Q7Digital Signal Processing
Question
2 marks
Q.7. State the Sampling theorem.
Answer
The sampling theorem states that a band-limited signal with maximum frequency B Hz can be perfectly reconstructed from its samples if sampled at a rate fs ≥ 2B (the Nyquist rate).
The Nyquist-Shannon Sampling theorem states that a continuous-time signal x(t) that is band-limited (contains no frequency components above B Hz) can be completely and uniquely reconstructed from its samples, provided the sampling frequency fs satisfies fs ≥ 2B (the Nyquist rate). If this condition is not met (undersampling), the original signal cannot be recovered without distortion, because higher-frequency components fold back and overlap with lower frequencies in the sampled spectrum, a phenomenon known as aliasing.