The Discrete Fourier Transform, Part 6: Cross-Correlation

The cross correlation has uses in many fields of scientific endeavor (music, identification of blood flow, astronomical event processing, speech processing, pattern recognition, financial engineering, etc.). One of the basic problems with the term normalization when applied to the cross-correlation is that it is defined in different places differently. For example, Pratt suggests that the number of elements in the normalization (an even a square root) is not needed [Pratt]. Lewis suggests using both the square root and the average [Lewis]. Therefore the question of which normalization to use is application-specific.