Optimizing signal smoothing using HERS algorithm and time fractional diffusion equation

Abstract

Signal processing is often affected by various sources of noise that can distort or modify the signals. Removing these noises from the original signal is a crucial step in signal processing, and researchers have proposed several approaches to address this issue. However, achieving an optimized solution remains a challenge. In this study, we introduce a novel approach called the Hybrid Ebola-based Reptile Search (HERS) model based on Time Fractional Diffusion Equation (TFDE). The TFDE is a conventional diffusion equation used for preserving the peak smoothness of spectra signals. In our proposed technique, we consider the processing spectrum of the signal as the reference signal, which serves as the design for the diffusion equation. By applying the diffusion function, we achieve signal peak preservation and smoothing, referred to as the filtering of diffusion. One potential challenge with the time fractional order diffusion equation is its susceptibility to variations in the time step size. To address this, we employ the HERS algorithm to select an optimal time step size that enables efficient signal smoothing. To validate the effectiveness of the proposed technique, we conduct simulations and compare the results with conventional techniques such as the wavelet model, Savitzky-Golay, and regularization techniques. The performance evaluation confirms the superiority of our proposed HERS-TFDE approach in noise removal and signal smoothing. This research aims to contribute to the development of an optimized solution for noise removal in signal processing, leveraging the Hybrid Ebola Reptile Search algorithm and TFDE. The findings have the potential to enhance various signal-processing applications where noise reduction is critical.