MathLiveConvolution of two functions
The convolution gives the integral of the product of one function with a reflected and shifted copy of another, evaluated for every shift x. It is used in signal processing, probability (sum of random variables), and solving linear systems.
(f \ast g)(x) = \int_{-\infty}^{\infty} f(y)\, g(x - y)\, \mathrm{d}yWhat the symbols mean
| two integrable functions of a real variable | |
| the convolution of f and g evaluated at shift x | |
| the shift variable | |
| the integration variable |
About this formula
- FieldMathematics
- TopicFunctional analysis
- LevelUniversity
- Also calledconvolution integral, convolution operation, convolution definition, continuous convolution, f star g, convolution of functions
- SourceWikidata Q210857
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