| dc.contributor.author |
Benidir, Messaoud |
|
| dc.contributor.author |
Boashash, Boualem |
|
| dc.date.accessioned |
2011-06-14T05:45:55Z |
|
| dc.date.available |
2011-06-14T05:45:55Z |
|
| dc.date.issued |
1995-07 |
|
| dc.identifier.citation |
Proc. SPIE 2563, 69 (1995) |
en_US |
| dc.identifier.other |
doi:10.1117/12.211426 |
|
| dc.identifier.uri |
http://hdl.handle.net/10576/10709 |
|
| dc.description |
This paper presents rigorous mathematical proofs of previous results presented in earlier papers for PTFDs.
(The most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia., and then continuously updated). |
en_US |
| dc.description.abstract |
We propose a representation of the derivitive (phi) ' of any general polynomial (phi) of degree N in terms of Q equals N + 1 given parameters: t1,...,tQ. This representation allows us to express the derivative as a linear comination of q arbitrary ratios of [(phi) (t + (tau) (kappa )) - (phi) (t - (tau) (kappa ))]/(tau) (kappa ) calculated at q arbitrary points (tau) 1,...,(tau) q, where q denotes the integer part of (N + 1)/2. The coefficients appearing in this decomposition are independent of the polynomial coefficients. As an application, we give a formula that allows us to compute (phi) '(t) without using the coefficients of the polynomial (phi) (t) and establish a property of the polynomial Wigner-Ville distribution. |
en_US |
| dc.language.iso |
en |
en_US |
| dc.publisher |
SPIE |
en_US |
| dc.subject |
Derivative |
en_US |
| dc.subject |
Polynomial |
en_US |
| dc.subject |
polynomial Wigner-Ville distributions |
en_US |
| dc.subject |
polynomes |
en_US |
| dc.subject |
time-frequency analysis |
en_US |
| dc.subject |
non-linear FM signals |
en_US |
| dc.subject |
Polynomial |
en_US |
| dc.subject |
phase derivative |
en_US |
| dc.title |
Polynomial Wigner-Ville distributions |
en_US |
| dc.type |
Article |
en_US |