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 :