Applications of Difference Equations in Enhancement of Digital Signal Processing and Reducing Signal Noise Ratio

Abstract

In digital signal processing (DSP), the enhancement of signal quality and the reduction of noise are paramount for accurate data interpretation and transmission. This paper investigates the use of difference equations in achieving these objectives. Through rigorous derivations, theorems, and lemmas, this paper demonstrates how difference equations can be effectively utilized to enhance digital signals and reduce signal-to-noise ratio (SNR). Control systems often need to handle perturbations, which are deviations in the system dynamics due to external disturbances or modeling inaccuracies. Perturbed difference equations provide a framework to analyze and design control systems that can maintain stability and performance despite these perturbations. This paper presents a detailed study on the application of perturbed difference equations in control systems, including recent mathematical developments and their derivations.