Approximation

The law of nature is approximate.

If you have done any approximation research, then it is impossible to avoid Fourier. It is one of most foundamental analysis tool for approximation. The big idea about Fourier analysis is that every complicated function is an infinite combination of some independent functions. And the nice property about these basic function space is that, we can get the weights easily by Fourier transform. Imaging that you have a fruite mixed drink, and you would like to get the recipe. If there is a filter, that only filter out the fruite you specified. Say, banana filter, you just need to filter the banana out of drink, then you would know the percentage of banana. The famous example is Taylor expansion.