GATE 2014 EC (EC3) – Question 32
A received passband waveform has phase $\varphi(f)=-2\pi\alpha(f-f_c)-2\pi\beta f_c$, with center frequency $f_c$ and positive $\alpha,\beta$. Find actual signal propagation delay.
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Correct answer: (C) $\alpha$
Explanation
The delay of the modulated envelope is the group delay −(1/2π)dφ/df. Differentiating φ(f)=−2πα(f−fc)−2πβfc gives dφ/df=−2πα, hence **delay=α,C**. The constant carrier-phase term involvingβdoes not change the waveform’s group delay.