Signal classification: If g(t) = A (a non-zero constant) for all t, is g(t) an energy signal, a power signal, or neither?

Introduction / Context:Signals are commonly classified as energy or power signals based on the finiteness of their total energy and average power. Constant signals are a classic test case that clarifies the definitions.

Given Data / Assumptions:

• g(t) = A, with A ≠ 0 constant for all t.
• Energy: E = ∫{−∞}^{∞} |g(t)|^2 dt.
• Average power: P = lim{T→∞} (1/(2T)) ∫{−T}^{T} |g(t)|^2 dt.

Concept / Approach:

An energy signal has finite E and zero power. A power signal has finite, non-zero P and infinite energy (over infinite duration). A nonzero constant over infinite time accumulates infinite energy but has finite average power equal to A^2.

Step-by-Step Solution:

Verification / Alternative check:

For periodic or constant signals, power is finite and equal to the time average of |g(t)|^2. Here that equals A^2, consistent with power-signal classification.

Why Other Options Are Wrong:

• Energy signal requires finite energy; here energy diverges.
• “Neither” is incorrect because average power is finite and well-defined.
• “Insufficient data” is incorrect; information given is adequate.

Common Pitfalls:

• Assuming finite amplitude implies finite energy even over infinite duration.
• Confusing definitions of energy and power criteria.

Final Answer:

Power signal