Discreet Fourier transform
The Discrete Fourier Transform (DFT) is a mathematical technique used to analyse the frequency content of discrete signals, such as digital signals or sampled data. It is a discrete counterpart to the continuous Fourier transform, and it is particularly useful for processing digital signals in computer-based systems.
Given a sequence of N complex numbers x₀, x₁, …, xₙ₋₁, the DFT transforms this sequence into another sequence of complex numbers X₀, X₁, …, Xₙ₋₁ according to the following formula DFT of X(k) is :