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The signal \(x(t)\) is described by \[ x(t)=\begin{cases} 1, & -1\le t\le 1\\ 0, & \text{otherwise} \end{cases} \] Two of the angular frequencies at which its Fourier transform becomes zero are

1. \(\pi, 2\pi\)
2. \(0.5\pi, 1.5\pi\)
3. \(0, \pi\)
4. \(2\pi, 2.5\pi\)

Correct answer: \(\pi, 2\pi\)

Solution

For a rectangular pulse from \(-1\) to \(1\), the Fourier transform is proportional to \(\frac{\sin\omega}{\omega}\). Its zeros occur at \(\omega=n\pi\), where \(n\neq 0\). Therefore two such frequencies are \(\pi\) and \(2\pi\).

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