A New DDE Smoothing Filter for ECG Signal Denoising

Signal filtering is a challenging problem arising in many applications such as Electrocardiogram (ECG) signal processing. Among the techniques that are used for signal denoising, quadratic variation (QV) regularization and smoothness priors have received significant attention during the past. In this paper, we propose a new approach to smoothing filter design, which is based on a delay differential equation (DDE). The proposed method is generic and can be used for smoothing filter design with different frequency responses. As an example, a specific DDE is used in the regularization term of the optimization algorithm. It depends on the regularization parameter and the delay, where the former is related to the cutoff frequency and the latter is set by user. The DDE smoothing filter was analyzed in the frequency domain. It was shown that smoothness priors and QV regularization are special cases of the DDE smoothing filter when the delay tends to infinity. As an application, the proposed smoothing filter was used for ECG signal denoising over data from the PhysioNet PTB database. The results confirm that the proposed smoothing filter outperforms QV regularization for ECG baseline wander removal.