If the sampling frequency is greater than twice the signal bandwidth, what is the outcome?

If the sampling frequency is greater than twice the signal bandwidth, what is the outcome?

• A. A Perfect reconstruction of the original analog signal is possible
• B. B The spectrum will alias
• C. C The sampling rate has no effect on reconstruction
• D. D The signal cannot be reconstructed in any case

Answer: (A)

The key idea here is the Nyquist rate: if a signal is strictly band-limited to a certain bandwidth and you sample at a rate greater than twice that bandwidth, the spectral copies created by sampling do not overlap. This non-overlap means you can perfectly recover the original continuous-time signal from the samples using an ideal low-pass filter (sinc interpolation). So, when the sampling frequency exceeds twice the signal bandwidth, the reconstruction can be exact under ideal conditions (bandlimited signal, perfect filter, no noise).

If you sample below that threshold, aliasing would occur and exact reconstruction wouldn’t be possible. The idea that the sampling rate has no effect on reconstruction is false because the rate directly determines whether aliasing happens. And stating that the signal cannot be reconstructed in any case is also incorrect for the same reason—the correct condition (sampling > 2B) enables perfect reconstruction.