Complex Numbers and Exponentials. (pdf file) These notes introduce complex numbers and exponentials. As an application, they show why the discrete Fourier series formula is true.
Fourier Series This demo shows a Fourier series adding up to the expected answer.
The Fast Fourier Transform. (pdf file) The fast Fourier transform is an algorithm for computing Fourier coefficients very efficiently. These notes explain the principle upon which the algorithm is based.