Right choice is (d) G(f) = τ sinc(f)
The explanation: Fourier transform of gate function, G(ω) = \(\frac{2}{ω} sin(\frac{wτ}{2})\)
Multiplying and dividing by τ we get
\(G(ω) = τ \frac{sin(\frac{wτ}{2})}{\frac{wτ}{2}} = τ \frac{sin(\frac{2πfτ}{2})}{\frac{2πfτ}{2}}= τ \frac{sin(πτf)}{πτf} = τ sinc(τf)\).