For the Discrete-Fourier Transform
You have the following variables/values:
- Xk: An output of the DFT
- xn: Input values for the DFT
- N: The number of complex numbers in x = x0, ... , xN-1 and X = X0, ... , XN-1
- n: A summation variable, as denoted by the summation
- e: The mathematical constant, approximately equal to 2.71828 (sometimes called Euler's number, but don't confuse it with Euler's constant γ!)
- i: The imaginary unit
- π: Pi
- k: The "index" of X for the current value being computed
To take e to an imaginary power (eix), you use Euler's formula (eix = cosx + isinx)
I hope you're familiar with imaginary numbers, as they're the foundation for the DFT.
The FFT is a way of computing the DFT. That is, it's just an algorithm for computing the DFT in O(NlogN) time (computing the DFT by dumbly following the above equation requires O(N2) complexity).