Correlation, Square-Integrable Functions and the Fundamental Identity
The three main topics in this chapter involve integral formulas that are very similar to the convolution formula. So you could view this chapter as a continuation of the one on convolution.
The first integral formula will define correlation, an operation often used in applications to measure similarities between two functions. This operation is so much like convolution that we’ll be able to prove some of the major results regarding correlation by simply referring to analogous results already proven for convolution.
One thing we will discover is that applications of correlation often involve integrals of squares of functions. This will naturally lead to a brief discussion ...
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