Abstract

The use of the Wigner distribution function (WDF) as a signal processing technique has recently been recognized. One interesting application is signal detection and classification. The simplest (but nonoptimal) approach to signal detection is to use a filter in the time-frequency (ω-t) plane that is matched to the WDF of the signal; in fact, this has been previously suggested. An alternative is to find the optimum filter in the ω-t plane. Because signal-independent white noise in the t domain translates into signal-dependent colored noise in the ω-t plane, the optimization problem is more difficult. Using signal-to-noise ratio as an optimization criterion we obtain an integral equation for the optimum filter. The first-order term of an iterative solution turns out to be the matched filter. The integral equation is solved numerically and examples of the results will be presented. A comparison between the performance of the t-ω optimum filter and that of the matched filter for both detection and classification shows that in some conditions the ω-t optimum filter outperforms the matched filter.

© 1985 Optical Society of America