Fourier Series

What Does Fourier Series Mean?

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.


Techopedia Explains Fourier Series

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.


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Margaret is an award-winning technical writer and teacher known for her ability to explain complex technical subjects to a non-technical business audience. Over the past twenty years, her IT definitions have been published by Que in an encyclopedia of technology terms and cited in articles by the New York Times, Time Magazine, USA Today, ZDNet, PC Magazine, and Discovery Magazine. She joined Techopedia in 2011. Margaret's idea of a fun day is helping IT and business professionals learn to speak each other’s highly specialized languages.