FOURIER TRANSFORM AND IT’S APPLICATIO

Abstract

The Fourier Transform is a powerful mathematical tool that decomposes a function or a signal into its constituent frequencies, revealing the underlying frequency content and pro viding insights into its behavior. This thesis presents a comprehensive exploration of the Fourier Transform, covering its theoretical foundations, various techniques for implemen tation, and a wide range of applications across different fields. The thesis begins by providing a comprehensive overview of Fourier series, introducing the key concepts and mathematical foundations. The fundamental properties of periodic functions and the Fourier series representation are elucidated, including the convergence, linearity, and symmetry properties. Furthermore, this thesis explores the broad spectrum of applications of the Fourier Trans form. It examines its role in signal processing, such as filtering, spectral analysis, and noise reduction. Additionally, it discusses the use of Fourier Transform in image processing, in cluding image enhancement, compression, and pattern recognition. In conclusion, this thesis provides a comprehensive overview of the Fourier Transform, elu cidating its theoretical foundations, implementation techniques, and versatile applications. It highlights the transformative impact of the Fourier Transform in diverse fields and em phasizes its significance as a fundamental tool for understanding and manipulating signals and data in the frequency domain.