Time Series Analysis: The Cross-Correlation Function

Abstract

<p>The concept of cross-correlation has been developed in two distinct fields: signal processing and statistics. In the area of signal processing, the cross-correlation function can be used to transform one or more signals so that they can be viewed with an altered perspective. For instance, cross-correlation functions can be used to produce plots that make it easier to identify hidden signals within the data. Cross-correlation functions provide the basis for many more sophisticated signal-processing procedures as well. Digital imaging techniques also rely heavily on cross-correlation procedures, but these methods are not covered in the chapter. In the realm of statistics, cross-correlation functions provide a measure of association between signals. The Pearson product-moment correlation coefficient is simply a normalized version of a cross-correlation. When two times series data sets are cross-correlated, a measure of temporal similarity is achieved. The cross-correlation function in its simplest form is easy to use and quiet intuitive. This chapter builds on simple cross-correlation procedures to illustrate the wide variety of uses they have in the field of biomechanics and to give the reader an intuitive feel for some more complicated analysis procedures. Concepts from both signal processing and statistics are discussed, and the procedures are applied to several practical problems.</p>