What is the effect on the spectrum when a continuous-time signal is sampled?

What is the effect on the spectrum when a continuous-time signal is sampled?

• A. It creates multiple copies of the spectrum spaced by the sampling frequency.
• B. It leaves the spectrum unchanged.
• C. It removes high-frequency components entirely.
• D. It makes the spectrum single-sided.

Answer: (A)

Sampling a continuous-time signal is like multiplying it by a train of impulses in time. In the frequency domain, that multiplication becomes a convolution with a train of impulses, which creates replicas of the original spectrum at intervals equal to the sampling frequency. So the spectrum appears in copies centered at multiples of Fs (and for real signals, on both sides of zero). If the sampling rate is high enough, these copies don’t overlap and the original spectrum can be recovered; if it’s too low, the copies overlap and aliasing occurs. That’s why the effect is described as generating multiple copies spaced by the sampling frequency.