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February 10th, 2017, 12:23 AM   #1
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Need hint for this discrete transfer function

The question ask me to calculate and sketch the step response of the disrete transfer functions shown below for the first 6 sampling instants. What conclusion can you make about the effect of the pole zero locations?

(1) 1/(1+0.7z^-1)

My answer:

Let X(z) = 1/(1+0.7z^-1) = z / (z+0.7)

Inverse z-transform

X(k) = (-0.7)^k and at k=0 to 5

X(k) = 1 , -0.7 , 0.49 , -0.343 , 0.2401 and -0.16807.

i sketch the unit step response at k=0 , X(k) =1 and all the way to k=5 , X(k)=-0.16807. so now i need to answer the questions what conclusion can you make about the effect of the pole zero location? I think it is stable since it becomes smaller and smaller (as k goes to infinity , X(k) = 0)

Did I do it correctly?
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