1. Fourier transform. FFT. FFT

Preliminaries. Notations

A Fourier analyzer provides the spectral characteristics of the signal applied to it by processing it digitally.

Although digital processing itself can be envisaged without explicit recourse to the notions of time and frequency, these notions remain indispensable if we want to relate the calculated spectral values to the physical frequency content of the a priori analog – – signal being analyzed.

Discrete-time signals can be written in two ways.

The first, and most frequently encountered, is to consider the "time" signal as an ordered sequence of values, generally noted x [k ] ; $k\in \mathbb{Z};\mathbb{Z}$...