Title :
2-D affine generalized fractional Fourier transform
Author :
Ding, Jian-Jiun ; Pei, Soo-Chang
Author_Institution :
Dept. of Electr. Eng., Nat. Taiwan Univ., Taipei, Taiwan
Abstract :
The 2-D Fourier transform has been generalized into the 2-D separable fractional Fourier transform (replaces the 1-D Fourier transform by the l-D fractional Fourier transform for each variable) and the 2-D separable canonical transform (further replaces the fractional Fourier transform by canonical transform) of Sahin, Ozaktas and Mendlovic (see Appl. Opt., vol.37, no.11, p.2130-41, 1998). It also has been generalized into the 2-D unseparable fractional Fourier transform with 4 parameters of Sahin et al. (see Appl. Opt., vol.37, no.23, p.5444-53, 1998). In this paper, we introduce the 2-D affine generalized fractional Fourier transform (AGFFT). These 2-D transforms has been further generalized. We show it can deal with many problems that can not be dealt with by these 2-D transforms and extend their utility
Keywords :
Fourier transforms; Hilbert transforms; digital arithmetic; filtering theory; image processing; pattern recognition; signal synthesis; 2D Fourier transform; 2D affine Hilbert transform; 2D affine generalized fractional Fourier transform; 2D separable canonical transform; 2D separable fractional Fourier transform; 2D unseparable fractional Fourier transform; beam shaping; filter design; image processing; optical system analysis; pattern recognition; signal synthesis; Chirp; Convolution; Equations; Fourier transforms; Kernel; Optical design; Optical filters; Pattern analysis; Pattern recognition; Two dimensional displays;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5041-3
DOI :
10.1109/ICASSP.1999.757517
