Signal Rectification Using the Fourier Series

Abstract

The article focuses on the application of the Fourier series as a powerful mathematical tool to decompose complex periodic signals into combinations of sines and cosines, allowing the transformation of non-sinusoidal signals into pure sinusoidal and cosine signals. Its main objective is to analyze how Fourier series and filters can rectify periodic signals and improve their quality by eliminating unwanted interference and obtaining pure signals. The work was carried out using the Matlab software, where periodic signals are analyzed and high-pass and low-pass filters are applied, studying the influence of the number of harmonics in the approximation to a pure sinusoidal signal. Key results include the demonstration that the Fourier series can be used effectively to rectify complex periodic signals and how the order of the filters impacts the quality of the output signal. Graphs are presented showing the transformation of original signals into pure sinusoidal signals, particularly through the use of high-pass and low-pass filters of various orders. It is concluded that the Fourier series is a valuable tool for the rectification of periodic signals and that filters are essential to eliminate unwanted disturbances and improve the signal. The importance of using high-order filters to obtain a higher quality signal is emphasized. This study has significant implications in electronics and signal processing, highlighting the usefulness of Matlab in filter analysis and design.