Circular convolution: Difference between revisions

Revision as of 18:24, 12 April 2024

Revision as of 10:42, 21 May 2024

Line 1:

{{Short description|Mathematical operation}}

'''Circular convolution''', also known as '''cyclic convolution''', is a special case of '''periodic convolution''', which is the [[convolution]] of two periodic functions that have the same period. Periodic convolution arises, for example, in the context of the [[discrete-time Fourier transform]] (DTFT). In particular, the DTFT of the product of two discrete sequences is the periodic convolution of the DTFTs of the individual sequences. And each DTFT is a [[periodic summation]] of a continuous Fourier transform function (see {{slink|DTFT#DefinitionDiscrete-time Fourier transform|Relation to Fourier_Transform}}). Although DTFTs are usually continuous functions of frequency, the concepts of periodic and circular convolution are also directly applicable to discrete sequences of data. In that context, circular convolution plays an important role in maximizing the efficiency of a certain kind of common filtering operation.

==Definitions==