A New Approach based Delay Differential Equation to Smoothing Filter Design

Among the techniques that are used for signal denoising, smoothing filters have received significant attention during the past. However, these methods are particularly suited for polynomial signal smoothing. Therefore, their performance is significantly decreased for signals that cannot be well modelled with a polynomial function. To overcome this limitation, in this paper, we propose a new approach to smoothing filter design, which is based on the delay differential equation model. In this approach, we propose to substitute the derivative of the signal with a DDE model of the signal. As an example, a delay differential equation of moving average (MA) model is used as penalty term in the optimization problem. The results indicate that a better solution can be found by appropriate balancing a trade-off between the MA model of the signal and the minimum mean square error. The proposed MA smoothing filter is analyzed in frequency domain. It is shown that the proposed MA smoothing filter displays good properties within its pass-band and stop-band bands for small values of window length. As an application, the proposed MA smoothing filter was used for electrocardiogram (ECG) signal denoising. We tested the method over data from the PhysioNet PTB database. The results show that the proposed MA smoothing filter outperforms the original smoothness priors or QV regularization.