The GATE Grind

GATE 2025 IN – Question 16

Signals and Systems · Signals and linear time-invariant systems · 1 mark · Multiple choice

Let the continuous-time signal be $x(t)=e^{j9t}+e^{j5t}$, where $j=\sqrt{-1}$ and $t$ is in seconds. The fundamental period of $|x(t)|$, in seconds, is

  1. $\pi$
  2. $\pi/2$
  3. $\pi/5$
  4. $\pi/9$

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Show answer and explanation

Correct answer: (B) $\pi/2$

Explanation

Factor $x(t)=e^{j7t}(e^{j2t}+e^{-j2t})=2e^{j7t}\cos2t$.

Since $|e^{j7t}|=1$, the magnitude is $2|\cos2t|$.

The cosine period is $\pi$, but its sign reverses after $\pi/2$, leaving the absolute value unchanged.

Thus the fundamental magnitude period is **$\pi/2$ s (B)**.