# Fourier Series ### Key Intuition > The Fourier Series is simply how we write a function $f$ in an orthogonal basis of sines and cosines, exactly as we are used to writing a vector $\vec{v}$ in an orthogonal basis ### Thoughts * My best notes for this are actually on paper in my filing cabinet. Those are where you shoul start, along with this video [Fourier Series Part 1](https://www.youtube.com/watch?v=MB6XGQWLV04&list=PLMrJAkhIeNNT_Xh3Oy0Y4LTj0Oxo8GqsC&index=2) * [Exponentials > Why do imaginary exponentials lead to rotation](Exponentials.md#Why%20do%20imaginary%20exponentials%20lead%20to%20rotation) * Here we must recall what it means to take the [inner product](Function-orthogonality.md#Inner%20Product) of functions and for them to be [orthogonal](Function-orthogonality.md#Orthogonality). [test](file:///Users/nathanieldake/development/data-science/resources/information%20theory/Entropy%20Derivation.pdf) --- References * [But what is a Fourier series? From heat flow to circle drawings](https://www.youtube.com/watch?v=r6sGWTCMz2k&t=165s) * Paper notes on Fourier Series * [Fourier Series Part 1](https://www.youtube.com/watch?v=MB6XGQWLV04&list=PLMrJAkhIeNNT_Xh3Oy0Y4LTj0Oxo8GqsC&index=2)