# AFNI Message Board

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 May 28, 2022 07:11AM Admin Registered: 10 years ago Posts: 2,114
Philipp-

For your power-slope estimate, you would only use the positive half of the spectrum, anyways, and likely not include the k=0 (baseline) wave number. This is due to the nature of the Fourier spectrum coefficients for real input time series: they have a mirror symmetry around 0. That is why most FFT-based outputs are just comprised of essentially the k=0...N/2-1 wavenumbers, and not k=-N/2....N/2-1, or k=0...N-1. In the latter two cases, you would be fitting a half-downward set of points and then equal-but-oppose half upward set of points---that would give you zero total slope. I believe you would likely want to *not* include any k=0 baseline value in your estimation, because that is just the average value---it doesn't seem appropriate to include in most power spectrum slope estimations.

Also, since we are talking about slope, you should get the exact same slope with only a factor of 2 difference when using either sps.periodogram() or 3dPeriodogram with:
+ the same tapering (e.g., none) and
+ same detrending (e.g., linear) and
+ both ignoring the k=0 value (not output by 3dPeriodogram, and de-selectable in sps.periodogram() output with index selectors: array_freq[1:])

The issue of how much detrending changes the spectral estimate or not depends strongly on what your data looks like. If you are using residuals and/or processed resting state time series, then I would expect detrending to do very little to change the power spectrum.

--pt
Subject Author Posted

#### 3dPeriodogram and 1dFFT - How exactly is the power computed?

Philipp May 27, 2022 10:36AM

#### Re: 3dPeriodogram and 1dFFT - How exactly is the power computed?

ptaylor May 27, 2022 03:28PM

#### Re: 3dPeriodogram and 1dFFT - How exactly is the power computed?

Philipp May 27, 2022 03:58PM

#### Re: 3dPeriodogram and 1dFFT - How exactly is the power computed?

ptaylor May 27, 2022 08:52PM

#### Re: 3dPeriodogram and 1dFFT - How exactly is the power computed?

Philipp May 28, 2022 03:36AM

#### Re: 3dPeriodogram and 1dFFT - How exactly is the power computed?

ptaylor May 28, 2022 07:11AM

#### Re: 3dPeriodogram and 1dFFT - How exactly is the power computed?

Philipp May 28, 2022 11:03AM

#### Re: 3dPeriodogram and 1dFFT - How exactly is the power computed?

ptaylor May 31, 2022 05:41PM

#### Re: 3dPeriodogram and 1dFFT - How exactly is the power computed?

Philipp June 01, 2022 12:24AM

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