##  [Convolution](/convolution) 

  ##  [Convolution](https://natural.quantumdictionary.io/convolution-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A binary operation that combines two functions (or sequences) into a third by integrating (or summing) the product of one function with a shifted copy of the other: (f * g)(t) = ∫ f(τ) g(t−τ) dτ (or discrete analogue).

 

 

 

 

 





 

 



 ##  [Convolution](https://puremath.quantumdictionary.io/convolution-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A binary operation on functions, measures, or distributions defined (in the classical case) by (f * g)(x) = ∫ f(y) g(x − y) dy (or an analogous formula on groups) that produces a combined function used for smoothing, filtering, and representing translation-invariant linear operators.