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I want to study how the Z transform changes with the sampling rate T, in a closed loop system.

The command I'm using to do this is:

InverseZTransform[(-1 - T + z + E^T (1 + (-1 + T) z))/
                  (-T +  E^T (1 + (-2 + T) z + z^2)), z, n]

However, it takes a while to do so, and the result that appears is insanely huge and impractical.

For substitutions of T = 1, T = 0, etc, the inverse transform is very very easily found. I was wondering if someone could give any suggestions as to whats going on, because I really don't want to have to solve it by hand.

Also, for some reason, Apart[ y[z] , z] Also doesn't work. (y[z] is the function to invert).

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