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WOLFRAM|DEMONSTRATIONS PROJECT

Convolution Sum

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enter data value
0
x
0
enter filter value
0
h
0
n
0
reversed and shifting x
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
h
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
y
0
0
0
0
0
0
1
2
2
2
2
2
1
0
0
0
0
0
The
th
n
component of the convolution of
h
and
x
is defined by
y
n
=
∞
∑
k=-∞
h
k
x
n-k
. Note that
x
-k
is the sequence
x
k
written in reverse order, and
x
n-k
shifts this sequence
n
units right for positive
n
. Thus one can think of the component
y
n
as an inner product of
h
and a shifted reversed
x
. For purposes of illustration
x
and
h
can have at most six nonzero terms corresponding to
n=0,1,2,3,4,5
. These terms are entered with the controls above the delimiter. In the table the gray-shaded cells mark the position
n=0
. The bold number in the table and larger point on the plot indicate
y
n
.
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