Wigner Distribution Function: Relation to Short-Term Spectral Estimation, Smoothing, and Performance in Noise

摘要

The properties and behavior of the Wigner Distribution Function (WDF) are investigated both analytically and by means of a number of simple informative examples. The lack of local temporal averaging when obtaining the instantaneous correlation function, and the lack of weighting the longer delay values when transforming to the instantaneous spectrum, are shown to be the causes of the deleterious interference effects that are inherent to the WDF. The equivalence of short-term spectral estimation to the smoothed WDF offers an attractive alternative with guaranteed positive distribution values and no interference effects. The performance of a processor which estimates the WDF of a signal waveform in the presence of additive noise is investigated in terms of the output mean, bias, and variance. Dependence on filtering the input and time-weighting is allowed and included in the analysis. Numerical application to a particular example is carried out. Keywords: Wigner distribution function; Short term spectral estimation; Smoothing; Noise performance; Linear frequency; Modulation; Interference effects; Gaussian amplitude modulation; Marginals; Moments; Spread of distribution; Positive distributions; Ambiguity function.