## 1 Introduction
High-Q finite impulse response (FIR) comb filters benefit from a linear phase response but introduce a large group delay. The concept of averaging several differences between samples shifted in multiple PLI periods could gain a high-Q response at the cost of a large amount of data [16]. Adaptive tunable notch FIR filters could increase the performance when PLI frequency deviates [17]. A smart PLI filtering approach is the subtraction procedure [18,19], which accurately measures the PLI waveform in linear or isoelectric signal segments and subtracts thisestimation in non-linear segments. Its advantage for the rejection of all PLI harmonics has been extensively studied for ECG signals; however, it is not applicable to other biosignals without linear segments. The proper operation requires accurate detection of signal linearity, and the sampling rate should be a multiple of the PLI frequency. While this is not the common case, many additional calculations are needed [20]. Novel modifications of the subtraction procedure for high-sampled signals have been recently reported [21]. Adaptive filters are very popular for PLI filtering. They change their characteristics and adapt to the filtered noise [22; 23]. Such filters operate like a servo system with negative feedback, which minimizes a given error function while optimizing the filter coefficients and extracting the noise. Usually, these filters minimize the output signal power by minimizing the mean squared error (MSE), and such an approach of iteratively modifying the filter coefficients using the MSE is referred to as a least-mean-square (LMS) algorithm [24; 25; 26]. Various modifications of a recursive least-squares algorithm [27], block-based time-frequency domain adaptive filters [28], or cascaded multistage adaptive structures [29] present improved efficiency. Digital lock-in techniques for adaptive PLI extraction have been introduced in [30]. The lock-in techniques are based on a quadrature amplitude demodulation (QAD) used to estimate the in-phase and quadrature PLI components. As soon as the in-phase and quadrature components are found, the PLI is orthogonally synthesized as a sine wave, which is subtracted from the input signal. A QAD frequency estimation scheme could be used to control a notch filter for precise PLI suppression [31]. Frequency domain filtering of PLI is based on Fourier transforms [32; 33; 34]. The signal is converted from the time into the frequency domain by fast Fourier transform (FFT), and after rejection of noise spectral components it is restored back into the time domain by inverse FFT (IFFT). Such FFT/IFFT filtering takes up a lot of computing resources and is usually implemented in special digital signal processing (DSP) chips or field-programmable gate arrays (FPGA). Similar in complexity is the wavelet decomposition, which transforms the signal into the time-frequency wavelet domain by a set of coefficients and mother wavelets, defining frequency sub-bands. After zeroing wavelet detail coefficients in the noise sub-bands, the signal is reconstructed out of the wavelet domain [35; 36]. A common disadvantage of most PLI filters is their reduced efficiency when PLI frequency deviates from the nominal value. Under such conditions, the sampling rate is not a multiple of the PLI frequency, so the latter does not match the filter notch frequency. Other disadvantages are the introduced group delay and the increased complexity, which interferes with their real-time processing application. A recently developed and validated impedance balancing approach overcomes these problems [37]. It syncs to the actual PLI frequency by a dedicated software phase-locked loop (SPLL), which uses the common-mode voltage as a synchronizing reference [38; 39]. PLI is canceled by an automatic summation of the differential signal with a part of the common-mode signal in a mixed analog-digital concept.