Gabor atoms or Gabor functions are functions used in the analysis proposed by Dennis Gabor in 1946 where a family of funcions is built from translations and modulations of a generating one.

Overview

In 1946, Dennis Gabor sugested the idea of using a granular system to produce sound. In his work, Gabor discussed the problems with the Fourier analysis, and, according to him, although the mathematics is perfectly correct, it is not possible to apply it physicaly, mainly in usual sounds, as the sound of a sirene, in which the frequency parameter ir variable through time. Another problem would be the undergonne suposition, as we use sine waves analysis, that the signal under concern has infinity duration. Gabor proposes to apply the ideas from quantum physics to sound, allowing an analogy between sound and quanta. Under a mathematical background he proposed a method to reduce the Fourier analysis into cells. His research aimed the information transmission through communication channels. Gabor saw in his atoms a possiblity to transmit the same information but using less data, instead of transmiting the signal itself it would be possible to transmite only the coefficients which represents the same signal using his atoms.

Mathematical Definition

The gabor function is defined by g_l,n(x) = g(x − al)e^2πibnx, . where a and b are constants and g is a fixed funcion in , such that . It works in almost the same way as in the wavelet families, we are creating a basis for , using for doing so translations and modulations (instead of escaling, as is done in wavelet analysis) of a base function.