Thread: Convolution operator

Give:
f: Z --> R
f(0) = -3
f(1) = f(-1) = 2
f(x) = 0, other wises.
And the kernel K (1/4, 1/2, 1/4).
How can we calculate f*K, where "*" is the convolution operator?

Originally Posted by le_su14

Give:
f: Z --> R
f(0) = -3
f(1) = f(-1) = 2
f(x) = 0, other wises.
And the kernel K (1/4, 1/2, 1/4).
How can we calculate f*K, where "*" is the convolution operator?

Take the definition of discrete convolution and plug in your values, there are
at most 5 non zero values to be computed.

RonL

So:
The first value: 0*1/4 + 0*1/2 + 2*1/4 = 1/2
The second one: 0*1/4 + 2*1/2 + (-3)*1/4 = 1/4
The third one: 2*1/4 + (-3)*1/2 + 2*1/4 = -1/2
The 4th one: 0*1/4 + 2*1/2 + (-3)*1/4 = 1/4
The last one: 2*1/4 + 0*1/4 + 0*1/2 = 1/2
Is it right?

Originally Posted by le_su14

So:
The first value: 0*1/4 + 0*1/2 + 2*1/4 = 1/2
The second one: 0*1/4 + 2*1/2 + (-3)*1/4 = 1/4
The third one: 2*1/4 + (-3)*1/2 + 2*1/4 = -1/2
The 4th one: 0*1/4 + 2*1/2 + (-3)*1/4 = 1/4
The last one: 2*1/4 + 0*1/4 + 0*1/2 = 1/2
Is it right?

Looks OK to me (which means someone will come along and point out some
minor error )

RonL