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I totally can't understand why f = k/K. What does k, K means, respectively?. I really want to know what they actually indicate in real world. Or, please give me an example. I spent 2 days night but could't catch the DFT.

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The DFT is, essentially, a sampled DTFT where the number of samples is \$K\$ and, thus, the spectrum is sampled at frequencies with spacing proportional to \$\frac{1}{K}\$ or, as in the image below, \$\frac{1}{N}\$

enter image description here

Note the \$k\$ indexes the samples in frequency just as \$n\$ indexes the samples in time.

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  • \$\begingroup\$ You said that "as in the image below, 1/N" And I have read many books, the authors take N samples with DTFT to get DFT. Why N? I think N is simply the sampling rate in time domain, right. In frequency domain, can we choose other sampling rate to get DFT? \$\endgroup\$ – Dongguo Nov 29 '15 at 13:20

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