The cutoff frequency is generally defined as the frequency where the signal is down by -3 dB (relative to the passband). So at the cutoff frequency some of the signal is removed (half power) but signal is still present.

If you are not using a brickwall filter (very high order), then you will see the amount of signal removed gradually increasing as frequency decreases.

On Mon, Sep 25, 2017 at 9:04 AM Wiktor Olszowy <[log in to unmask]> wrote:

Dear SPM community,

Recently I have analysed the code of the high-pass filter in SPM (spm_filter.m). The order of the filter is determined via:

n = fix(2*(k*K(s).RT)/K(s).HParam + 1);

where fix is the matlab's function that rounds towards zero, k is the number of time points/volumes, whereas K(s).RT is the repetition time. My understanding is that if e.g. number_of_volumes*TR=256 seconds and the cutoff has not been changed (from 128s), then the signal at 1/128 Hz will be removed (and at lower frequencies), as 256 is a multiple of 128 and there is no rounding in the above formula. However, the SPM manual says: "The default high-pass filter cutoff is 128 seconds. Slow signal drifts with a period longer than this will be removed.". Do I misunderstand sth or is there a small inaccuracy in the manual? For the default of 128 it does not make a large difference, but when one is interested in making the cutoff paradigm-dependent, it makes a huge difference if the cutoff frequency is filtered out or not.

Best wishes,

Wiktor Olszowy