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High-Pass Filtering and the Nyquist Frequency

July 25, 2017 Andrew Jahn
Illustration of how sampling rate can generate a different waveform. Black: Original waveform; Red dots: Sampling of the original waveform. When a line (red) is interpolated among the sampled points of the original waveform, a waveform of a differen…

Illustration of how sampling rate can generate a different waveform. Black: Original waveform; Red dots: Sampling of the original waveform. When a line (red) is interpolated among the sampled points of the original waveform, a waveform of a different frequency is generated.

Note: See Wiktor's comment below for a comparison of frequency cutoffs across AFNI, FSL, and SPM.

Yesterday I had the following conversation on one of my YouTube videos:

J: Thanks for the video. My question pertains the cut-off filtering frequency: When you apply a HP [High-Pass] filter in fMRI (typically it's .008 Hz), is this at the Nyquist frequency? Meaning that .008/2 is the actual frequency we are removing? Thank you.

Andy: Hi J,
I believe the Nyquist frequency is something different; i.e., the highest frequency that we're interested in (and therefore which we need to sample at a rate at least twice as high to recover the full signal). 0.008 is simply a standard cutoff to remove low frequency effects such as breathing, heart rate, and slow drifts in the scanner signal. Best, -Andy

J: I meant in the sense that if you wish to remove slow drift of a certain frequency (i.e., .01) one should remove at least double the .01 frequency to make sure the .01 slow drift is removed. Is this correct?

Andy: I think the filter removes the frequency that you specify; there's nothing in the documentation that leads me to believe that the specified cutoff is the frequency that it uses to identify other frequencies. (If it were, then yes, you would need to use a higher frequency cutoff.) You could test this empirically by combining two frequencies into a single waveform, then specifying a filter on one of the frequencies and seeing if it's deleted from the waveform. -Andy


I don't pay much attention to how I filter my data; usually I just accept whatever the defaults are for my software package. However, J brings up an interesting point: Are we actually removing the specified cutoff frequency, or is the cutoff frequency a sampling rate that we use to detect and remove other frequencies above (or below) that frequency? My opinion is that it's the former - frequencies up to and including the cutoff are filtered out of the data. If there is anyone with a better understanding of filters who can speak to this, I'd love to hear what they have to say.

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