# A Comparison Between Power Line Noise Level Fie...

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## A comparison between power line noise level fie...

Powerline noise is characterized by a chronic sinusoidal 50/60 Hz element which can be observed in raw recordings of biomedical data. The sinusoidal component is usually a result of the use of devices that employ alternating current as a source of power. Alternating current has been used in the design of biomedical devices because it has been demonstrated to possess the quality of being relatively stable, especially over long distances, as opposed to direct current. In some cases, powerline noise is removed by low-pass filters with cut-off frequencies below 50/60 Hz. Although this approach solves the problem of extinguishing powerline noise and has its applications, it is challenging to implement on some forms of biomedical data because of the importance of broadband signals. These include, but are not limited to, electroencephalogram signals and extracellular neural recordings. For some purposes, such as the extraction of action potentials from broadband neural tissue recordings, the pitfall of obtaining noisy recordings can be potentially avoided by employing a high-pass filter with a cut-off frequency above 250 Hz (Oweiss, 2010). Band-stop filters have been used to attenuate powerline noise to inconspicuous levels. Nevertheless, due to the instability of biomedical signals, band-stop filters sometimes fail in reducing noise with 50/60 Hz center frequency and thus may have to rely on correction methods (Ferdjallah & Barr, 1994; Ferdjallah & Barr, 1990; Hamilton, 1996). Although band-stop Butterworth filters obtain better powerline noise removal results with increasing filter orders, their step responses are usually characterized by ringing and overshoot. In the same vein, depending on the filter order, the rate of attenuation can be low. Although the rate of attenuation in Chebyshev filters are higher than Butterworth filters, their step responses are marked by higher levels of ringing. Bessel filters do have significantly lower levels of ringing and overshoot, however their slower attenuation rates make it possible for powerline noise to leak into the signal.

Many signal processing algorithms have been proposed to solve the issue of powerline noise interference. Some of the notable procedures involve blind source separation. Empirical mode decomposition has been proposed as a potent approach for eliminating powerline noise (Blanco-Velasco, Weng & Barner, 2008; De-xiang, Xiao-pei & Xiao-jing, 2008; Li et al., 2012; Naji, Firoozabadi & Kahrizi, 2011; Nimunkar & Tompkins, 2007; Zhang & Zhou, 2013; Chang, 2010; Chang & Liu, 2011; Zivanovic & GonzÃ¡lez-Izal, 2013). Independent component analysis has also been explored by many researchers as a potential approach for removing powerline noise (Xue et al., 2006; Iriarte et al., 2003; Castellanos & Makarov, 2006; Kuzilek et al., 2014; Chawla, 2011; Kuzilek, Kremen & Lhotska, 2014). A combination of empirical mode decomposition and independent component analysis has also been looked into as a potential approach for eliminating powerline noise (Mariyappa et al., 2015).

This paper proposes an algorithm which uses blind source separation and wavelet analysis to detect and remove powerline noise in biomedical signals. The approach is subsequently compared with a band-stop 4th order Butterworth filter, empirical mode decomposition, independent component analysis and a combination of empirical mode decomposition with independent component analysis. This unsupervised machine learning approach is fully automatable and void of the need to apply adaptive self-correction mechanisms.

(A) On the left is the original snippet of an ECG signal corrupted with powerline noise (green). Seven IMFs obtained via EEMD have been shown on the right. A constriction of the windows of IMF 4 and IMF 5 reveals that a chronic sinusoidal modulation exists within them. (B) The frequency spectra of the IMFs shown in A have been plotted. From this, it is plausible that the modulations seen in IMFs 4 and 5 are powerline noise at 60 Hz.

where x represents the expected frequency of the powerline noise (50 Hz or 60 Hz). In essence, the ui(t) that satisfies Eq. (8) is the most appropriate approximation of powerline noise. The motivation behind this approach has been explicated in Powerline noise recognition of the Appendix.

(A) The blue, green and red signals are the recovered, original and noised signals respectively. (B) The blue, green and red signals are the power spectrum for the recovered, original and noised signals respectively. (C) The grey trace is the AC noise extracted and the black trace is the Manhattan distance between the original signal and the recovered signal. (D) The upper image is the pseudo-convolution of the selected independent component for the first 200 ms of the data. The lower represents that of the final 50 ms. Note that they both peak at circa 60 Hz.

The off-diagonal elements are scatterplots of the signal amplitudes and the diagonal elements are Fourier transformations of the signals. For each of the off-diagonal elements, the abscissa is the label of nearest diagonal element above or below and the ordinate is the label of the nearest diagonal element on its side. For example, on the first row and second column the amplitudes of neural signals without noise is compared with the same version adulterated with powerline noise using a scatterplot. On the first row and third column, neural signals without noise is compared with a reconstructed version using a 4th order Butterworth filter. On the first row and fourth column, the results obtained via the proposed approach is compared with the original neural signals. This convention is used throughout the figure.

However, due to the loss of amplitude information after ICA this inversion does not result in an optimal model for denoising. In order to recover the amplitude of the powerline noise, the amplitude of the convolution between the mentioned wavelet at 50/60 Hz center frequency and the denoising component dcomp(t) is projected unto that of the original signal y(t). This projection is accomplished via least squares. An initial powerline noise amplitude prediction is done by normalizing the root-mean-square of the wavelet transformation of the extracted component at xHz to that of the wavelet transformation of the original signal, y(t), at xHz.

The powerline noise with the appropriate amplitude is obtained by a regression approach which learns and estimates the parameter Î» which minimizes the sum of the square distances between the signal and putative powerline noise:

The best technique to reduce unbalanced cable noise is to be careful with cable placement. A single perpendicular crossing of power and audio cables is much better than a parallel run. If parallel can't be avoided, leave as much space as possible between audio and power cables.

Original MEG signal and MEG signal with added simulated abrupt on- and offsets of line noise interference. A) Example time series of the line-noise-free original MEG raw data and the respective power spectral density (PSD, Log scale). The frequencies of interest (FOI) around line noise interference are shown in a magnified view on the right. B) Time series of the simulated line noise with abrupt on- and offsets added to the original noise free MEG signal are shown and the respective power spectrum, with a magnified view of the FOI (right panel). C) PSD of the signal after the application of spectrum interpolation (blue) D) a notch filter (Butterworth, red) and E) the regression based method CleanLine (light blue) reveal that spectrum interpolation and the notch filter attenuate power line noise to a sufficient extent, while CleanLine does not. All magnified views of the FOI are shown on the right side.

MEG signal with added simulated fluctuating line noise interference. A) Example time series (20 s length) of the simulated amplitude modulated line noise signal (amplitude modulation in a lighter blue) mixed with the original MEG signal (mixed signal in dark blue) and the respective power spectrum (PSD, Log scale, right panel). The magnified view of the FOI is shown on the right. B) PSD (Log scale) after the application of spectrum interpolation (blue), C) the notch filter (red) and D) after the application of CleanLine (light blue) reveal that spectrum interpolation and notch filtering attenuate line noise interference, while CleanLine is not able to attenuate it to a sufficient extent. All magnified views of the FOI are shown on the right.

MEG signal with added simulated fluctuating line noise interference. A) The ERFs (here the MLR) after the application of spectrum interpolation (blue, first panel), the notch filter (red, second panel), the DFT filter (green, third panel), CleanLine (light blue, fourth panel) and for the original noise-free MEG signal (black, all panels) reveal residual line noise interference after the application of CleanLine. B) An example trial reveals also substantial residual line noise after DFT filtering (in addition to CleanLine), only visible on a single trial level. C) The single trial difference curves (relative to the original MEG signal) for the same trial show the signal distortions in the time domain more clearly. D) The boxplot of the nRMSE (arbitrary units) relative to the original data reveals that over all single trials of the MLR component, CleanLine shows the largest signal distortion followed by the DFT filter. Spectrum interpolation shows a slightly better performance than the notch filter (Butterworth). The magnified view of the boxplot is shown on the right.

Example segment for EEG sleep data with massive power line noise due to acquisition in unshielded settings. A) The power spectra (PSD, Log scale) of the original EEG signal (dark blue) and B) after the application of spectrum interpolation (blue), C) a notch filter (red) and D) the regression based method CleanLine (light blue) reveal that spectrum interpolation and the notch filter attenuate power line noise to a sufficient extent. CleanLine does not attenuate the line noise interference sufficiently while even adding artificial components in the frequency domain. All magnified views of the FOI are shown on the right side. 041b061a72