Discrete Calculus
Table of Contents
1. Discrete Fourier Transform
- Fourier transform of discrete functions.
1.1. Definition
\[ X_{k}=\sum_{n=0}^{N-1}x_n\cdot e^{-i2\pi k n/N} \] for \(\lbrace x_n\rbrace_{n=0}^{N-1}, \lbrace X_k\rbrace_{k=0}^{N-1}\).
The reaseon that there's no \(1/N\) factor is because it is a Fourier transform not a Fourier series.