Electrical Engineering Department
When a function gT is periodic, with period T, then for functions, ƒ, such that ƒ∗gT exists, the convolution is also periodic and identical to:
![(f * g_T)(t) equiv int_{t_0}^{t_0+T} left[sum_{k=-infty}^infty f( au + kT)
ight] g_T(t - au), d au,](https://upload.wikimedia.org/wikipedia/en/math/0/f/a/0faa715620b8509fac821808bc56098c.png)
where to is an arbitrary choice. The summation is called a periodic summation of the function ƒ.
If gT is a periodic summation of another function, g, then ƒ∗gT is known as a circular, cyclic, or periodic convolution of ƒ and g.
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Georgia Institute of Technology
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