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I have been applying ensemble averaging (adding signals of different trials to obtain one signal) to improve Signal to noise ratio in my data. I have achieved good results in terms of classification accuracy when I apply the data to a classifier.

However what if the data for different trials are out of phase w.r.t each other , then they cancel out and we lose data. Hence are there any methods like averaging in the frequency domain or time alignment which can be used to overcome such a situation ?

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  • $\begingroup$ Votes and best answer validation are required for this question $\endgroup$ – Laurent Duval Jul 28 at 12:07
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Amplitude (of the signal and the noise realizations) is an important factor too when averaging. I suggest to check S. Palit, Signal extraction from multiple noisy sensors. Multiple trials could be interpreted as different sensors.

Without much information about your data properties, many methods could improve ensemble averaging with synchronized data: principal component analysis (PCA), independent component analysis (ICA) and generally blind source separation methods. If the signal is piece-wise regular, you can think about combining wavelets and PCA or ICA. Recently, low-rank methods have proved useful.

As the Fourier transform is linear, frequency averaging won't help much, unless you want reduced noise in the magnitude spectrum domain.

Time-alignment can help, you may have a look at concepts like "similarity matching for time-series". DUST: a generalized notion of similarity between uncertain time series, by Sarangi and Murthy, could be a starting point.

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  • $\begingroup$ If Averaging technique is applied in magnitude spectrum domain, and obtain the averaged signal in time domain by taking inverse Fourier transform, we will lose phase information in frequency domain. Can this signal be then used for feature extraction? Also will it improve SNR? $\endgroup$ – Anoop Bhushan Jun 30 '16 at 11:35
  • $\begingroup$ There is a huge risk (depending on the lags) if you go back to the time domain that the "averaged" signal is disturbed, indeed. Yet some features can be useful in the frequency domain for classification. If you compute a frequency SNR, magnitude averaging can reduce it. $\endgroup$ – Laurent Duval Jun 30 '16 at 12:21

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