Question

The number of inverse lapalace transform of a function is equal to ________

(a) the number of poles

(b) the number of poles+1

(c) the number of poles-1

(d) cannot be determined

The question was posed to me in an online interview.

My query is from Laplace Transform in chapter Control System Applications of MATLAB

Answer 1

Right option is (b) the number of poles+1

For explanation: It is seen that the number of possible inverse laplace transform of any function is equal to the number of poles it has +1. Considering a function F(s)=A/s+1 + B/s+3=F1(s)+F2(s), the inverse laplace transform would exist if the inverse laplace transform is absolutely converging in a region. There are 3 regions that can have an absolutely converging state for F1(s) and F2(s) simultaneously and hence, only option the number of poles+1 is correct.