Find a stable transfer function $G(z)$ such that $|G(z)| = |H(z)|$

1. How do you know if a transfer function is stable?
2. How do you find the stability of Z-transform?
3. What is Z in transfer function?
4. What is the condition for stability in Z domain?

How do you know if a transfer function is stable?

▶ A transfer function is stable if its zero-input response converges to zero in the steady state regardless of initial conditions.

How do you find the stability of Z-transform?

The stability of a system can also be determined by knowing the ROC alone. If the ROC contains the unit circle (i.e., |z| = 1) then the system is stable.

What is Z in transfer function?

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.

What is the condition for stability in Z domain?

Equation (3.7. 6) gives the condition of stability in Z domain. This condition requires that, unit circle must be present in the ROC of H(Z). Otherwise we cannot find H(Z) on unit circle at all.