Definition:Convolution Integral/Cross-Correlation

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This page is about Cross-Correlation in the context of Integral Calculus. For other uses, see Convolution.

Definition

Let $f$ and $g$ be real functions which are integrable.


The cross-correlation of $f$ and $g$ is defined as:

$\ds \map f t \star \map g t := \int_{-\infty}^\infty \map f u \map g {t + u} \rd u$


Also known as

The cross-correlation operator $\map f t \star \map g t$ is sometimes referred to as pentagram notation.


Also see

  • Results about convolution integrals can be found here.


Sources