Lecture 36 : Analysis of LTI Systems with Rational System Functions
Conclusion:
In this lecture you have learnt:
Necessary and sufficient condition for causality in a continuous rational system :
The region of convergence must include .
Necessary and sufficient condition for causality in a discrete rational system :
The region of convergence must include .
In general, Re{s} = 0 lies in ROC is not sufficent condition to imply stability. But for rational
systems Re{s} = 0 lies in ROC system is stable.
In a rational system, with ROC of the system function including Re(s)=0, the poles to the left of
imaginary axis contribute right-sided exponentially decaying term and poles to the right of the
imaginary axis contribute left-sided exponentially decaying term.
For a discrete rational system stability implies and is implied by the unit circle in the z plane
belonging to the ROC of the system function.
Congratulations, you have finished Lecture 36. To view the next lecture select it from the
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system is stable. 
