User talk:2A01:E35:2F57:DB30:8566:8EE3:C7E5:2D35

Hi,

You wrote:

These N/2 coefficients represent the frequencies 0 to fs/2 (Nyquist) and two consecutive coefficients are spaced apart by fs/N Hz.

It seems to me there is an off-by-one problem in this statement:

- there are N/2 coefficient, let me number them 0 to N/2-1, and use the letter i for the coefficient index.

- there are N/2 coefficient, there are N/2 frequencies those coefficients correspond to. I'll note them f(i), where i goes from 0 to N/2 - 1.

- the first coefficient, where i = 0, represents the frequency 0 Hz: f(i=0) = 0 Hz

- the coefficients are spaced apart by fs/N Hz. so f(i=1) = f(i=0) + fs/N, ..., f(i+1) = f(i) + fs/N

- by induction: f(i) = i * fs/N

- the last possible value for i is N/2 - 1, so the last value for f(i) is f(N/2 - 1) = (N/2 - 1) * fs/N = fs/2 - fs/N

so the N/2 coefficients CANNOT represent the frequencies 0 to fs/2, but only 0 to fs/2 - fs/N

OR

they may also represent the frequencies fs/N to fs/2

OR

they may also represent the frequencies 0 to fs/2, but then two consecutive coefficients are spaced apart by (fs/2) / (N/2 - 1) Hz, not (fs/2) / (N/2) Hz.

OR there are actually one more coefficient in the output, to reach N/2 + 1

I am not competent enough to understand which of these cases is correct.

Thanks Jdmuys (talk) 12:38, 16 March 2016 (UTC)