Time Series Analysis: The Cross-Correlation Function

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Derrick, Timothy
Thomas, Joshua
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Derrick, Timothy
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The Department of Kinesiology seeks to provide an ample knowledge of physical activity and active living to students both within and outside of the program; by providing knowledge of the role of movement and physical activity throughout the lifespan, it seeks to improve the lives of all members of the community. Its options for students enrolled in the department include: Athletic Training; Community and Public Health; Exercise Sciences; Pre-Health Professions; and Physical Education Teacher Licensure. The Department of Physical Education was founded in 1974 from the merger of the Department of Physical Education for Men and the Department of Physical Education for Women. In 1981 its name changed to the Department of Physical Education and Leisure Studies. In 1993 its name changed to the Department of Health and Human Performance. In 2007 its name changed to the Department of Kinesiology. Dates of Existence: 1974-present. Historical Names: Department of Physical Education (1974-1981), Department of Physical Education and Leisure Studies (1981-1993), Department of Health and Human Performance (1993-2007). Related Units: College of Human Sciences (parent college), College of Education (parent college, 1974 - 2005), Department of Physical Education for Women (predecessor) Department of Physical Education for Men
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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.


This book chapter is published as Derrick, T.R. and Thomas, J.M. (2004). Chapter 7. Time-Series Analysis: The cross-correlation function. In: Innovative Analyses of Human Movement, (pp. 189-205), Stergiou, N. (ed). Human Kinetics Publishers, Champaign, Illinois, 189-205. Posted with permission.

Thu Jan 01 00:00:00 UTC 2004