalizations and extensions of the classical uncertainty principle to the novel transforms are becoming one of the most hottest research topics recently. In this paper, we firstly obtain the uncertainty principle for Wigner-Ville distribution and ambiguity function associate with the linear canonical transform, and then the -dimensional cases are investigated in detail based on the proposed Heisenberg uncertainty principle of the -dimensional linear canonical transform
Direct Measurement of Kirkwood-Rihaczek distribution for spatial properties of coherent light beam
We present direct measurement of Kirkwood-Rihaczek (KR) distribution for
spatial properties of coherent light beam in terms of position and momentum
(angle) coordinates. We employ a two-local oscillator (LO) balanced heterodyne
detection (BHD) to simultaneously extract distribution of transverse position
and momentum of a light beam. The two-LO BHD could measure KR distribution for
any complex wave field (including quantum mechanical wave function) without
applying tomography methods (inverse Radon transformation). Transformation of
KR distribution to Wigner, Glauber Sudarshan P- and Husimi or Q- distributions
in spatial coordinates are illustrated through experimental data. The direct
measurement of KR distribution could provide local information of wave field,
which is suitable for studying particle properties of a quantum system. While
Wigner function is suitable for studying wave properties such as interference,
and hence provides nonlocal information of the wave field. The method developed
here can be used for exploring spatial quantum state for quantum mapping and
computing, optical phase space imaging for biomedical applications.Comment: 27 pages, 14 figure
Fast directional spatially localized spherical harmonic transform
We propose a transform for signals defined on the sphere that reveals their
localized directional content in the spatio-spectral domain when used in
conjunction with an asymmetric window function. We call this transform the
directional spatially localized spherical harmonic transform (directional
SLSHT) which extends the SLSHT from the literature whose usefulness is limited
to symmetric windows. We present an inversion relation to synthesize the
original signal from its directional-SLSHT distribution for an arbitrary window
function. As an example of an asymmetric window, the most concentrated
band-limited eigenfunction in an elliptical region on the sphere is proposed
for directional spatio-spectral analysis and its effectiveness is illustrated
on the synthetic and Mars topographic data-sets. Finally, since such typical
data-sets on the sphere are of considerable size and the directional SLSHT is
intrinsically computationally demanding depending on the band-limits of the
signal and window, a fast algorithm for the efficient computation of the
transform is developed. The floating point precision numerical accuracy of the
fast algorithm is demonstrated and a full numerical complexity analysis is
presented.Comment: 12 pages, 5 figure
Time-frequency methods for coherent spectroscopy
Time-frequency decomposition techniques, borrowed from the signal-processing field, have been adapted and applied to the analysis of 2D oscillating signals. While the Fourier-analysis techniques available so far are able to interpret the information content of the oscillating signal only in terms of its frequency components, the time-frequency transforms (TFT) proposed in this work can instead provide simultaneously frequency and time resolution, unveiling the dynamics of the relevant beating components, and supplying a valuable help in their interpretation. In order to fully exploit the potentiality of this method, several TFTs have been tested in the analysis of sample 2D data. Possible artifacts and sources of misinterpretation have been identified and discussed
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