Question 24.9: Given that the Fourier transform of u(t) e^−t is 1/1 + jω us......
Given that the Fourier transform of u(t)\operatorname{e}^{-t} is \frac{1}{1+\mathrm{j}\omega} use the duality principle to deduce the transform of {\frac{1}{1+{jt}}}.
Step-by-Step
We know {{F(\omega)}}\ =\ {\frac{1}{1+\mathrm{j}\omega}} is the Fourier transform of \textstyle f(t)\;=\;u(t)\,\mathrm{e}^{-t}. Therefore 2\pi(u(-\omega)\operatorname{e}^{\omega}) is the Fourier transform of {\frac{1}{1+{{jt}}}}.
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