1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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??
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook