6. Idealized Input Functions




Function \(\boldsymbol{x(t)}\) \(\boldsymbol{X(s)}\)
Step \(x(t) = \left\{\begin{array}{ll}A & t>0 \\ 0 & t<0\end{array}\right.\) \(\dfrac{A}{s}\)
Ramp \(at\) \(\dfrac{a}{s^2}\)
Sinusoidal \(\sin(\omega t)\) \(\dfrac{\omega}{s^2+\omega^2}\)
Impulse \(\delta(t)\) 1
Rectangular pulse \(x(t) = \left\{\begin{array}{ll} 0 & t<0 \\ A & 0 < t < T \\ 0 & t>T \end{array} \right.\) \(\frac{A}{s}\left(1-e^{-sT}\right)\)