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?
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.