# Convolution Sum

Convolution Sum

The component of the convolution of and is defined by =. Note that is the sequence written in reverse order, and shifts this sequence units right for positive . Thus one can think of the component as an inner product of and a shifted reversed . For purposes of illustration and can have at most six nonzero terms corresponding to . These terms are entered with the controls above the delimiter. In the table the gray-shaded cells mark the position . The bold number in the table and larger point on the plot indicate .

th

n

h

x

y

n

∞

∑

k=-∞

h

k

x

n-k

x

-k

x

k

x

n-k

n

n

y

n

h

x

x

h

n=0,1,2,3,4,5

n=0

y

n