I came across this question and I've been pretty confused if its a trick question or I'm just wrong. Having a signal x[n] with 6 samples, it's DFT has values (6,3+j,0,0,0,3-j), what is the DC componente Value?

Shouldn't it always be 0? Or am I thinking wrongly?


You're thinking wrongly.

The DC bin is the name of the zeroth bin.

Assuming the indexing of your DFT spectrum is 0 to N-1, then the DC value here is six. What is true is that for a real valued signal, the DC bin will always be real valued (usually being the sum or average, depending on the normalization factor), so it's imaginary component will be zero.

  • $\begingroup$ But the only options to answer the question are a) 0 b)1 or c)2. Is it wrong then? $\endgroup$ – HelpMeBro Sep 17 '20 at 16:52
  • $\begingroup$ @HelpMeBro No, that means they are using an unnormalized DFT, and the average value of the signal is 6/6 = 1, and I was wrong in interpreting DC component as DC bin value. Sorry. $\endgroup$ – Cedron Dawg Sep 17 '20 at 16:58

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