Relations between Gabor transforms and fractional Fourier transforms and their applications for Signal Processing
Journal
IEEE Transactions on Signal Processing
Journal Volume
55
Journal Issue
10
Pages
4839-4850
Date Issued
2007-10
Author(s)
Abstract
Many useful relations between the Gabor transform (GT) and the fractional Fourier transform (FRFT) have been derived. First, we find that, like the Wigner distribution function (WDF), the FRFT is also equivalent to the rotation operation of the GT. Then, we show that performing the scaled inverse Fourier transform (IFT) along an oblique line of the GT of f (t) can yield its FRFT. Since the GT is closely related to the FRFT, we can use it for analyzing the characteristics of the FRFT. Compared with the WDF, the GT does not have the cross-term problem. This advantage is important for the applications of filter design, sampling, and multiplexing in the FRFT domain. Moreover, we find that if the GT is combined with the WDF, the resultant operation [called the Gabor-Wigner transform (GWT)] also has rotation relation with the FRFT. We also derive the general form of the linear distribution that has rotation relation with the FRFT. © 2007 IEEE.
Subjects
Fractional filter design; Fractional Fourier transform (FRFT); Fractional multiplexing; Fractional sampling; Gabor transform (GT); Gabor-Wigner transform (GWT); Wigner distribution function (WDF)
Other Subjects
Fourier transforms; Inverse problems; Multiplexing; Probability distributions; Signal filtering and prediction; Fractional filter design; Fractional fourier transform; Fractional multiplexing; Gabor-Wigner transform; Signal analysis
Type
journal article
File(s)![Thumbnail Image]()
Loading...
Name
17.pdf
Size
1.18 MB
Format
Adobe PDF
Checksum
(MD5):3250e78749b5f058fa53ed03dbbc35ed