engineering recuitment GATE IN Test Series 2023-24 Mock Test Signals and Systems Fourier Transform Fourier Transform of Standard Signals
The output of a causal LTI system is related to the input x(t) by the differential equation
\(\frac{{dy\left( t \right)}}{{dt}} + 2y\left( t \right) = x\left( t \right)\)
If x(t) = e-t u(t), the value of Y(ω) at ω = 2 rad/sec is _______
Y(ω) is the Fourier transform of the output y(t).
1
\(\frac{{ - 1}}{{20}}\left( {1 + j3} \right)\)
2
\(\frac{1}{{16}}\left( {1 + j3} \right)\)
3
\(\frac{{ - 1}}{{20}}\left( {1 - j3} \right)\)
4
\(\frac{{ - 1}}{{16}}\left( {1 + j3} \right)\)