Question

Which of the following statements is correct?

• [I.] All periodic signals are energy signals while aperiodic signals are power signals
• [II.] Periodic signals have finite and non-zero average power
• [III.] Both periodic and aperiodic signals have infinite power and energy
• [IV.] All periodic signals are power signals while aperiodic signals are energy signals

• A. I and II only
• B. II only
• C. III only
• D. II and IV only

Hint:

Remember: Periodic signals are usually classified as power signals} (infinite energy but finite power), whereas aperiodic signals (those that decay over time) are often energy signals} (finite energy, zero power).

Answer 1

The Correct Option is D

To determine which statements are correct regarding periodic and aperiodic signals, let's analyze each statement:

• [I.] All periodic signals are energy signals while aperiodic signals are power signals. 
  This is incorrect because periodic signals are typically classified as power signals, as they possess finite and non-zero power over an infinite period. Aperiodic signals, having non-repetitive nature, are typically energy signals with finite energy distributed over time.
• [II.] Periodic signals have finite and non-zero average power. 
  This is a correct statement. Periodic signals, by definition, possess a stable waveform that repeats over time, resulting in finite and non-zero average power.
• [III.] Both periodic and aperiodic signals have infinite power and energy. 
  This is incorrect. Both periodic and aperiodic signals do not have infinite power and energy. Generally, periodic signals are power signals with a finite average power, and aperiodic signals are energy signals with finite energy.
• [IV.] All periodic signals are power signals while aperiodic signals are energy signals. 
  This statement is accurate. Periodic signals, due to their repetitive nature, are classified as power signals as they typically have finite average power. Aperiodic signals are classified as energy signals due to their finite energy over time.

Therefore, the correct statements are II and IV only.