FOURIER TRANSFORM AND ITS RECENT ADVANCEMENT

Abstract

Fourier analysis and signal processing are vital aspects in the various scientific fields of mathematics, engineering and physics, among others. This abstract provides an extensive overview of the essential aspects, approached and applications of Fourier analysis and signal processing. Fourier analysis is a process invented by the renowned scientist Joseph Fourier, revolving around the decomposition of complicated signals into simple units known as Fourier series or transforms. The central theme to Fourier’s discovery is expressing a signal as a sum of sinusoidal functions, and this representation facilitates the analysis and the synthesis of signals, including time and frequency domains. Signal processing, on the other hand, entails the manipulation, improvement, and extraction of significant content from the signals. This includes a variety of approaches and algorithms that intend to optimize, clean, or evaluate signals for numerous uses. The connection between Fourier analysis and signal processing can be seen in different fields, including speech and picture processing, data compression, pattern recognition, and wireless communication. Therefore, this method may deliver the ability of Fourier analysis to effectively extract important components from complicated signals. It can help advance performance in various realms where the presented summarized perspective. This means that Fourier analysis and signal processing themselves form a critical but insufficiently explored aspect in which further discoveries and enhancements are possible. I anticipate that more comprehensive study will reveal new possibilities, allowing me and other scholars and professionals to be more creative.