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Convolution Product

  1. Sep 27, 2009 #1
    I need to find the convolution product f*g when the functions f, g on [tex]P_{4}[/tex] 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 [tex](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)][/tex]


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

    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. jcsd
  3. Sep 27, 2009 #2
    Wait, on [tex]P_{4}[/tex] does g[-1]=g[3]?
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