# Laplace Transform (LT)

Laplace transform of *x*(*t*) function is

Properties of Laplace Transform:

**Linearity**

**Time-Reversal :***x*(*t*) â†”*X*(s) then*x*(â€“*t*) â†”*X*(â€“*s*),*ROC*= â€“*R***Shift in S-domain :***x*(*t*) â†”*X*(s) with*ROC*= R then**Time-shifting:**It*x*(*t*) is input-signal whose*ROC*is*R*.*ROC*=*R***Differentiation in S-domain:**If*x*(*t*) â†”*X*(s)*ROC*=*R*, then**Differentiation in Time :**If then**Integration in Time :**for unilateral LT**Frequency Integration :****Convolution in Time :**and with then**Initial and Final Value Theorem :**If*x*(*t*)*X*(*s*)*x*(0) = s*X*(*s*)*x*(âˆž) = s*X*(*s*)