I filtered my signal with low pass filter butterworth forth order with cutoff frequency of 50 hz. However when I compare the filtered signal with original one in frequency domain, it seems that the cut off frequency started from 25 hz instead of 50.

The comparison of the original with filtered signal in frequency domain

this is my matlab code and my data from here

%sampling frequency is 146

[b,aa] = butter(10, 50/146,'low');
data_filtered = filtfilt (b,aa,data);

did i make some mistake ?


1 Answer 1


did i make some mistake ?

Yes. The cutoff frequency is specified relative to the Nyquist Frequency and not the sample rate

From the documentation

Wn must be 0.0 < Wn < 1.0, with 1.0 corresponding to half the sample rate.

Also: you design a 10th order butterworth and filtfilt() doubles that again to 20. That will give you significant domain "ringing".

  • $\begingroup$ From dsp.stackexchange.com/questions/31671/…: “One final note for the sake of clarification. The normalized cutoff you've used is 0.5 pi radians/sample. This means the filter's cutoff frequency in Hertz will be 0.5 * 50 Hz -> 25 Hz.“ $\endgroup$ Commented Jul 26, 2020 at 17:00

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