Fractional Calculus in Signal Processing: The Use of Fractional Calculus in Signal Processing Applications, Such as Image Denoising, Filtering, and Time Series Analysis

Abstract

Fractional calculus has transformed signal processing by providing a more flexible representation of complex signals. This article explores its applications in image denoising, filtering, and time series analysis, highlighting its potential to revolutionize signal processing methodologies. Fractional calculus, dealing with derivatives and integrals of non-integer orders, captures long-memory and self-similar properties in real-world signals. Image denoising benefits from fractional derivatives and integrals, preserving essential details while removing noise. Filtering signals with fractional calculus allows for dynamic adaptability to changing signal characteristics. Time series analysis benefits from more accurate modelling, enhancing predictive capabilities. The future scope of fractional calculus in signal processing promises further advancements, making it a valuable tool for researchers and practitioners seeking to analyze complex signals across various domains.