Circular convolution: Difference between revisions

Revision as of 15:43, 16 June 2020

Revision as of 15:11, 21 June 2020

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where ''t''_o is an arbitrary parameter and ''h''_''T'' is a [[periodic summation]] of ''h''.&nbsp; The second integral is called the '''periodic convolution'''<ref name=Jeruchim/><ref name=Udayashankara/> of functions ''x''_''T'' and ''h''_''T''.&nbsp; When ''x''_''T'' is expressed as the [[periodic summation]] of another function, ''x'', the same operation may also be referred to as a '''circular convolution'''<ref name=Udayashankara/><ref name=Priemer/> of functions ''h'' and ''x''.{{efn-ua

|This terminology is not consistent across all authors. Some authors constrain both <math>h</math> and <math>x</math> to the interval <math>[0,T]</math> and callwrite &nbsp;<math>\int_{0}^{T} h(\tau)\cdot x(\mathrm{mod}_T(t - \tau))\scriptstyle \mathrm{mod}\ T\displaystyle) d\tau,</math>&nbsp; which gives rise to the interpretation of a ''circular convolution''.}}

== Discrete sequences ==