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I am preparing for the written test conducted by IISc Bangalore for admission into their graduate program. I happened to come across a sample paper from 2016, I think.

I am struggling to understand the 11th question,

q11

Since phasors are sinusoids, I think the answer is 0. But, here they called it a "time signal" and specified a finite time range.

So even if I considered a windowed version of the periodic signal, then since the Fourier transform of the signal at 0 frequency is finite, I can conclude the time average value is still 0.

So my question is, what is the answer? which of my interpretation would be correct? Also how can complex signals be "time signals", is there any physical interpretation of "dc component" of sum of spinning phasors?

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    \$\begingroup\$ In time T, how many cycles of the first signal? how many cycles of the 2nd signal? are the # of cycles EXACTLY integer? by the way, signals happen in time, not in frequency. \$\endgroup\$ Apr 12, 2019 at 20:44
  • \$\begingroup\$ I don't think your Fourier transform argument about "finite" has relevance. \$\endgroup\$ Apr 12, 2019 at 21:20
  • \$\begingroup\$ I'm not clear why phasors should be involved in this question at all. This is a time domain representation of the signal, not a phasor representation. (And if there is a way to represent signals with multiple frequency components as phasors, I was never taught it) \$\endgroup\$
    – The Photon
    Apr 12, 2019 at 22:42
  • \$\begingroup\$ It's the DC component of the Fourier series expansion of x(t), which is zero. Phasors are not relevant. \$\endgroup\$
    – Chu
    Apr 12, 2019 at 23:54
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    \$\begingroup\$ Integrate the function between 0 and \$2\pi /\omega_0\$. This gives zero, hence DC component is zero. \$\endgroup\$
    – Chu
    Apr 13, 2019 at 12:00

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