Discussion
For the given signal, find its discrete time fourier transform.
Answer: B
The signal is the unit impulse \(x(n) = \delta(n)\): one at \(n = 0\) and zero everywhere else. The discrete time Fourier transform is
\[ \begin{aligned} X(e^{j\omega}) \\ &= \sum_{n=-\infty}^{\infty} x(n)e^{-j\omega n} \\ &= \delta(0)\,e^{0} = 1 \end{aligned} \]
Only the term \(n = 0\) survives, so the transform is 1 for all frequencies: the impulse contains all frequencies equally. The values 0, 2 and 3 would belong to other signals (for example, a zero signal or multiples of the impulse). The answer is 1, option B.
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