Spectral decomposition of the timefrequency distribution kernels.
This paper addresses the general problem of approximating a given timefrequency distribution (TFD) in terms of other distributions with desired properties. It relates the approximation of two timefrequency distributions to their corresponding kernel approximation. It is shown that the singularval...
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1994

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Spectral decomposition of the timefrequency distribution kernels. Amin, Moeness G. This paper addresses the general problem of approximating a given timefrequency distribution (TFD) in terms of other distributions with desired properties. It relates the approximation of two timefrequency distributions to their corresponding kernel approximation. It is shown that the singularvalue decomposition (SVD) of the timefrequency (tf) kernels allows the expression of the timefrequency distributions in terms of weighted sum of smoothed pseudo WignerViUe distributions or modified periodograms, which are the two basic nonparametric power distributions for stationary and nonstationary signals, respectively. The windows appearing in the decomposition take zero and/or negative values and, therefore, are different than the time and lag windows commonly employed by these two distributions. The centrosymmetry and the timesupport properties of the kernels along with the fast decay of the singular values lead to computational savings and allow for an efficient reduced rank kernel approximations. 1994 Villanova Faculty Authorship vudl:173660 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 42, NO. 5, MAY 1994. en 
dc.title_txt_mv 
Spectral decomposition of the timefrequency distribution kernels. 
dc.creator_txt_mv 
Amin, Moeness G. 
dc.description_txt_mv 
This paper addresses the general problem of approximating
a given timefrequency distribution (TFD) in terms of
other distributions with desired properties. It relates the approximation
of two timefrequency distributions to their corresponding
kernel approximation. It is shown that the singularvalue decomposition
(SVD) of the timefrequency (tf) kernels allows
the expression of the timefrequency distributions in terms of
weighted sum of smoothed pseudo WignerViUe distributions or
modified periodograms, which are the two basic nonparametric
power distributions for stationary and nonstationary signals,
respectively. The windows appearing in the decomposition take
zero and/or negative values and, therefore, are different than the
time and lag windows commonly employed by these two distributions.
The centrosymmetry and the timesupport properties of
the kernels along with the fast decay of the singular values lead
to computational savings and allow for an efficient reduced rank
kernel approximations. 
dc.date_txt_mv 
1994 
dc.format_txt_mv 
Villanova Faculty Authorship 
dc.identifier_txt_mv 
vudl:173660 
dc.source_txt_mv 
IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 42, NO. 5, MAY 1994. 
dc.language_txt_mv 
en 
author 
Amin, Moeness G. 
spellingShingle 
Amin, Moeness G. Spectral decomposition of the timefrequency distribution kernels. 
author_facet 
Amin, Moeness G. 
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IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 42, NO. 5, MAY 1994. 
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Villanova Faculty Authorship 
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Amin, Moeness G. 
dc_date_str 
1994 
dc_title_str 
Spectral decomposition of the timefrequency distribution kernels. 
description 
This paper addresses the general problem of approximating
a given timefrequency distribution (TFD) in terms of
other distributions with desired properties. It relates the approximation
of two timefrequency distributions to their corresponding
kernel approximation. It is shown that the singularvalue decomposition
(SVD) of the timefrequency (tf) kernels allows
the expression of the timefrequency distributions in terms of
weighted sum of smoothed pseudo WignerViUe distributions or
modified periodograms, which are the two basic nonparametric
power distributions for stationary and nonstationary signals,
respectively. The windows appearing in the decomposition take
zero and/or negative values and, therefore, are different than the
time and lag windows commonly employed by these two distributions.
The centrosymmetry and the timesupport properties of
the kernels along with the fast decay of the singular values lead
to computational savings and allow for an efficient reduced rank
kernel approximations. 
title 
Spectral decomposition of the timefrequency distribution kernels. 
title_full 
Spectral decomposition of the timefrequency distribution kernels. 
title_fullStr 
Spectral decomposition of the timefrequency distribution kernels. 
title_full_unstemmed 
Spectral decomposition of the timefrequency distribution kernels. 
title_short 
Spectral decomposition of the timefrequency distribution kernels. 
title_sort 
spectral decomposition of the timefrequency distribution kernels. 
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1994 
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language 
English 
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