A fractional Gabor transform (FRGT) is proposed. This new transform is
a generalization of the conventional Gabor transform (GT) based on th
e Fourier transform to the windowed fractional Fourier transform (FRFT
). The FRGT provides analyses of signals in both the real space and th
e FRFT frequency domain simultaneously. The space-FRFT frequency patte
rn can be rotated as the fractional order changes. The FRGT has an add
itional freedom, compared with the conventional GT, i.e., the transfor
m order. The FRGT may offer a useful tool for guiding optimal filter d
esign in the FRFT domain in signal processing. (C) Optical Society of
America.