In this topic, you study the Laplace Transform Pairs of Basic Signals as Decaying Exponential, Impulse function, Cosine function, Sine function, Unit step function, etc.
Sine Function
\[\sin {\omega _0}t.u(t) \rightleftarrows \frac{{{\omega _0}}}{{{s^2} + \omega _0^2}}\]
Region of convergence $\sigma$ :
\[\sigma > 0\]
Cosine Function
\[\cos {\omega _0}t.u(t) \rightleftarrows \frac{{{s}}}{{{s^2} + \omega _0^2}}\]
Region of convergence $\sigma$ :
\[\sigma > 0\]
Unit step Function
\[u(t) \longleftrightarrow \frac{1}{s}\]
Region of convergence $\sigma$ :
\[\sigma > 0\]
Impulse Function
\[\delta (t) \longleftrightarrow 1\]
Region of convergence $\sigma$ :
Entire $s$-plane
Exponential Decaying
\[{e^{ – at}}.u(t) \longleftrightarrow \frac{1}{{s+a}}\]
Region of convergence $\sigma$ :
\[\sigma > -a\]
${t^n}.u(t)$
\[{t^n}.u(t) \rightleftarrows \frac{{n!}}{{{s^{n + 1}}}}\]
Region of convergence $\sigma$ :
\[\sigma > 0\]
