Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Circular convoluti

When a function gT is periodic, with period T, then for functions, ƒ, such that ƒgT 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,

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 ƒgT is known as a circular, cyclic, or periodic convolution of ƒ and g.

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