Noise analysis of band pass filters using stochastic differential equations

Purpose The purpose of this paper is to analyze the effects of white noise perturbations of the input voltage on the band pass filter response, both on pass band and reject band. Design/methodology/approach By adding white noise term in the input voltage of the filter circuit, the deterministic ordinary differential equation (ODE) is replaced by a stochastic differential equation (SDE). With the application of Ito lemma, the analytical solution of SDE has been obtained. Furthermore, based on the Euler-Maruyama approximation, the numerical simulation for SDE has been done. Practical implications Numerical examples are performed using MATLAB programming to show the efficiency and accuracy of the present work. Originality/value All previous noise analyses of filter circuits were done using ODEs or component noise formulas in the electrical domain. The stochastic perspective for these circuits is adopted for the first time in this paper.