It's been a long time since I played with Z transforms but the formula you started with appears incorrect.
I have that the advance theorem shows
not
as you have listed.
I have the following sequence: where i and p are constants. I need to find an equation for the sequence that is independent of the previous elements except .
The Z-transform gives: or .
Doing partial fractions yields:
Now when I take the reverse Z-transform with gives me the wrong answer. If I substitute instead, I get the correct answer. Any ideas what I've done wrongly?
P.S.
I thought I had made a mistake and it should be instead of , but I double checked everything and cannot find any mistakes. That would suggest I've probably made a mistake in the Z-transform.
were you able to solve this? I worked it through and your approach works if you correct that small error.
one small note. Don't use as a constant unless it's an iterator. It's just too easily mistaken for sqrt{-1}