GATE 2015 EC – Question 28
The waveform of a periodic signal $x(t)$ is shown in the figure.
[Figure: A periodic sawtooth. In each period of 3 s the signal starts at 3 and falls linearly to $-3$ over 2 s, then jumps back and stays at 0 for 1 s.]
A signal $g(t)$ is defined by $g(t) = x\left(\frac{t - 1}{2}\right)$. The average power of $g(t)$ is ________.
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Correct answer: 2
Explanation
Shifting and stretching the time axis does not change the average power of a periodic signal. In one period of $x(t)$, the ramp from 3 to $-3$ over 2 s has the mean square value $\frac{1}{2}\int_0^2 \left(3 - 3t\right)^2 dt$, so the energy over the ramp is $\frac{3^2 \times 2}{3} = 6$. Dividing by the period 3 gives $\frac{6}{3} = 2$.