Ok, let me explain the Discrete Fourier Transform (DFT). I won't delve into why the Fourier Transform is important, but it is used in many fields: physics, image processing, signal processing, and many more. Let's start with the Fourier series. A periodic function $$f(x)$$ can be approximated by an infinite summation of sine and cosine functions. Sine and cosine can be represented using the Euler formula, $$e^{ix} = \cos(x) + i\sin(x)$$. Thus, $$f(x) = \sum_{n=-\infty}^{\infty} C_n ...