In the context of reconstructing a continuous signal from samples, is the sampled signal assumed to be periodic?

In the context of reconstructing a continuous signal from samples, is the sampled signal assumed to be periodic?

• A. No, the samples are not assumed to be periodic.
• B. Yes, the samples are assumed to be strictly periodic.
• C. Only if the original signal is periodic.
• D. Periodicity is assumed for all discrete-time signals.

Answer: (A)

Periodicity is not assumed for the samples. When we reconstruct a continuous-time signal from its samples, we treat the sampled data as a discrete-time sequence x[n] = xc(nT). This sequence does not have to repeat itself; it can be nonperiodic depending on the original signal. The key requirements are that the original signal is bandlimited and the sampling rate is at least twice its highest frequency (the Nyquist criterion), so that an interpolation (often using a sinc function or a practical reconstruction filter) can perfectly recover xc(t). Periodicity would only arise as a special case if the original signal itself is periodic and the sampling pattern happens to produce a repeating sample sequence, but it is not a general assumption of the reconstruction process.

Periodicity is not assumed for the samples. When we reconstruct a continuous-time signal from its samples, we treat the sampled data as a discrete-time sequence x[n] = xc(nT). This sequence does not have to repeat itself; it can be nonperiodic depending on the original signal. The key requirements are that the original signal is bandlimited and the sampling rate is at least twice its highest frequency (the Nyquist criterion), so that an interpolation (often using a sinc function or a practical reconstruction filter) can perfectly recover xc(t). Periodicity would only arise as a special case if the original signal itself is periodic and the sampling pattern happens to produce a repeating sample sequence, but it is not a general assumption of the reconstruction process.