The Initial Value Theorem
If a signal $ x(t) = 0, t < 0 $and x(0) is not an impulse or higher-order singularity, then
- $ x(0^+) = lim_{s->\infty} s*X(s) $, where X(s) denoted the laplace transformation of x(t)
The Final Value Theorem
If a signal x(t) = 0, t < 0 and $ lim_{t->\infty} x(t) $ exists, then
- $ lim_{t->\infty} x(t) = lim_{s->0} s*X(s) $, where X(s) denoted the laplace transformation of x(t)
