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What do you mean by stability how it is determined using pole-zero plot?
In order to relate the Pole-Zero plot to the frequency response, the system needs to be stable. Since the system in stable, we can relate the pole-zero plot to the frequency response of the system. A stable system is that, which produces a bounded output, when the input to the system is bounded.
How can we determine response of a circuit from pole-zero plots?
The poles are located at s = ± j ω from s2 + ω2 = 0. The locations of poles and corresponding time response is shown in the Fig. 3.22 (a) and (b). If such a pair of poles has a zero at origin or a finite zero then in the corresponding time response, cosine waveform or both sine and cosine waveforms are present.
How are ROCS determined in a pole zero plot?
Other than that, I am having trouble applying those rules to a pole-zero plot. For systems with more than one pole (with different radii), there are 3 types of ROCs: inside the circle with a radius corresponding to the smallest pole radius; the corresponding time-domain sequence is left-sided
Do you need a ROC for stability and causality?
I know that for stability, the ROC must include the unit circle. And for causality, h [ n] = 0 for n < 0. Other than that, I am having trouble applying those rules to a pole-zero plot. For systems with more than one pole (with different radii), there are 3 types of ROCs:
Can a causal system have a ROC outside a circle?
Since a ROC equal to a ring between two poles corresponds to a two-sided sequence, the system can’t be causal. A causal system has a ROC outside a circle (case 2 in the list above).
Is the ROC of the Z transform stable?
If the ROC extends outward from the outermost pole, then the system is causal. If the ROC includes the unit circle, then the system is stable. Below is a pole/zero plot with a possible ROC of the Z-transform in the Simple Pole/Zero Plot (Example 12.5.