Which statement about non-periodic signals is true?

Which statement about non-periodic signals is true?

• A. It has zero energy.
• B. It is always continuous.
• C. It does not repeat after a fixed period.
• D. It repeats with a fixed nonzero period.

Answer: (C)

Non-periodic signals have no fixed time interval after which the waveform repeats. That means there is no T > 0 such that x(t + T) = x(t) for all t. So the statement that matches this is that it does not repeat after a fixed period. You can have non-periodic signals with finite energy, like x(t) = e^{-t}u(t); it decays and never repeats, yet its energy is finite because the integral of |x(t)|^2 over all time converges. Non-periodic signals are not required to be continuous; they can be discontinuous and still be non-periodic. Conversely, a signal that repeats with a fixed nonzero period would be periodic, not non-periodic, so that option doesn’t apply.

Non-periodic signals have no fixed time interval after which the waveform repeats. That means there is no T > 0 such that x(t + T) = x(t) for all t. So the statement that matches this is that it does not repeat after a fixed period. You can have non-periodic signals with finite energy, like x(t) = e^{-t}u(t); it decays and never repeats, yet its energy is finite because the integral of |x(t)|^2 over all time converges. Non-periodic signals are not required to be continuous; they can be discontinuous and still be non-periodic. Conversely, a signal that repeats with a fixed nonzero period would be periodic, not non-periodic, so that option doesn’t apply.