如何在Matlab中设计1至20 Hz的零相位带通滤波器？

Question

I am using Matlab to filter ECG data. There is noise in the data and I have tried using a Butterfilter. The problem is that there a higher power butter filter, anything above 3 makes the data disappear.

I have looked through Matlab's Help guide on filter design but I am unclear and still confused on how to actually use it and implement it.

Goal: Filter ECG data with zero phase distortion, filter all outside 1 to 20 Hz

My code right now:

%takes in one channel of data from the dataMatrix, plots it, filters, and plots again in a new figure

channel = 150;
x = dataMatrix(:,channel);

plot(x)
rawTitle = sprintf('Raw Channel %d ', channel);
title(rawTitle)

figure
[b_pass a_pass] = butter(3, [1/1000 20/1000], 'bandpass');
plot(filtfilt(b_pass, a_pass, x))
channelTitle=sprintf('Filtered Channel %d ', channel);
title(channelTitle)

Answer 1

Designing the filter

Let's start with the basics of designing the Butterworth-filter in Matlab. Here, we can only define a filter using normalized frequencies. Therefore we need to know the sampling frequency fs to determine the normalized frequency fn like this: fn = f/fs . Then we need the order order and the two cutoff-frequencies fc1 and fc2 . The second argument of butter takes 'frequencies' from 0 to 1 where 1 corresponds to the Nyquist-rate which is the half of the sampling frequency fs . Therefore we have to divide fs by 2 in the second argument.

[b,a] = butter(order, [fc1,fc2]/(fs/2), 'bandpass');

Application

Now we can go into your code and apply the filter. Note that filtfilt is zero-phase and doubles the order of the original filter. We can take some sample data from here ( fs assumed to be 500Hz) and see if it works as expected.

% load sample data and assign it to x
load('ecg.mat');
fs = 500;
x = ecg;

% define to use OP's code
channel = 150;

% plot the raw data
figure
plot(x)
rawTitle = sprintf('Raw Channel %d ', channel);
title(rawTitle)

% design filter
[b_pass,a_pass] = butter(3,[1,20]/(fs/2), 'bandpass');

% filter data and plot it
figure
plot(filtfilt(b_pass, a_pass, x))
channelTitle=sprintf('Filtered Channel %d ', channel);
title(channelTitle)

This is the result: