Gabor Function

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A Gabor Function is a exponential function that ...



References

2014


  • (Wikipedia, 2014) ⇒ http://wikipedia.org/wiki/Gabor_atom#Mathematical_definition Retrieved:2014-7-26.
    • The Gabor function is defined by :[math]\displaystyle{ g_{\ell,n}(x) = g(x - a\ell)e^{2\pi ibnx}, \quad -\infty \lt \ell,n \lt \infty, }[/math] where a and b are constants and g is a fixed function in L2(R), such that ||g|| = 1. Depending on [math]\displaystyle{ a }[/math], [math]\displaystyle{ b }[/math], and [math]\displaystyle{ g }[/math], a Gabor system may be a basis for L2(R), which is defined by translations and modulations. This is similar to a wavelet system, which may form a basis through dilating and translating a mother wavelet.

2010