这个巴特沃斯滤波器有什么问题

Question

i am trying to remove the base wander noise from ecg signal, base wander noise is low-frequency artefact of around 0.5Hz, for that i tried a digital butterworth highpass filter:

code of filter

frequency response

the ecg signal used is the record 100 from mit bih arrhythmia data base ( record sampled at 360 samples per second), first i read the record using wfdb package and then i applied the filter on it, but the result looks something like this:

code of filtering the signal

the result

the result looks kinda off. i want to know where is the problem?

Answer 1

I think the problem is that your filter does not know the time step of your dataset, particularly in your call to bilinear where you explicitly give a sampling frequency of 1.

To demonstrate, let's start with a pretty strong signal:

import numpy as np
import matplotlib.pyplot as plt

N = 1_000
T = 4.
tau = 0.25 # period of signal, frequency of 4 Hz
f = 1 / tau # frequency
omega = 2 * np.pi * f # angular frequency

t, dt = np.linspace(0, T, N, endpoint = False, retstep = True)
fs = 1 / dt # sampling frequency in Hz

noise = np.random.random(N)
sig = np.sin(t * omega)
x = 0.2 * noise + sig

plt.plot(t, x)
plt.xlabel('time')

Now let's start with the filter you've developed. My wave is higher frequency than your cutoff so it should be caught, but it isn't.

from scipy import signal
b, a = signal.butter(4, 0.5, 'high', analog = True, output = 'ba')
z, p = signal.bilinear(b, a, 1.)

x_filt = signal.lfilter(z, p, x)
plt.figure()
plt.plot(t, x)
plt.plot(t, x_filt)
plt.xlabel('time')

Note that in your call to bilinear you are setting a sampling frequency of 1. Let's instead use our sampling frequency (defined above as fs ).

z, p = signal.bilinear(b, a, fs)
x_filt = signal.lfilter(z, p, x)
plt.figure()
plt.plot(t, x)
plt.plot(t, x_filt)
plt.xlabel('time')

As a last note, you may sometimes observe a phase shift with Butterorth filters. Again, I am not an expert and have only ever used them in cases where I was not worried about the phase, but see here for suggestion on using a different type of filter if this is an issue. The comments here also suggest using a different filter for this reason.