Howtosignalprocessing
- How do you know if a Z-transform is stable?
- What is the use of stability in Z-transform?
- What is the condition of stability in Z domain?
- What is causality and stability in Z-transform?
How do you know if a Z-transform is stable?
A system is stable if the absolute sum of its impulse response is finite: ch=∞∑n=−∞|h(n)|<∞
What is the use of stability in 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. In the above systems the causal system (Example 2) is stable because |z| > 0.5 contains the unit circle.
What is the condition of stability in Z domain?
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.
What is causality and stability in Z-transform?
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.
