# Butterworth cutoff frequency normalization

The issue: I am trying to reproduce the step detection technique as described in this paper. You can see the proposed step detection in the image below. The first part of this technique is to use a 2nd order Butterworth digital high-pass filter with a sampling rate fs=50 Hz and cut off frequency fc=1000 Hz. Is this a valid cut off frequency (fc>>fs)?

The problem: I know that i have to normalize the cut-off frequency by fs/2. For example in python according to scipy.butter documentation i have:

fs = 50
fc = 1000  # Cut-off frequency of the filter
w = fc / (fs / 2) # Normalize the frequency
b, a = signal.butter(2, w, 'hp')


But this is not correct because w must be 0 to 1 where 1 is the Nyquist frequency.

• Probably a typo. They later filter the signal with a 5 Hz lowpass, so a high pass filter with $f_c=1000Hz$ makes no sense whatsoever. – Hilmar Jul 2 at 15:39