GATE 2015 EE – Question 19
A moving average function is given by $y(t) = \frac{1}{T}\int_{t-T}^{t} u(\tau)\,d\tau$. If the input $u$ is a sinusoidal signal of frequency $\frac{1}{2T}$ Hz, then in steady state, the output $y$ will lag $u$ (in degree) by ________.
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Correct answer: 90
Explanation
The averaging window has the frequency response $H(j\omega) = \frac{1 - e^{-j\omega T}}{j\omega T} = e^{-j\omega T/2}\,\frac{\sin(\omega T/2)}{\omega T/2}$, so the phase lag is $\frac{\omega T}{2}$. For a frequency of $\frac{1}{2T}$ Hz, $\omega = \frac{\pi}{T}$, and the lag is $\frac{\pi}{2}$ radians, which is 90°.