 Solution

ID: 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

τ

multiplies its transform by

e^{- iω τ}

. Hence

r (ω) = (1 + α e^{- iω τ}) b (ω) = (1 + α e^{- iω τ}) \frac{4 sin ω ( 1 - cos ω )}{ω ^{3}} .

The removable value at zero is

2 (1 + α)

. For real

α

, the squared spectral magnitude is multiplied by

1 + α^{2} + 2 α cos (ω τ)

, showing the interference between the direct and reflected signals.

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