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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) U_{n-m}V_{m}

=Ʃ(from m=0 to n)2^{n-m}5^{m}

=Ʃ(from m=0 to n)2^{n}(5^{m}/2^{m}

=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[(5^{n+1}-2^{n+1})/2^{n+1}×3/2]

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

I dont get the last 3 steps, I would REALLY appreciate it if somebody would explain that ^^

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# Homework Help: Convolution for Z-transform

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