Inverse z transform of z^2

1. What is the inverse Z-transform of z?
2. What is the inverse Z-transform of 1 z?
3. What are the inverse Z-transform methods?
4. What is the Z-transform of 0?

What is the inverse Z-transform of z?

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 inverse Z-transform methods?

Inverse Z Transform by Partial Fraction Expansion

This technique uses Partial Fraction Expansion to split up a complicated fraction into forms that are in the Z Transform table. If you are unfamiliar with partial fractions, here is an explanation.

What is the Z-transform of 0?

The z-transform of the zero order hold is 1.