The numerical spread as a measure of non-stationarity: boundary effects in the numerical expected ambiguity function

Establishing measures for local stationarity is an open problem in the field of time-frequency analysis. One promising theoretical measure, known as the spread, provides a means for quantifying potential correlation between signal elements. In previous papers we investigated the issue of implementing such a measure for discrete signals. The numerical spread was introduced as a means of applying and investigating the techniques previously only studied theoretically. When implementing such a scheme it became necessary to augment the covariance matrix so that the resulting ambiguity space has a uniform resolution. In this paper we compare three extension schemes: zero padding, circular extension, and edge replication, to determine which provides the best estimate of the numerical spread. Based on our results, we determined that the method of normalized edge replication is least likely to inflate the estimate of the spread