Discussion
Statement I: A short pulse in time has a wide spectrum.
Statement II: The time duration and the bandwidth of a signal cannot both be made arbitrarily small.
In the light of the above statements, choose the correct answer.
Answer: A
Both statements are correct, and the second is the general principle behind the first. The time-bandwidth product has a lower bound, so compressing a signal in time necessarily spreads it in frequency and vice versa. It is why radar uses short pulses and pays for them in bandwidth, and why a narrowband channel cannot carry fast transitions. The relationship is a property of the Fourier transform itself rather than of any particular waveform, which is what makes it inescapable.
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