With reference to aliasing in sampled signals, consider the following statements:1.Aliasing occurs when higher frequency components overlap with lower frequencies after sampling.2.It results in irreversible distortion in the reconstructed signal.3.Anti-aliasing filters are used prior to sampling to limit bandwidth.4.Aliasing is more prominent when the signal is oversampled.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.
  Aliasing occurs when higher frequency components overlap with lower frequencies after sampling.
  The sampling theorem requires a band-limited signal to be sampled at at least twice its highest frequency for ideal reconstruction.
• Statement 2 - Correct.
  It results in irreversible distortion in the reconstructed signal.
  The sampling theorem requires a band-limited signal to be sampled at at least twice its highest frequency for ideal reconstruction.
• Statement 3 - Correct.
  Anti-aliasing filters are used prior to sampling to limit bandwidth.
  Anti-aliasing filters limit input bandwidth before sampling, and ideal reconstruction uses a low-pass interpolation filter.
• Statement 4 - Incorrect.
  Aliasing is more prominent when the signal is oversampled.
  Oversampling makes aliasing less likely; undersampling causes spectral overlap

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

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