A periodic signal is defined as:

A periodic signal is defined as:

• A. It has finite energy.
• B. It never repeats.
• C. It is defined only for t>=0.
• D. A signal is periodic if it is shifted in time by a certain amount (fundamental period) and the signal is the same.

Answer: (D)

Periodic signals are those that repeat themselves after a fixed time interval. There exists a positive T, the fundamental period, such that x(t+T) = x(t) for all t; shifting the signal by T leaves its values unchanged, and T is the smallest such shift. This captures why the signal is described as repeating after a certain time step. Finite energy is not a typical property of a periodic signal because, when considered over all time, the energy accumulates without bound as the pattern repeats endlessly. A signal being defined only for t ≥ 0 isn’t required for periodicity, since the repeating behavior applies for all time. And a statement claiming it never repeats contradicts the very idea of periodicity.

Periodic signals are those that repeat themselves after a fixed time interval. There exists a positive T, the fundamental period, such that x(t+T) = x(t) for all t; shifting the signal by T leaves its values unchanged, and T is the smallest such shift. This captures why the signal is described as repeating after a certain time step. Finite energy is not a typical property of a periodic signal because, when considered over all time, the energy accumulates without bound as the pattern repeats endlessly. A signal being defined only for t ≥ 0 isn’t required for periodicity, since the repeating behavior applies for all time. And a statement claiming it never repeats contradicts the very idea of periodicity.