Hi ,

I can propose a solution to this problem from the definition of Signal to Noise Ratio SNR = S/N.

You get the signal prior to any filtering but that I mean

So The Signal you get a first will the " Clean Signal + Noise (S+N)" then you do the suggested filtering to get the "Clean Signal Alone(S)" and from there you substract :

Noise = (S+N) - S => SNR = S/N

In doing Noise Removal ,you must be careful not to attenuate your signal or a part of its band which can impact on your result .There exists technique i.e Noise Removal using Reference Electrode for EMG in particular (Signal = Signal with Noise +/- K*Reference ) ,Check Literature on this,it may help.

You could use adaptive filter such as RLS to identify the system. Then proceed to estimate noise power and from there estimate signal to noise ratio.

Thanks Yves Matanga and Pui Ho Lam for your responses, but both methods present the same limitation:

For the use of the Reference Electrode, I don't know much, I will check that.

Hi Mahmoud,

Of course, you will be able to get the signal to noise ration.

The signal before filtering is the signal with the noise as I explained before (S+N) and the filtered signal is the true signal (S) and finally ,noise will just be signal before filtering (S+N) minus signal after filtering (S).

You may check this link for artifacts removal as well.

https://www.researchgate.net/publication/6629695_EMG_and_EOG_artifacts_in_brain_computer_interface_systems_A_survey

especially for the reference electrode I mentioned

Article EMG and EOG artifacts in brain computer interface systems: A survey

Yes, RLS without a reference signal can only suppress noise from outside the band of the narrow band signal. But even without a reference signal, it should produce good results.

With a reference noise signal, RLS would provide even better results than simply subtracting.

Hello,

Thank you, Yves, the reference was very informative, even if it did not answer my question (yet).

Pui Ho, I know that the RLS algorithm is effective for such application, but it can't help with my problem. I want to estimate the residual error in the filtered data too, not only the raw data.

Thanks everybody for your responses. I found adequate methods and I thought it may help to share it.

In the case of actual EEG data, the true morphology of the clean ERP is unknown. Hence, it is not possible to rigorously evaluate the efficacy of a denoising methods with the MSE or the SNR metrics. So I used two SNR estimators to quantify the performance of the methods.

You may check this link for more details about the two SNR estimators and the results they give:

http://ietdl.org/t/F1tsM