Signal Averaging Noise Reduction under Dynamic Time Warping

Signal averaging (SA) is a procedure used to increase signal-to-noise ratio (SNR), applied in various fields, such as biomedical engineering or nanotechnology. Assuming that the noise is random and of zero mean, its average across multiple signals tends to zero. As a result, every additional measurement in the average should raise the SNR. In order for the SA to work, however, averaged signals should be in-phase. Otherwise, obtained average will not properly represent the sample signals, since their characteristic fragments will be deformed or repeated. Dynamic Time Warping (DTW) is an algorithm which can solve synchronicity problems. Using DTW, however, causes changes in the character of noise; it is no longer completely random, since its values get warped along with the desired signal. Violating the randomness of noise requirement results in weakened capability of the SA to increase the SNR. In this work, two main questions were answered: for which level of the input signals' SNR, DTW average works well, and how many sample signals should be used in order to improve SNR. Results were obtained using a modeled electrocardiogram, which has been distorted by randomly warping it and adding white noise. To average signals under the DTW, Nonlinear Alignment and Averaging Filter (NLAAF) algorithm was used.