| [1] Namias V. The fractinal order Fourier transform and its application to quantum mechanics. J Inst Math Appl, 1980, 25: 241--265
[2] McBride A C, Kerr F H. On Namias' fractional Fourier transform. IMA J Appl Math, 1987, 39: 159--175
[3] Mendlovic D, Ozaktas H M. Fractional Fourier transforms and their optical implementation (I). J Opt Sco AM A, 1993, 10: 1875--1881
[4] Ozaktas H M, Mendlovic D. Fractional Fourier transforms and their optical implementation (II). J Opt Sco AM A, 1993, 10: 2522--2531
[5] 陶然, 邓兵, 王越. 分数阶Fourier变换在信号处理领域的研究进展.中国科学E辑, 信息科学, 2006, 36: 113--136
[6] 陶然, 邓兵, 王越. 分数阶Fourier 变换的原理与应用. 北京: 清华大学出版社, 2004
[7] Ozaktas H M, Kutay M A, Zalevsky Z. The Fractional Fourier Transform with Applications in Optics and Signal Processing. New York: John Wiley & Sons, 2000
[8] Zayed A I. Hilbert transform associated with the fractional Fourier transform. IEEE Signal Processing Letters, 1998, 5: 206--208
[9] Fu Y X, Li L Q. A generalized Bedrosian theorem in fractional Fourier Domain. IEEE Proc, 2006: 1785--1788
[10] Lohmann A W, Mendlovic D, Zalevsky Z. Fractional Hilbert transform. Opt Lett, 1996, 21: 281--283
[11] Pei S C, Yeh M H. Discrete fractional Hilbert transform. IEEE Trans Circuits and Systems-II: Analog and Digital Signal Processing, 2000, 11: 1307--1311
[12] Tseng C C, Pei S C. Design of discrete-time fractional Hilbert transformer. IEEE Proc, ISCAS, 2000, V: 525--528
[13] Pei S C, Ding J J. The generalized Hilbert transform and its applications to 2-D edge detection. IEEE Proc, ICASSP, 2003, III: 357--360
[14] Stark H. An extension of the Hilbert transform product theorm. IEEE Proc, 1971, 59: 1359--1360
[15] Havlicek J P, Havlicek J W, Ngao D, et al. Skewed 2D Hilbert transforms and computed AM-FM models. IEEE Proc, 1998, 59 : 602--606
[16] Hahn L S. Multidimensional complex signals with single-orthant spectra. IEEE Proc, 1992, 80: 1287--1300
[17] Thomas B, Gerald S. Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case. IEEE Trans Signal Processing, 2001, 49: 2844--2852
[18] Chang J H, Pei S C, Ding J J. 2D quaternion Fourier spectral analysis and its applications.IEEE Proc, 2004, 3: 241--244
[19] Sangwine S J, Ell T A. Hypercomplex Fourier transforms of color images. IEEE Proc, 2001, 1: 137--140
[20] 徐冠雷, 王孝通, 徐晓刚. 二象Hilbert变换. 自然科学进展, 2007, 17: 168--178
[21} Pei S C, Yeh M H. Two dimensional discrete fractional Fourier transform. Signal Processing, 1998, 67: 99--108
[22] Pei S C, Ding J J. Two-Dimensional Affine generalized fractional Fourier transform. IEEE Trans Signal Processing, 2001, 49: 878--897
[23] Gabor D. Theory of communication. IEEE, 1946, 93: 429--457
[24] Ville J. Theorie et applications de la notion de signal analytique. Cables et Transmission, 1948, 2A: 61--74
[25] Boashash B. Estimating and interpreting the instantaneous frequency of a signal-part 1: fundamentals. IEEE Proc, 1992, 80: 520--539
[26] Boashash B. Estimating and interpreting the instantaneous frequency of a signal-part 2: algorithms and applications. IEEE Proc, 1992, 80: 540--568
[27] Cohen L, Lee C. Standard deviation of instantaneous frequency. International Conference on Acoustics, Speech, and Signal Processing, 1989, 4: 2238--2241
[28] Joseph M F, Friedlander B. Parameter estimation of 2-D random amplitude polynomial-phase signals. IEEE Trans Signal Processing, 1999, 47: 1795--1810
[29] Maragos P, Bovik A C. Demodulation of images modeled by amplitude-frequency modulationsusing multidimensional energy separation. IEEE Proc, ICIP, 1994, 3: 421--425
[30] Spagnolini U. 2-D phase unwrapping and instantaneous frequency estimation. IEEE Trans Geoscience and Remote Sensing, 1995, 33: 579--589
[31] Cohen L. What is a multicomponent signal. IEEE Proc, ICASSP'92, 1992, 5: 113--116
[32] 徐冠雷, 王孝通, 徐晓刚等. 多分量到单分量可用EMD分解的条件及判据. 自然科学进展, 2006, 16: 1356--1360
[33] Bedrosian E. A product theorem for Hilbert transform. IEEE, 1963, 51: 868--869
[34] 黄晋, 吕涛, 朱瑞. 解带有Hilbert核的奇异积分方程的高精度组合算法. 数学物理学报, 2009, 29A(1): 103--113
[35] 唐立, 杨文胜. 边值问题的概率数值方法.数学物理学报, 2008, 28A(1): 81--85 |