How to obtain noise

I am trying to to calculate Signal-to-noise ratio (SNR) values for an ECG signal. To estimate the SNR I need a "clean" signal and "noise" signal.

Let's say I use a filter to "clean" the signal. The filter outputs the filtered signal but not the noise signal. Is it posssible to obtain the noise that was filtered out as a signal?

I could be misunderstanding how filters work, but basically what I need is to obtain the noise signal too, not just the filtered signal.

Thank you.

[Mathieu NOE]

hello

yes you can make a clean signal out of the noisy signal (filters or wavelet denoising)

the noise is simply the difference (substration) of noisy signal minus clean signal

[ANDRES FELIX CHAVEZ]

Thank you for your reply.

Since noise is the subtraction of noisy signal - clean signal, I analyzed the signal heartbeat by heartbeat, subtracting a clean heartbeat from a noisy heartbeat.

Answer 1

[William Rose]

@ANDRES FELIX CHAVEZ,

I have attached a real EKG signal which I have on my computer. I don't recall where it came from, or what lead it was, nor do I recal details about the subject. It is rather strange, with no obvious P waves, and a peculiar S-T segment. Sampling rate = 1 kHz.

x=load('cm_ekg1.txt','-ascii');
fs=1000; %sampling rate (Hz)
fc=100;  %cutoff frequency (Hz)
[b,a]=butter(4,fc/(fs/2));
xfilt=filter(b,a,x);
noise=x-xfilt;
t=(1:length(x))/fs;  %time vector
figure; subplot(211), plot(t,x,'-r',t,xfilt,'-b'); 
legend('raw','filtered'); title('EKG'); grid on
subplot(212), plot(t,noise,'-k'); 
xlabel('Time (s)'); title('Noise'); grid on

The lower plot shows that the "noise", computed as the difference between the raw and filtered signal, is not random noise. The "noise" becomes large at every QRS complex, in a reproducible, non-random way.

Let's do it again, but this time, we wil use filtfilt() instead of filter(). filtfilt() has no phase lag or delay at any frequency.

xff=filtfilt(b,a,x);
noiseff=x-xff;
t=(1:length(x))/fs;  %time vector
figure; subplot(211), plot(t,x,'-r',t,xff,'-b'); 
legend('raw','filtfilt'); title('EKG'); grid on
subplot(212), plot(t,noiseff,'-k'); 
xlabel('Time (s)'); title('Noise'); grid on

This is a lot better: the spikes in the noise associated with the QRS complexes are a lot smaller now.

These examples illustrate that, if the filter introduces a delay, then the difference between the raw and filtered signal will be due to noise and to the delay.