Definition:Convolution Integral/Cross-Correlation
< Definition:Convolution Integral(Redirected from Definition:Pentagram Notation)
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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
- 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Frontispiece
- 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Chapter $4$: Notation for some useful Functions: Summary of special symbols: Table $4.1$ Special symbols
- 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Inside Back Cover