Fourier analysis is a mathematical technique used to study the way functions can be represented as a sum of sine and cosine waves. It is named after the mathematician Joseph Fourier, who discovered that many complex functions can be broken down into simpler trigonometric functions. Fourier analysis is used in a wide range of fields including signal processing, image analysis, engineering, physics, and mathematics. It allows researchers to understand and manipulate signals and data in the frequency domain, which can provide valuable insights into the underlying patterns and structure of the data. Overall, Fourier analysis is a powerful tool for decomposing complex functions into simpler components, making it easier to analyze and understand the behavior of systems in various disciplines.