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Homework Help: Convolution for Z-transform

  1. Apr 30, 2012 #1
    Greetings,
    We just had 1.5 classes about this topic (due to some unavoidable circumstances in our country...) so our teacher just scribbled and roughly explained them on the board...So after i got home i couldnt get some steps he did for convolution in z-transform:

    find inverse z-transform of z^2/(z-2)(z-5)

    so here, inverse of z/(z-2) is 2^n which is Un and inverse of z/(z-5) is 5^n which is Vn
    so Vn*Un = Ʃ(from m=0 to n) Un-mVm

    =Ʃ(from m=0 to n)2n-m5m
    =Ʃ(from m=0 to n)2n(5m/2m
    =2^nƩ(from m=0 to n)[5/2]m
    =2^n[1+(5/2)+(5/2)^2 + (5/2)^3.......(5/2)^n]

    By convolution-

    =2^n{[1(5/2)n+1 - 1]/(5/2 -1)}
    =2^n[(5n+1-2n+1)/2n+1×3/2]
    =1/3[5n+1-2n+1]

    I dont get the last 3 steps, I would REALLY appreciate it if somebody would explain that ^^
     
  2. jcsd
  3. Apr 30, 2012 #2
    anyone??
     
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