If you have access to the Signal Processing Toolbox, then check out the Savitzky-Golay filter, namely the function sgolay
. There s an accompanying demo, just run sgolaydemo
.
The following is an example to show the various ways you can apply filtering and de-noising to a signal. Note some of these functions requires certain toolboxes to be present:
% load ecg: simulate noisy ECG
Fs=500;
x = repmat(ecg(Fs), 1, 8);
x = x + randn(1,length(x)).*0.18;
% plot noisy signal
figure
subplot(911), plot(x), set(gca, YLim , [-1 1], xtick ,[])
title( noisy )
% sgolay filter
frame = 15;
degree = 0;
y = sgolayfilt(x, degree, frame);
subplot(912), plot(y), set(gca, YLim , [-1 1], xtick ,[])
title( sgolayfilt )
% smooth
window = 30;
%y = smooth(x, window, moving );
%y = smooth(x, window/length(x), sgolay , 2);
y = smooth(x, window/length(x), rloess );
subplot(913), plot(y), set(gca, YLim , [-1 1], xtick ,[])
title( smooth )
% moving average filter
window = 15;
h = ones(window,1)/window;
y = filter(h, 1, x);
subplot(914), plot(y), set(gca, YLim , [-1 1], xtick ,[])
title( moving average )
% moving weighted window
window = 7;
h = gausswin(2*window+1)./window;
y = zeros(size(x));
for i=1:length(x)
for j=-window:window;
if j>-i && j<(length(x)-i+1)
%y(i) = y(i) + x(i+j) * (1-(j/window)^2)/window;
y(i) = y(i) + x(i+j) * h(j+window+1);
end
end
end
subplot(915), plot( y ), set(gca, YLim , [-1 1], xtick ,[])
title( weighted window )
% gaussian
window = 7;
h = normpdf( -window:window, 0, fix((2*window+1)/6) );
y = filter(h, 1, x);
subplot(916), plot( y ), set(gca, YLim , [-1 1], xtick ,[])
title( gaussian )
% median filter
window = 15;
y = medfilt1(x, window);
subplot(917), plot(y), set(gca, YLim , [-1 1], xtick ,[])
title( median )
% filter
order = 15;
h = fir1(order, 0.1, rectwin(order+1));
y = filter(h, 1, x);
subplot(918), plot( y ), set(gca, YLim , [-1 1], xtick ,[])
title( fir1 )
% lowpass Butterworth filter
fNorm = 25 / (Fs/2); % normalized cutoff frequency
[b,a] = butter(10, fNorm, low ); % 10th order filter
y = filtfilt(b, a, x);
subplot(919), plot(y), set(gca, YLim , [-1 1])
title( butterworth )