Fourier analysis

A visual representation of a fourier transform, the time axis is shown in red, the frequency axis is shown in blue. Since the time signal is periodic, it only shows certain parts of the spectrum

Fourier transforms
Fourier transform Fourier series Discrete-time Fourier transform Discrete Fourier transform Discrete Fourier transform over a ring Fourier transform on finite groups Fourier analysis Related transforms

Fourier analysis is a branch of analysis that looks at how more complex functions can be built with simpler ones. It is also known as classical harmonic analysis. It is named after Joseph Fourier who first used it in the 19th century. The process itself is called Fourier transform. Fourier analysis is widely used in fields such as physics, partial differential equations, number theory, combinatorics, signal processing, imaging, probability theory, statistics, option pricing, cryptography, numerical analysis, acoustics, oceanography, sonar, optics, diffraction, geometry and protein structure analysis.

Fourier Analysis Media

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  Bass guitar time signal of open string A note (55 Hz).

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  Fourier transform of bass guitar time signal of open string A note (55 Hz). Fourier analysis reveals the oscillatory components of signals and functions.

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  A Fourier transform and 3 variations caused by periodic sampling (at interval T) and/or periodic summation (at interval P) of the underlying time-domain function. The relative computational ease of the DFT sequence and the insight it gives into S(f) make it a popular analysis tool.