Impulse response of a causal system from transfer function in z-domain

1. How do you find the impulse response of z transfer function?
2. How do you find the impulse response of LTI system using Z-transform?
3. What is the Z-transform of the impulse function?

How do you find the impulse response of z transfer function?

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.

How do you find the impulse response of LTI system using Z-transform?

x[n]∗h[n]Z⟶X(z)H(z). In case the impulse response is given to define the LTI system we can simply calculate the Z-transform to obtain :math:`H(z). In case the system is defined with a difference equation we could first calculate the impulse response and then calculating the Z-transform.

What is the Z-transform of the impulse function?

Therefore, the Z-transform of the unit impulse function is given by, Z[x(n)]=X(z)=Z[δ(n)]