In recent years, kernel methods have provided an important alternative solution, as they offer a simple way of expanding linear algorithms to cover the non-linear mode as well. In this paper, we propose a novel recursive kernel approach allowing to identify the finite impulse response (FIR) in non-linear systems, with binary value output observations. This approach employs a kernel function to perform implicit data mapping. The transformation is performed by changing the basis of the data In a high-dimensional feature space in which the relations between the different variables become linearized. To assess the performance of the proposed approach, we have compared it with two other algorithms, such as proportionate normalized least-meansquare (PNLMS) and improved PNLMS (IPNLMS). For this purpose, we used three measurable frequency-selective fading radio channels, known as the broadband radio access Network (BRAN C, BRAN D, and BRAN E), which are standardized by the European Telecommunications Standards Institute (ETSI), and one theoretical frequency selective channel, known as the Macchi’s channel. Simulation results show that the proposed algorithm offers better results, even in high noise environments, and generates a lower mean square error (MSE) compared with PNLMS and IPNLMS.
The acquisition of ECG signals offers physicians and specialists a very important tool in the diagnosis of cardiovascular diseases. However, very often these signals are affected by noise from various sources, including noise generated by movement during physical activity. This type of noise is known as Motion Artifact (MA) which changes the waveform of the signal, leading to erroneous readings. The elimination of this noise is performed by different filtering techniques, where the adaptive filtering using the LMS (least mean squares) algorithm stands out. The objective of this article is to determine which algorithms best deal with motion artifacts, taking into account the use of instruments or wearable equipment, in different conditions of physical activity. A comparison between different algorithms derived from LMS (NLMS, PNLMS and IPNLM) used in adaptive filtering is carried out using indicators such as: Pearson's Correlation Coefficient, Signal to Noise Ratio (SNR) and Mean Squared Error (MSE) as metrics to evaluate them. For this purpose, the mHealth database was used, which contains ECG signals taken during moderate to medium intensity physical activities. The results show that filtering by IPNLMS as well as PNLMS offers an improvement both visually and in terms of SNR, Pearson, and MSE indicators.
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