Numerical Spread: Quantifying Local Stationarity

Abstract Hedges, Robert A., and Suter, Bruce W., Numerical Spread: Quantifying Local Stationarity, Digital Signal Processing 12 (2002) 628–643 One of the fundamental assumptions in signal processing is that of signal stationarity; i.e., the statistics of all orders are not time dependent. Many real data sets are not stationary but can, however, be described as locally stationary; that is, they appear stationary over finite time intervals. We develop numerical spread as a means of quantifying local stationarity. Based on the theoretical spread as introduced by W. Kozek and colleagues the numerical spread provides a means for quantifying potential correlation between signal elements. Implementation of such a scheme on finite, discrete data, requires the augmentation of the associated covariance matrix. Three augmentation methods were investigated: zero padding, circular extension, and edge replication. It was determined that the method of edge replication is most desirable. The theoretical techniques estimate the spread as the rectangular region of support of the associated expected ambiguity function oriented parallel to the axes. By applying Radon transform techniques we can produce a parameterized model which describes the orientation of the region of support providing tighter estimates of the signal spread. Examples are provided that illustrate the utility of numerical spread and the enhancement resulting from the new methods.

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