With reference to the classification of signals based on energy and power considerations, consider the following statements:1.An energy signal is one whose total energy is finite while its average power over an infinite duration is zero.2.A power signal is characterized by finite average power but infinite total energy when integrated over time.3.A periodic signal with non-zero amplitude always qualifies as an energy signal due to repetition.4.A time-limited signal that exists only over a finite duration necessarily has finite energy.Which of the above statements is/are correct?

Correct Answer: A - 1, 2 and 4 only

Quick Concept Explanation

Energy and power are mutually exclusive classifications for ordinary nonzero signals: an energy signal has finite total energy and zero average power, while a power signal has finite nonzero average power and infinite energy. A finite-duration bounded signal normally has finite energy. Key relation: E=∫|x(t)|²dt; P=lim(T→∞)(1/2T)∫_{−T}^T|x(t)|²dt.

Exam focus: Periodic nonzero → usually power signal, not energy signal. Common trap: Repetition does not make a periodic signal finite-energy.

Statement-wise Verification

• Statement 1 - Correct.
  An energy signal is one whose total energy is finite while its average power over an infinite duration is zero.
  Energy and power are mutually exclusive classifications for ordinary nonzero signals: an energy signal has finite total energy and zero average power, while a power signal has finite nonzero average power and infinite energy.
• Statement 2 - Correct.
  A power signal is characterized by finite average power but infinite total energy when integrated over time.
  Energy and power are mutually exclusive classifications for ordinary nonzero signals: an energy signal has finite total energy and zero average power, while a power signal has finite nonzero average power and infinite energy.
• Statement 3 - Incorrect.
  A periodic signal with non-zero amplitude always qualifies as an energy signal due to repetition.
  A nonzero periodic signal has infinite total energy and finite average power, so it is a power signal
• Statement 4 - Correct.
  A time-limited signal that exists only over a finite duration necessarily has finite energy.
  A finite-duration bounded signal normally has finite energy.

Core Concept

Energy and power are mutually exclusive classifications for ordinary nonzero signals: an energy signal has finite total energy and zero average power, while a power signal has finite nonzero average power and infinite energy. Nonzero periodic signals are power signals. A finite-duration bounded signal normally has finite energy.

Formula / Key Relationship

E=∫|x(t)|²dt; P=lim(T→∞)(1/2T)∫_{−T}^T|x(t)|²dt.

Why the Other Options Are Wrong

Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 2, 4. Option C is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 1, 4. Option D is incorrect because it includes incorrect statement(s) 3.

Exam Shortcut / Approach

Periodic nonzero → usually power signal, not energy signal.

Common Mistake

Repetition does not make a periodic signal finite-energy.

Quick Revision

Energy Power and Time-Limited Signals is linked with Energy and Power Signals, Signal Classification and Signals and Systems. Periodic nonzero → usually power signal, not energy signal.