Cross Correlation

Definition
Cross correlation is a measure of similarity of two series of data.

Auto correlation
Convolution
Understanding
Basically, if two sets of data are real numbers, really the cross correlation between the two data is the sum of the multiplications of DataA, and DataB. If the two data sets have different sizes, one slides over the other to get the overall cross correlation; usually, the shorter data is the one sliding, in this example is DataA. Every time, grab the same size of data in the DataB as the size of DataA, and multiple the two numbers with the same indexes and sum them up. The final product will be a number to represent the similarity between the subset of DataB and DataA. Along with DataA slides over DataB, every time, there is a number for the window data. At the end, the index where the biggest number is is the best matching between the two data sets.
Apparently, the number is not unified, so correlation coefficient can be used to unify the result into the range from -1 to 1.
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