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Jean Baptiste Joseph Fourier (1768-1830)
Crédit : Paris Observatory

The Fourier analysis allows us to characterize the frequencies of a periodic signal, the set of these frequencies is called spectrum of the signal.

The discovery of this spectral decomposition dates back to the XIXth century. Joseph Fourier discovered a mathematical method of analysis for complex periodic phenomena, used by the physicists under the name of "decomposition in the Fourier series" or "spectral analysis". Joseph Fourier had the idea of this decomposition in a trigonometric series to solve the heat equation : a real and periodic function f, continous and with a period T, can be decomposed in a weighted sum of simple sinusoidal functions.

Periodic signal

A signal is periodic if its amplitude varies regularly with time, with a constant period T :
x(t0 + T) = x(t0)


One of the features of a sound is the frequency, which is measured in Hertz (Hz). It is directly related to the height of a sound, and it represents the inverse of a time :

A low frequency corresponds to a deep sound, a high frequency corresponds to a high-pitched sound.


Another important feature of a sound is the amplitude. A sound can be strong or soft, and the intensity received depends, among other things, on the amplitude. The amplitude corresponds to the pressure variations of the wave.

A periodic signal can be decomposed in a sum of sinusoidal signals with stable frequencies and amplitudes (decomposition in the Fourier series).