-
1
-
-
44949106254
-
-
K. B. Wolf, Integral Transforms in Science and Engineering. New York: Plenum, 1979, Construction and Properties of Canonical Transforms, ch. 9.
-
K. B. Wolf, Integral Transforms in Science and Engineering. New York: Plenum, 1979, vol. Construction and Properties of Canonical Transforms, ch. 9.
-
-
-
-
3
-
-
0000010577
-
Wigner distribution function and its application to first-order optics
-
M. J. Bastiaans, "Wigner distribution function and its application to first-order optics," J. Opt. Soc. Amer., vol. 69, pp. 1710-1716, 1979.
-
(1979)
J. Opt. Soc. Amer
, vol.69
, pp. 1710-1716
-
-
Bastiaans, M.J.1
-
5
-
-
21344493264
-
Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation: An operator approach
-
S. Abe and J. T. Sheridan, "Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation: An operator approach," J. Phys. A, vol. 27, pp. 4179-4187, 1994.
-
(1994)
J. Phys. A
, vol.27
, pp. 4179-4187
-
-
Abe, S.1
Sheridan, J.T.2
-
6
-
-
0028546432
-
Optical operations on wavefunctions as the Abelian subgroups of the special affine Fourier transformation
-
S. Abe and J. T. Sheridan, "Optical operations on wavefunctions as the Abelian subgroups of the special affine Fourier transformation," Optics Letters, vol. 19, pp. 1801-1803, 1994.
-
(1994)
Optics Letters
, vol.19
, pp. 1801-1803
-
-
Abe, S.1
Sheridan, J.T.2
-
7
-
-
0003434416
-
-
Mill Valley, CA: University Science Books
-
A. E. Siegman, Lasers. Mill Valley, CA: University Science Books, 1986.
-
(1986)
Lasers
-
-
Siegman, A.E.1
-
8
-
-
0030145797
-
The generalized Fresnel transform and its applications to optics
-
D. F. V. James and G. S. Agarwal, "The generalized Fresnel transform and its applications to optics," Opt. Commun., vol. 126, pp. 207-212, 1996.
-
(1996)
Opt. Commun
, vol.126
, pp. 207-212
-
-
James, D.F.V.1
Agarwal, G.S.2
-
9
-
-
0011712141
-
Extension of the Fresnel transform to ABSD systems
-
C. Palma and V. Bagini, "Extension of the Fresnel transform to ABSD systems," J. Opt. Soc. Amer. A, vol. 14, pp. 1774-1779, 1997.
-
(1997)
J. Opt. Soc. Amer. A
, vol.14
, pp. 1774-1779
-
-
Palma, C.1
Bagini, V.2
-
10
-
-
0001201391
-
Extended fractional Fourier transforms
-
J. Hua, L. Liu, and G. Li "Extended fractional Fourier transforms," J. Opt. Soc. Amer. A, vol. 14, pp. 3316-3322. 1997.
-
(1997)
J. Opt. Soc. Amer. A
, vol.14
, pp. 3316-3322
-
-
Hua, J.1
Liu, L.2
Li, G.3
-
11
-
-
0030243105
-
Digital cimputation of the fractional Fourier transform
-
Sep
-
H. M. Ozaktas, O. Arikan. M. A. Kutay, and Bozdaǧi, "Digital cimputation of the fractional Fourier transform," IEEE Trans. Signal Process., vol. 44, no. 9, pp. 2141-2150, Sep. 1996.
-
(1996)
IEEE Trans. Signal Process
, vol.44
, Issue.9
, pp. 2141-2150
-
-
Ozaktas, H.M.1
Arikan, O.2
Kutay, M.A.3
Bozdaǧi4
-
12
-
-
19944406134
-
Fast numerical algorithm for the linear canonical transform
-
B. M. Hennelly and J. T. Sheridan, " Fast numerical algorithm for the linear canonical transform," J Opt. Soc. Amer. A, vol. 22, 928-937, 2005.
-
(2005)
J Opt. Soc. Amer. A
, vol.22
, pp. 928-937
-
-
Hennelly, B.M.1
Sheridan, J.T.2
-
13
-
-
0000678867
-
Fractional Fourier-Kravchuk transform
-
N. M. Atakishiyev and K.B. Wolf, "Fractional Fourier-Kravchuk transform," J. Opt. Soc. Amer. A, vol. 14, pp. 1467-1477, 1997.
-
(1997)
J. Opt. Soc. Amer. A
, vol.14
, pp. 1467-1477
-
-
Atakishiyev, N.M.1
Wolf, K.B.2
-
14
-
-
0031190361
-
Improved discrete fractional Fourier transform
-
S.-C. Pei and M.-H. Yeh, "Improved discrete fractional Fourier transform," Opt. Lett., vol. 22, pp. 1047-1049, 1997.
-
(1997)
Opt. Lett
, vol.22
, pp. 1047-1049
-
-
Pei, S.-C.1
Yeh, M.-H.2
-
15
-
-
0032347073
-
Wigner distribution fubction for finite systems
-
N. M. Atakishiyev, S. M. Chumakov, and K. B. Wolf, "Wigner distribution fubction for finite systems," J. Math. Phys., vol. 39, pp. 6247-6261, 1998.
-
(1998)
J. Math. Phys
, vol.39
, pp. 6247-6261
-
-
Atakishiyev, N.M.1
Chumakov, S.M.2
Wolf, K.B.3
-
16
-
-
0033566157
-
Continous versus discrete fractional Foirier transforms
-
N. M. Atakishiyev, L. E. Vicent, and K. B. Wolf, "Continous versus discrete fractional Foirier transforms," J. Comput. Appl. Math., vol. 107, pp. 73-95, 1999.
-
(1999)
J. Comput. Appl. Math
, vol.107
, pp. 73-95
-
-
Atakishiyev, N.M.1
Vicent, L.E.2
Wolf, K.B.3
-
17
-
-
0032669485
-
Discrete fractional Fourier transform based on orthogonal projections
-
S. C. Pei, M. H. Yeh, and C. C. Tseng, "Discrete fractional Fourier transform based on orthogonal projections," IEEE Trans. Signal Process., vol. 47, no. 5, pp. 1335-1348, 1999.
-
(1999)
IEEE Trans. Signal Process
, vol.47
, Issue.5
, pp. 1335-1348
-
-
Pei, S.C.1
Yeh, M.H.2
Tseng, C.C.3
-
18
-
-
0033339817
-
Fractional Fourier series expansion fi finite sugnals and dual extension to discrete-time fractional Fourier transform
-
Oct
-
S. C. Pei, M. H. Yeh, and T.-L. Lup, " Fractional Fourier series expansion fi finite sugnals and dual extension to discrete-time fractional Fourier transform," IEEE Trans. Signal Process., vol. 47, no. 10, pp. 2883-2888, Oct. 1999.
-
(1999)
IEEE Trans. Signal Process
, vol.47
, Issue.10
, pp. 2883-2888
-
-
Pei, S.C.1
Yeh, M.H.2
Lup, T.-L.3
-
19
-
-
0033345657
-
Unified fractional Fourier transform and sampling theorem
-
Dec
-
T. Erseghe, P. Kraniaukas, and G. Cariolaro, "Unified fractional Fourier transform and sampling theorem," IEEE Trans. Signal Process. vol. 47. no. 12, pp. 3419-3423. Dec. 1999.
-
(1999)
IEEE Trans. Signal Process
, vol.47
, Issue.12
, pp. 3419-3423
-
-
Erseghe, T.1
Kraniaukas, P.2
Cariolaro, G.3
-
20
-
-
0033177815
-
The fractional Fourier domain decomposition
-
M. A. Kutay, H. Özaktaş, H. M. Ozaktas, and O. Arikan, "The fractional Fourier domain decomposition," Signal Process. vol. 77, pp. 105-109, 1999.
-
(1999)
Signal Process
, vol.77
, pp. 105-109
-
-
Kutay, M.A.1
Özaktaş, H.2
Ozaktas, H.M.3
Arikan, O.4
-
21
-
-
0033177623
-
New sampling formulae forthe fractional Fourier transform
-
A. I. Zayed and A. D. Garcia, "New sampling formulae forthe fractional Fourier transform," Signal Process., vol. 77, pp. 111-114, 1999.
-
(1999)
Signal Process
, vol.77
, pp. 111-114
-
-
Zayed, A.I.1
Garcia, A.D.2
-
22
-
-
0041072734
-
-
C. Candan, M. A. Kutay, and H.M. Ozaktas, The discrete fractional Fourier transform, IEEE Trans. Signal Process., v48, no. 5, pp. 1329-1337, May 2000.
-
C. Candan, M. A. Kutay, and H.M. Ozaktas, "The discrete fractional Fourier transform," IEEE Trans. Signal Process., vol.v48, no. 5, pp. 1329-1337, May 2000.
-
-
-
-
23
-
-
0033677070
-
Continous and discrete fractional Fourier domain decomposition
-
I. Ş. Yetik, M. A. Kutay, Özaktaş, and H. M. "Continous and discrete fractional Fourier domain decomposition," in Proc. IEEE Int. Conf. Acoustics, Speech, Sugnal Processing, 2000, pp. I:93-96.
-
(2000)
Proc. IEEE Int. Conf. Acoustics, Speech, Sugnal Processing
-
-
Yetik, I.S.1
Kutay, M.A.2
Özaktaş, H.M.3
-
24
-
-
0035368817
-
The discrete fractional cosine and sine transforms
-
S. C. Pei and M. H. Yeh, "The discrete fractional cosine and sine transforms," IEEE Trans. Signal Process., vol. 49, no, 6, pp. 1198-1207.
-
IEEE Trans. Signal Process
, vol.49
, Issue.6
, pp. 1198-1207
-
-
Pei, S.C.1
Yeh, M.H.2
-
25
-
-
0036537824
-
The fractional discrete cosine transform
-
Apr
-
G. Cariolaro T. Erseghe, and P. Kraniauskas, "The fractional discrete cosine transform," IEEE transactions Signal Process., vol. 50, no. 4, pp. 902-911, Apr. 2002.
-
(2002)
IEEE transactions Signal Process
, vol.50
, Issue.4
, pp. 902-911
-
-
Cariolaro, G.1
Erseghe, T.2
Kraniauskas, P.3
-
26
-
-
0037396099
-
Continuum quantum system as limits of discrete quantum systems. IV. Affine canonical transforms
-
L. Barker, "Continuum quantum system as limits of discrete quantum systems. IV. Affine canonical transforms," J. Math. Phys., vol. 44, pp. 1535-1553, 2003
-
(2003)
J. Math. Phys
, vol.44
, pp. 1535-1553
-
-
Barker, L.1
-
27
-
-
0141892675
-
Sampling and series expansion theorems for fractional Fourier and other transforms
-
C. Candan and H. M. Ozaktas, "Sampling and series expansion theorems for fractional Fourier and other transforms," Signal Process., vol. 83, pp. 1455-1457, 2003.
-
(2003)
Signal Process
, vol.83
, pp. 1455-1457
-
-
Candan, C.1
Ozaktas, H.M.2
-
28
-
-
17644399112
-
On the multiangle centered discrete fractional Fourier transform
-
J. G. Vargas-Rubio and B. Santhanam, "On the multiangle centered discrete fractional Fourier transform," IEEE Signal Process. Lett. vol. 12, no. 4, pp. 273-276, 2005.
-
(2005)
IEEE Signal Process. Lett
, vol.12
, Issue.4
, pp. 273-276
-
-
Vargas-Rubio, J.G.1
Santhanam, B.2
-
29
-
-
13444302708
-
Angular decompositions for the discrete fractional signal transforms
-
M. H. Yeh, "Angular decompositions for the discrete fractional signal transforms," Signal Process., vol. 85, pp. 537-547, 2005.
-
(2005)
Signal Process
, vol.85
, pp. 537-547
-
-
Yeh, M.H.1
-
30
-
-
30544433781
-
Finite systems, fractional Fourier transforms and their finite phase spaces
-
K. B. Wolf, "Finite systems, fractional Fourier transforms and their finite phase spaces," Czech. J. Phys., vol. 55, pp. 1527-1534, 2005.
-
(2005)
Czech. J. Phys
, vol.55
, pp. 1527-1534
-
-
Wolf, K.B.1
-
31
-
-
33744540016
-
-
K. B. Wolf, Finite systems on phase space, Int. J. Mod. Phys. B 20, pt. 2 Sp. Iss, pp. 1956-1967, 2006.
-
K. B. Wolf, "Finite systems on phase space," Int. J. Mod. Phys. B vol. 20, pt. 2 Sp. Iss, pp. 1956-1967, 2006.
-
-
-
-
32
-
-
34047152302
-
Geometry and dynamics in the fractional discrete Fourier transform
-
K. B.Wolf and G. Krotzsch, "Geometry and dynamics in the fractional discrete Fourier transform," J. Opt. Soc. Amer. A, vol. 24, pp. 651-658, 2007.
-
(2007)
J. Opt. Soc. Amer. A
, vol.24
, pp. 651-658
-
-
Wolf, K.B.1
Krotzsch, G.2
-
33
-
-
0000170077
-
Computation considerations and fast algorithms for calculating the diffraction integral
-
D. Mendlovic, Z. Zalevsky, and N. Konforti, "Computation considerations and fast algorithms for calculating the diffraction integral," J. Mod. Opt., vol. 44, pp. 407-414, 1997.
-
(1997)
J. Mod. Opt
, vol.44
, pp. 407-414
-
-
Mendlovic, D.1
Zalevsky, Z.2
Konforti, N.3
-
34
-
-
0032648792
-
Fast algorithms for free-space diffraction patterns calculation
-
D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, "Fast algorithms for free-space diffraction patterns calculation," Opt. Commun., vol. 164, pp. 233-245, 1999.
-
(1999)
Opt. Commun
, vol.164
, pp. 233-245
-
-
Mas, D.1
Garcia, J.2
Ferreira, C.3
Bernardo, L.M.4
Marinho, F.5
-
35
-
-
31144447295
-
-
H. M. Ozaktas, A.Ko&, I. Sari, and M. A.Kutay, Efficient computation of quadratic-phase integrals in optics, Opt. Lett., 31, pp. 35-37, 2006.
-
H. M. Ozaktas, A.Ko&, I. Sari, and M. A.Kutay, "Efficient computation of quadratic-phase integrals in optics," Opt. Lett., vol. 31, pp. 35-37, 2006.
-
-
-
-
36
-
-
85032751591
-
Linear and quadratic time-frequency signal representations
-
Apr
-
F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations," IEEE Signal Process. Mag. vol. 9, no. 2, pp. 21-67, Apr. 1992.
-
(1992)
IEEE Signal Process. Mag
, vol.9
, Issue.2
, pp. 21-67
-
-
Hlawatsch, F.1
Boudreaux-Bartels, G.F.2
-
37
-
-
0003733873
-
-
Englewood Cliffs, NJ: Prentice-Hall
-
L. Cohen, Time-Frequency Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1995.
-
(1995)
Time-Frequency Analysis
-
-
Cohen, L.1
-
38
-
-
0027652515
-
Fractional Fourier transforms and their optical implementation: I
-
D. Mendlovic and H. M. Ozaktas, "Fractional Fourier transforms and their optical implementation: I," J. Opt. Soc. Amer. A, vol. 10, pp. 1875-1881, 1993.
-
(1993)
J. Opt. Soc. Amer. A
, vol.10
, pp. 1875-1881
-
-
Mendlovic, D.1
Ozaktas, H.M.2
-
39
-
-
0027740848
-
Fractional Fourier transforms and their optical implementation: II
-
H. M. Ozaktas and D. Mendlovic, "Fractional Fourier transforms and their optical implementation: II," J. Opt. Soc. Amer. A, vol. 10, pp. 2522-2531, 1993.
-
(1993)
J. Opt. Soc. Amer. A
, vol.10
, pp. 2522-2531
-
-
Ozaktas, H.M.1
Mendlovic, D.2
-
40
-
-
0027641018
-
Fourier transforms of fractional order and their optical interpretation
-
H. M. Ozaktas and D. Mendlovic, "Fourier transforms of fractional order and their optical interpretation," Opt. Commun., vol. 101, pp. 163-169, 1993.
-
(1993)
Opt. Commun
, vol.101
, pp. 163-169
-
-
Ozaktas, H.M.1
Mendlovic, D.2
-
41
-
-
0028382656
-
Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms
-
H. M. Ozaktas, B. Barshan, D. Mendlovic, and L. Onural, "Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms," J. Opt. Soc. Amer. A, vol. 11, pp. 547-559, 1994.
-
(1994)
J. Opt. Soc. Amer. A
, vol.11
, pp. 547-559
-
-
Ozaktas, H.M.1
Barshan, B.2
Mendlovic, D.3
Onural, L.4
-
42
-
-
0028546458
-
The fractional Fourier transform and time-frequency representations
-
Nov
-
L. B. Almeida, "The fractional Fourier transform and time-frequency representations," IEEE Trans. Signal Process., vol. 42, no. 11, pp. 3084-3091, Nov. 1994.
-
(1994)
IEEE Trans. Signal Process
, vol.42
, Issue.11
, pp. 3084-3091
-
-
Almeida, L.B.1
-
44
-
-
0031276318
-
Relationships among ray optical, Gaussian beam, and fractional Fourier transform descriptions of first-order optical systems
-
H. M. Ozaktas and M. F. Erden, "Relationships among ray optical, Gaussian beam, and fractional Fourier transform descriptions of first-order optical systems," Opt. Commun., vol. 143, pp. 75-86, 1997.
-
(1997)
Opt. Commun
, vol.143
, pp. 75-86
-
-
Ozaktas, H.M.1
Erden, M.F.2
-
45
-
-
19944379483
-
Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms
-
B. M. Hennelly and J. T. Sheridan, "Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms," J. Opt. Soc. America. A, vol. 22, pp. 917-927, 2005.
-
(2005)
J. Opt. Soc. America. A
, vol.22
, pp. 917-927
-
-
Hennelly, B.M.1
Sheridan, J.T.2
-
46
-
-
30744454586
-
Alternative representation of the linear canonical integral transform
-
T. Alieva and M. J. Bastiaans, "Alternative representation of the linear canonical integral transform," Opt. Lett., vol. 30, pp. 3302-3304, 2005.
-
(2005)
Opt. Lett
, vol.30
, pp. 3302-3304
-
-
Alieva, T.1
Bastiaans, M.J.2
-
47
-
-
33749457637
-
Synthesis of an arbitrary ABCD system with fixed lens positions
-
M. J. Bastiaans and T. Alieva, "Synthesis of an arbitrary ABCD system with fixed lens positions," Opt. Lett., vol. 31, pp. 2414-2416, 2006.
-
(2006)
Opt. Lett
, vol.31
, pp. 2414-2416
-
-
Bastiaans, M.J.1
Alieva, T.2
-
48
-
-
33751235245
-
Optical system design for orthosymplectic transformations in phase space
-
J. A. Rodrigo, T. Alieva, and M. L. Calvo, "Optical system design for orthosymplectic transformations in phase space," J. Opt. Soc. Amer. A, vol. 23, pp. 2494-2500, 2006.
-
(2006)
J. Opt. Soc. Amer. A
, vol.23
, pp. 2494-2500
-
-
Rodrigo, J.A.1
Alieva, T.2
Calvo, M.L.3
-
49
-
-
4544267358
-
Improved fast fractional-Fourier-transform algorithm
-
X. Yang, Q. Tan, X.Wei, Y. Xiang, Y. Yan, and G. Jin, "Improved fast fractional-Fourier-transform algorithm," J. Opt. Soc. Amer. A, vol. 21, pp. 1677-1681, 2004.
-
(2004)
J. Opt. Soc. Amer. A
, vol.21
, pp. 1677-1681
-
-
Yang, X.1
Tan, Q.2
Wei, X.3
Xiang, Y.4
Yan, Y.5
Jin, G.6
-
50
-
-
0000216419
-
Fractional Fourier transform calculation through the fast Fourier transform algorithm
-
J. Garcia, D. Mas, and R. G. Dorsch, "Fractional Fourier transform calculation through the fast Fourier transform algorithm," Appl. Opt., vol. 35, pp. 7013-7018, 1996.
-
(1996)
Appl. Opt
, vol.35
, pp. 7013-7018
-
-
Garcia, J.1
Mas, D.2
Dorsch, R.G.3
-
51
-
-
0000578198
-
Numerical calculation of fractional Fourier transforms with a single fast Fourier transform algorithm
-
F. J. Marinho and L. M. Bernardo, "Numerical calculation of fractional Fourier transforms with a single fast Fourier transform algorithm," J. Opt. Soc. Amer. A, vol. 15, pp. 2111-2116, 1998.
-
(1998)
J. Opt. Soc. Amer. A
, vol.15
, pp. 2111-2116
-
-
Marinho, F.J.1
Bernardo, L.M.2
-
52
-
-
44949150984
-
Design of efficient digital interpolation filters for integer upsampling,
-
M.E. thesis, MIT, Cambridge, MA
-
D. B. Turek, "Design of efficient digital interpolation filters for integer upsampling," M.E. thesis, MIT, Cambridge, MA, 2004.
-
(2004)
-
-
Turek, D.B.1
-
53
-
-
0031079193
-
Optimal filtering with linear canonical transformations
-
B. Barshan, M. A. Kutay, and H. M. Ozaktas, "Optimal filtering with linear canonical transformations," Opt. Commun., vol. 135, pp. 32-36, 1997.
-
(1997)
Opt. Commun
, vol.135
, pp. 32-36
-
-
Barshan, B.1
Kutay, M.A.2
Ozaktas, H.M.3
|