With reference to sampling and reconstruction of signals, consider the following statements:1.The sampling frequency must be at least twice the maximum frequency component present in the signal.2.Aliasing occurs when the sampling frequency is insufficient to capture the signal bandwidth.3.Reconstruction of a continuous-time signal from its samples requires an ideal low-pass filter.4.Increasing the sampling frequency beyond requirement leads to aliasing effects.Which of the above statements is/are correct?

Correct Answer: D - 1, 2 and 3 only

Quick Concept Explanation

The sampling theorem requires a band-limited signal to be sampled at at least twice its highest frequency for ideal reconstruction. Anti-aliasing filters limit input bandwidth before sampling, and ideal reconstruction uses a low-pass interpolation filter. Key relation: f_s≥2f_max; Nyquist rate=2f_max.

Exam focus: Filter before the ADC, not after aliasing has already occurred. Common trap: Oversampling reduces aliasing risk; it does not create aliasing.

Statement-wise Verification

• Statement 1 - Correct.
  The sampling frequency must be at least twice the maximum frequency component present in the signal.
  The sampling theorem requires a band-limited signal to be sampled at at least twice its highest frequency for ideal reconstruction.
• Statement 2 - Correct.
  Aliasing occurs when the sampling frequency is insufficient to capture the signal bandwidth.
  The sampling theorem requires a band-limited signal to be sampled at at least twice its highest frequency for ideal reconstruction.
• Statement 3 - Correct.
  Reconstruction of a continuous-time signal from its samples requires an ideal low-pass filter.
  Anti-aliasing filters limit input bandwidth before sampling, and ideal reconstruction uses a low-pass interpolation filter.
• Statement 4 - Incorrect.
  Increasing the sampling frequency beyond requirement leads to aliasing effects.
  Oversampling increases separation of spectral replicas and reduces aliasing risk

Core Concept

The sampling theorem requires a band-limited signal to be sampled at at least twice its highest frequency for ideal reconstruction. Sampling below this Nyquist rate folds spectral replicas onto one another, causing aliasing that cannot be undone from samples alone. Anti-aliasing filters limit input bandwidth before sampling, and ideal reconstruction uses a low-pass interpolation filter.

Formula / Key Relationship

f_s≥2f_max; Nyquist rate=2f_max.

Why the Other Options Are Wrong

Option A is incorrect because it omits correct statement(s) 3. Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 1, 3. Option C is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 3.

Exam Shortcut / Approach

Filter before the ADC, not after aliasing has already occurred.

Common Mistake

Oversampling reduces aliasing risk; it does not create aliasing.

Quick Revision

Nyquist Rate Aliasing and Reconstruction is linked with Sampling Theorem, Sampling and Signals and Systems. Filter before the ADC, not after aliasing has already occurred.