How can I calculate discrete fourier transform of this signal?

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I'm confused as in the normal cases signal always start from 0 to N-1 but in this case it starts from 3 to 8 instead.

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So what would be N and signal here?

N = 6 and signal = {3,4,5,6,7,8}


N = 9 and signal = {0,0,0,3,4,5,6,7,8}
  • 4
    $\begingroup$ By convention, DFT is always stated as N-point DFT to indicate the number of samples included in the DFT frame as $n \in [0 , N-1]$. You must have been given this N to make the DFT computable. Otherwise, the best guess is to assume N = 9 in your case. $\endgroup$
    – Fat32
    Commented May 24, 2022 at 22:53
  • $\begingroup$ @Fat32 I see. N is not given in this exercise. So if N = 6 then the data would be {0, 0, 0, 3, 4, 5}? $\endgroup$
    – hana
    Commented May 24, 2022 at 22:57
  • 1
    $\begingroup$ yes, if N = 6 were given, then you would discard the rest of the input data (by assuming them as zero) out of the frame $ 0 \leq n \leq 5 $ $\endgroup$
    – Fat32
    Commented May 24, 2022 at 23:36
  • 1
    $\begingroup$ If the creator of this problem didn't specify $N$, then shame on that person. That means you have to guess what is the input sequence. (That is, are the leading and trailing zero-valued blue dots part of the input, or not?) My guess is that $N=11$. $\endgroup$ Commented May 25, 2022 at 9:37


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