Python High Pass Filter

Question

I implemented an high pass filter in python using this code:

from scipy.signal import butter, filtfilt
import numpy as np

def butter_highpass(cutoff, fs, or         


        

Answer 1

Since my reputation is low I am unable to comment on your question - "What is the relationship between cutoff and filter order?" This is not an answer to your original question.

For an FIR filter, for a given cutoff frequency, the slope of the impulse response plot (|H(f)| vs f) is steeper for a higher order filter. So, to achieve higher attenuation for the undesired frequency range, you increase the filter order. But what happens when the filter order is so high that the impulse response is an ideal box function? You will see an inter-symbol interference (ISI in digital communications) like effect. The intensity of this effect increases when the ratio of cutoff frequency to the sampling frequency gets smaller (think of the relation between the width of box function in frequency domain and the width of the main lobe of the sinc function).

I first observed this when I tried to implement a very narrow band low-pass IIR filter on a TI DSP microcontroller. The TI library, implemented the filter as a cascaded bi-quad structure to handle the well known truncation effects. This still did not solve the problem because the problem is not due to truncation alone. The way I solved this problem was to use an anti-aliasing filter followed by down-sampling the input signal, followed my desired low-pass IIR filter.

I understand that you are implementing a HPF, which is an LPF translated in frequency domain. Hope this answers some of your questions. Let me know if down-sampling works for you.