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A Fourier series is a representation of a wave form or other periodic function as a sum of sines and cosines. It is named after the French mathematician and physicist Jean-Baptiste Joseph Fourier (1768–1830). Since sound waves are made up of sine waves, Fourier transforms are widely used in signal processing.
A Fourier series is a way to represent complex waves, such as sound, as a series of simple sine waves. The series breaks down a wave into a sum of sines and cosines. This means that elements of a wave can be isolated from each other. The field of Fourier analysis is the study of various Fourier series. The practice of isolating a signal into individual frequencies is known as a Fourier transform.
While it is possible to calculate a Fourier series manually, computers can more easily analyze the complex harmonics of everyday sounds. Fourier analysis is widely used in audio processing, such as picking out individual sounds from a recording.