Representation of poles and zeros

Consider representation of the system function

poles to left of imaginary axis poles to right of imaginary axis  α, β -- poles of order 1  --pole of order 2   δ -- pole of order 3

Thus H(s) can be represented as .

On expansion of H(s) in terms of partial fraction we would get

Recall that 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.

Thus, as we have seen earlier, α contributes a right handed decaying exponential and β contributes a left handed decaying exponential and the contributions of following terms in the denominator are