Discrete Calculus

Table of Contents

1. Discrete Fourier Transform

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.

Author: Jeemin Kim

Created: 2026-08-09 Sun 07:11