Determing inverse Z-transform using impulse response?

1. What is the Z-transform of impulse response?
2. How many types of methods are there to determine inverse Z-transform?
3. What is the Z-transform H z of the impulse response of this filter?

What is the Z-transform of impulse response?

A LTI system is completely characterized by its impulse response h[n] or equivalently the Z-transform of the impulse response H(z) which is called the transfer function. Remember: x[n]∗h[n]Z⟶X(z)H(z).

How many types of methods are there to determine inverse Z-transform?

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

What is the Z-transform H z of the impulse response of this filter?

The impulse response of the discrete-time filter is expressed by the z transform function as: H ( z ) = 1 − z − 1 1 + 0.5 z − 1.