Fourier series
lastmod 2018-08-17created 2017-01-221 edits
In mathematics, a Fourier series is a series that decomposes a periodic function into a weighted sum of trigonometric functions. In most cases, the coefficients of the series correspond one-to-one with the original function.
The Fourier coefficients of a function are useful because they are easier to work with than the original function. Fourier series are used in electronic engineering, vibration analysis, acoustics, optics, signal processing and image processing, data compression, and more. In astronomy, they are used to decompose the frequencies of starlight with a spectroscope to identify the chemical substances that make up a star, and in communications engineering, they are used to optimize the design of communication systems using the spectrum of the data signals to be transmitted.