engineering recuitment GATE ECE 2023-24 Test Series Signals and Systems Laplace Transform Properties of Laplace Transform
Consider two signals x(t) and y(t) shown in the figure and their Laplace transform pairs:
\(x\left( t \right)\mathop \leftrightarrow \limits^{\cal L} X\left( s \right)\;and\;y\left( t \right)\mathop \leftrightarrow \limits^{\cal L} Y\left( s \right)\)
If X(s) \(= \frac{1}{s}\left[ {5 - 10{e^{ - 2s}} + 5{e^{ - 4s}}} \right],\) then Y(s) will be:
1
5 – 10e-2s + 5e-4s
2
\(\frac{1}{{2{s^2}}}\left[ {5 - 10{e^{ - 2s}} + 5{e^{ - 4s}}} \right]\)
3
s[5 – 10e-2s + 5e-4s]
4
\(\frac{1}{{{s^2}}}\left[ {5 - 10{e^{ - 2s}} + 5{e^{ - 4s}}} \right]\)