Mathematics behind signal analysis

Abstract

This work is devoted to investigation of how does Fourier Transform works and what purpose of it. Also was mentioned two types of transformation, Discrete Fourier Transform and Fast Fourier Transform and their specific uses. Finally, some of the most common applications of the Fourier Transform in fields such as signal processing, image processing, communication systems, and quantum mechanics will be discussed. The Fourier Transform is a fundamental mathematical tool that has revolutionized the way we analyze and understand signals, and its applications continue to expand to new fields and technologies so it is important to understand the way it works and what benefits it might bring