# Convolution Product

1. Sep 27, 2009

### BustedBreaks

I need to find the convolution product f*g when the functions f, g on $$P_{4}$$ are given by:

(a) f:=(1,2,3,4), g:=(1,0,0,0)
(b) f:=(1,2,3,4), g:=(0,0,1,0)

I know that $$(f*g)[n]=f[0]\cdot g[n]+f[1]\cdot g[n-1]+f[2]\cdot g[n-2]+...+f[N-1]\cdot g[n-(N-1)]$$

and

$$\sum_{m=0}^{N-1}f[m]g[n-m]$$ when f, g, and f*g are functions on $$P_{N}$$

I need to find (f*g)[n] for n =0,1,2,3. when I plug in 0 for n in the sum above, I get f[0]g[0] which is fine. f[0] and g[0] both correspond to 1 considering what is given in (a). However, when I plug 1 into the sum above, I get f[1]g[-1] . f[1] corresponds to 2 from (a) but I don't know what g[-1] corresponds to. Am I doing this right?

Last edited: Sep 27, 2009
2. Sep 27, 2009

### BustedBreaks

Wait, on $$P_{4}$$ does g[-1]=g[3]?