# calculation of f/ALFF

Dear AFNI experts.

I have a question related to the 3dRSFC function. f/ALFF is defined as the power within a low-frequency range (for example: 0.01-0.1 Hz) divided by the total power. How does the function calculate the total power used as the denominator to calculate fALFF?

I would like to know if the function internally uses the option fbot=0 and ftop=9999 to get the total power of the full spectrum or if it uses a different range to calculate the denominator.

Does the full spectrum frequency range vary depending on the dataset acquisition parameters (for example, depending on the sampling rate)?

Thank you very much in advance!

Best regards,
Marina

Hi, Marina-

Using 3dRFSC requires inputting a time series that has not been previously bandpassed, nor censored (so that there would be gaps in it).

A new LFF (low-frequency fluctuation) time series is calculated from the input one by standard Fourier-based bandpassing; typical ranges used for this (“fbot” - “ftop”) are ~0.01 - 0.1 Hz. ALFF is the sum of amplitudes in that time series; see the Appendix here for relevant formulae:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3621593/

The denominator in fALFF is the sum of amplitudes of the Fourier transform of the original time series, in a range from the first frequency above the “baseline” (= the first non-zero frequency) to the maximum frequency in the time series (what is typically called the Nyquist frequency in signal processing). The numerator of fALFF is the ALFF value.

The spectrum does depend on acquisition parameters:

• because the input time series is finite, the spectrum has values at discrete frequencies; the spacing of those frequencies is determined by the length of the time series (in terms of digital frequencies, the spacing is 2\pi/N, where N is the total number of time points; in terms of physical frequency, the spacing is 1/(NTR) Hz, where TR is the repetition time, i.e., the sampling rate of the FMRI time series). The highest unique frequency in the spectrum, called the Nyquist frequency, is equal to 1/(2TR) Hz.

–pt