THEORETICAL AND PRACTICAL ASPECTS OF FOURIER SERIES AND INTEGRAL TRANSFORMATIONS

Abstract

In the current era of digital technologies, signal and image processing is widely used in various fields, including medicine, communications, audio and video technologies, artificial intelligence, and engineering. In these processes, Fourier analysis, that is, Fourier series and integral transforms, is one of the main mathematical methods for performing such important tasks as determining the composition of signals and images, their compression and filtering. This makes it easier to analyze signals and images, clear them of noise, and compress data. This article provides a detailed analysis of the basic concepts of Fourier series and integral transforms, their mathematical foundations, and areas of practical application.