Spectral decomposition of the time-frequency distribution kernels.
This paper addresses the general problem of approximating a given time-frequency distribution (TFD) in terms of other distributions with desired properties. It relates the approximation of two time-frequency distributions to their corresponding kernel approximation. It is shown that the singular-val...
| Main Author: | |
|---|---|
| Format: | |
| Language: | English |
| Published: |
1994
|
| Online Access: | http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:173660 |
| Summary: | This paper addresses the general problem of approximating
a given time-frequency distribution (TFD) in terms of
other distributions with desired properties. It relates the approximation
of two time-frequency distributions to their corresponding
kernel approximation. It is shown that the singular-value decomposition
(SVD) of the time-frequency (t-f) kernels allows
the expression of the time-frequency distributions in terms of
weighted sum of smoothed pseudo Wigner-ViUe 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 time-support 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. |
|---|