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Module 4 : Laplace and Z Transform

Lecture 36 : Analysis of LTI systems with rational system functions

Continuous Rational System

Causality

For a causal LTI system, the impulse response is zero for t=0 (and thus it is right sided!)

h(t) = 0 for all t<0

where H(s) is the system function (assuming system has a system function

with

for t > 0, as ,

Thus, if the region of convergence is non null, must be included in the ROC for the system to be causal.

Proof: As region of convergence is not null there exist an

as for which is given to be convergent

Hence H(S) is convergent for all Re(S)>Re(So)

is inthe region and belongs to ROC

Necessary and sufficient condition for causality in a rational system:

The region of convergence must include