What defines the fundamental period of a periodic signal?

• A. The smallest positive shift T such that x(t+T) = x(t) for all t.
• B. The average power of the signal.
• C. The integral of the signal over one period.
• D. The amplitude of the signal.

Answer: (A)

The key idea is that a periodic signal repeats itself after a certain time shift. The fundamental period is the smallest positive T for which x(t+T) = x(t) holds for every t. This ensures the signal repeats every T, and no smaller positive shift can produce the same waveform. Any integer multiple of that T will also be a period, but the smallest one is the fundamental period.

The other quantities—average power, the integral over one period, and the amplitude—are about how much energy, area, or height the signal has, not about how often the signal repeats. They don’t define the timing of the repetition, which is why they don’t determine the fundamental period. If no positive T satisfies x(t+T)=x(t) for all t, the signal isn’t periodic.