Inverse z-transform of a modulus square

1. What is the inverse transform of the Z-transform?
2. What is the inverse Z-transform of 1 z?
3. What are the methods of finding inverse Z-transform?

What is the inverse transform of the Z-transform?

The Inverse Z-Transform

(4) represents the integration around the circle of radius |z|=r in the counter clockwise direction. This is the direct method of finding inverse Z-transform. The direct method is quite tedious.

What is the inverse Z-transform of 1 z?

The Z-transform of a sequence an is defined as A(z)=∑∞n=−∞anz−n. In your case, A(z)=1/z=z−1, so this must mean an=0 for all n≠1, and a1=1. We don't need any fancy computations in this example, we just read off the one nonzero coefficient directly from A.

What are the methods of finding inverse Z-transform?

There are at least 4 different methods to do this: Inspection. Partial-Fraction Expansion. Power Series Expansion.