The Wigner Distribution Function with Minimum Spread

Abstract
The Wigner distribution function (WDF) with minimum quadratic spread corresponds to a Gaussian amplitude-modulated waveform with linear frequency- modulation. The optimum WDF is two-dimensional Gaussian and has contours of equal height which are identical to the penalty contours of the quadratic spread measure employed. An alternative measure of spread, involving an exponential reward for concentration, leads to identically the same optimum waveform and WDF. A generalization to a certain class of smoothed WDFs is also possible and is presented The sensitivity of the effective area of a smoothed WDF, to mismatch in shape factor and tilt in the time-frequency plane, is evaluated quantitatively. Keywords: Ellipses; Kernel function; Smoothing.

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