Discussion
The Fourier transform of a unit impulse is
Answer: C
An impulse contains every frequency in equal measure, so its transform is flat - the frequency-domain statement of the fact that a perfectly short event has infinite bandwidth. An impulse in frequency corresponds to a constant in time, which is the dual pair. A sinc arises from a rectangular pulse of finite width. And a transform that vanished everywhere would describe no signal at all. This pair underpins impulse-response testing, since exciting a system with an impulse probes all frequencies at once.
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