Power spectrum

nastia

1. The problem statement, all variables and given/known data
I am analyzing power spectrum of the series obtained using different approaches. I have 100 points series. First method is obtaining power spectrum by taking squared FT of series and divided by the period. Second method is taking IFT from ACVF of the series. In both cases, in terms of frequency, spectrums are the same, but the amplitudes are different, amplitudes are significantly higher for the first case (about 1000 times).
Also, as an additional question to that, I padded with 100 zeroes the original series in order to get the series 200 points long and the power spectrum is again the same, but with different amplitude


2. Relevant equations



3. The attempt at a solution
I know, that in first case we take FT out of series with length 100 points, in the second and third cases the length of series 200 points. And it has something to do with frequency scaling. But how exactly it is related and why? I can't seem to find the answer.