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