# How to calculate DFT of signal which occurs from 3 to 8?

How can I calculate discrete fourier transform of this signal?

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.

So what would be N and signal here?

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


or

N = 9 and signal = {0,0,0,3,4,5,6,7,8}

• 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. Commented May 24, 2022 at 22:53
• @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}?
– hana
Commented May 24, 2022 at 22:57
• 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 $0 \leq n \leq 5$ Commented May 24, 2022 at 23:36
• 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 $N=11$. Commented May 25, 2022 at 9:37