This paper addresses the fundamental concepts and applications of Fourier analysis, including Fourier series, Euler's formula, and the Fourier transform, and provides a practical example of implementing Fourier analysis in the Java programming language. The paper is divided into several key chapters. The first chapter explains the Fourier series, which is a method for expressing periodic functions as a sum of sine and cosine functions with different frequencies. An introduction to sequences and series provides the foundation for understanding Fourier series, which is essential in the analysis of periodic signals. The second chapter is dedicated to Euler's formula, which links exponential functions with trigonometric functions and serves as a key tool in Fourier analysis. This chapter includes applications and interpretations of Euler's formula, as well as the transition of the Fourier series into exponential form, making the manipulation of complex signals easier. The third chapter focuses on the Fourier transform, which extends the concept of the Fourier series to non-periodic functions and enables the analysis of a wide range of signals. The mathematical aspects of the transform are presented, along with its basic properties, the discrete Fourier transform (DFT), and the fast Fourier transform (FFT), which allows efficient analysis of large datasets. The fourth chapter presents the practical part of the paper, including descriptions of algorithms and the coding of Fourier analysis in the object-oriented programming language Java. Two classes, Complex and Fourier, are implemented to facilitate working with complex numbers and performing Fourier analysis. The complete code and results are presented at the end. This paper provides both theoretical and practical insights into Fourier analysis, highlighting its importance in signal analysis, data processing, and various applications in engineering and scientific disciplines.