Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / 4 / c / Solution

By the Fourier modulation and translation identity, delaying the pulse by $\tau$ multiplies its transform by $e^{-i\omega \tau }$. HenceThe removable value at zero is $2(1+\alpha )$. For real $\alpha$, the squared spectral magnitude is multiplied by $1+{\alpha }^2+2\alpha \cos (\omega \tau )$, showing the interference between the direct and reflected signals.