Schrödinger Equation Based ECG Signal Denoising

Abstract

It is a well-established fact that denoised ECG signals increase diagnostic accuracy. Motivated by this fact, by exploiting the theory of Fourier transform with a certain initial condition, a Gaussian type wavelet solution to the Schrödinger equation is obtained. Further, a new wavelet in the interval [0,1] specifically designed to denoise ECG signals has been proposed. Schrödinger equation plays a vital role in quantum mechanics as well as in signal denoising. We have shown that the proposed new wavelet satisfies the admissibility condition, forms proper mother wavelet and is orthonormal. The aforesaid solution to the Schrödinger equation, along with the new wavelet, is applied respectively to denoise ECG signals from MIT-BIH arrhythmia database as well as to denoise ECG signals collected by us. It is found that our results outperform state of the art methods for both types of signals. It was also observed that the denoised ECG signals obtained by the Schrödinger equation along with the new wavelet show superior results in comparison to the denoised ECG signals obtained from the application of the Schrödinger equation only. © 2021 The Physical Society of the Republic of China (Taiwan)