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Are there any real life applications of Fourier series? Are there examples of Fourier series which have an impact on students learning this topic. I have found the normal suspects of examples in this field such as signal processing, electrical principles but there must be a vast range of applications as it is taught on most undergraduate courses in mathematics, physics and engineering. I am looking for examples which will motivate why students should study Fourier series.

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It was originally used by Fourier to solve the heat equation, thus calculating the temperature field.

It is also a nice example of a base change of a function space (Taylor expansion vs Fourier expansion).

Maybe the JPEG compression by DCT is a nice example (Cell phone! Cell phone! :-)

BTW this is my favourite animation regarding Fourier series

http://bl.ocks.org/jinroh/7524988

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