The Fourier transform {\X}( {\j} \omega) of the signal x(t)=\frac{t}{ (1+t^2) ^2} is _______.

Correct Answer is : π2jωe−|.ω|.

\frac{\pi }{2j}\omega e^{−|.\omega |.}

\frac{\pi }{2}\omega e^{−|.\omega |.}

\frac{\pi }{2j}e^{−|.\omega |.}

\frac{\pi }{2}e^{−|.\omega |.}

GATE Electronics and Communications (EC) 2022 Solved Paper

Question : 14 of 65

Marks: +1, -0

The Fourier transform

{\X}( {\j} ω)

of the signal

x(t)=\;{t}/{ (1+t^2) ^2}

is _______.

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