Topic: Signals and Systems
Consider the signal $X(t) = \begin{cases} 2\cos(t) + \cos(2t) & t < 0 \\ 2\sin(t) + \sin(2t) & t \ge 0 \end{cases}$. The signal $X(t)$ is:
- A. Periodic with period $= 2\pi$
- B. Periodic with period $= \pi$
- C. Non-periodic
- D. Periodic with period $= \pi/2$
Answer: C. Non-periodic
Explanation: For a signal to be strictly periodic, it must repeat its exact pattern from $-\infty$ to $+\infty$. Since this signal has two different definitions for $t < 0$ and $t \ge 0$, it does not satisfy the periodicity condition across all time, making it non-periodic.