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Gabor filters are defined by harmonic functions modulated by a Gaussian distribution. As an example, in two dimensions and using a polar coordinate system with coordinates and :
Gabor filters bear some similarity to Fourier filters, but (by the Gaussian damping terms) are limited to certain frequency bands (passband filter). With a judicious choice of frequencies, e.g. by octaves (viz. by successive factors of 2), a succession of Gabor filters can be assimilated to a wavelet transform, and do an excellent job in image or information compaction.
that is to say, you can transform the signal into time frequency domain with Gabor transform. and then process the new signal, finally you can transform the processed signal into results signal with Gabor inverse transform.
i think Gabor filter is similar to FFT transform.
wish it helpful.
The Gabor Transform is also referred to as the Short Time Fourier Transform (STFT). Filtering the time-frequency content of a signal is indeed one of the main applications of Gabor multipliers. An important difference to wavelet theory is a consequence of the so-called Balian-Low principle.
To learn more about the Gabor Analysis you can read:
H. Bölcskei and F. Hlawatsch, “Oversampled modulated filter banks,”
in Gabor Analysis and Algorithms: Theory and Applications, H. G. Feichtinger
and T. Strohmer, Eds. Boston, MA: Birkhäuser, 1998, ch. 9,
pp. 295–322.
H. G. Feichtinger and T. Strohmer, Eds., “Gabor analysis and algorithms:
Theory and applications,” in Applied and Numerical Harmonic Analysis.
Boston, MA: Birkhäuser, 1998.
Gabor Wavelet Filter
The use of the 2D Gabor filter in computer vision was introduced by Daugman in the late 1980s. Since that time it has been used in many computer vision applications including image compression , edge detection , texture analysis , object recognition and facial recognition.The general form for a complex-valued 2D Gabor function is a planar wave attenuated by a Gaussian envelope:
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