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This technique is widely used in various fields such as physics, engineering, signal processing, and image processing. The Wikipedia page on Fourier analysis provides a comprehensive overview of this mathematical concept. It begins with an introduction to Joseph Fourier, the French mathematician who developed the theory of Fourier series in the early 19th century. The page then explains the basic principles behind Fourier analysis, including the concept of periodic functions and the representation of functions as infinite sums of sinusoidal functions. The page goes on to discuss the Fourier transform, which is an extension of Fourier analysis used to analyze non-periodic functions. It explains how the Fourier transform converts a function from the time or spatial domain to the frequency domain, allowing for the analysis of complex signals and systems. The page also covers other related topics, such as the discrete Fourier transform and the fast Fourier transform algorithm, which provide efficient methods for calculating Fourier transforms in practical applications. It discusses applications of Fourier analysis in various fields, including music, telecommunications, and medical imaging. Additionally, the page provides mathematical formulas, equations, and examples to help readers understand and apply Fourier analysis in different contexts. It also includes links to related topics, further reading, and external resources for those interested in diving deeper into this subject. In summary, the Wikipedia page on Fourier analysis serves as a valuable resource for understanding the theory, principles, and applications of this mathematical technique. It provides a comprehensive overview, covering both basic concepts and advanced topics, making it useful for both students and professionals in various fields.