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.
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