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).