Howtosignalprocessing
- What is the condition of stability in Z domain?
- Which of the following is the condition for causal and stable system in Z domain?
- Which of the following is the necessary condition to take Z-transform?
- How do you determine whether Z-transform is stable?
What is the condition of stability in Z domain?
ondition of stability is Z-domain is, [H(Z) < ∞ when evaluated on unit circle. That means the system transfer function should be finite if evaluated on unit circle. (3.7.10) Equation (3.7. 6) gives the condition of stability in Z domain.
Which of the following is the condition for causal and stable system in Z domain?
The condition for both causality and stability can now be derived as follows. A causal system should have a region of convergence outside the outermost pole. A stable system should have the unit circle in its region of convergence. Therefore, a causal and stable system should have all poles inside the unit circle.
Which of the following is the necessary condition to take Z-transform?
The one and only condition for BIBO stability of a 1D discrete-time system, in the z-domain, is that its transfer functions's ROC (region of convergence) should include the unit circle : |z|=1. Therefore, it's a necessary and sufficient condition for BIBO stability of a 1D SISO system.
How do you determine whether Z-transform is stable?
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.
