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[CrossRef]

F. Oktem and H. M. Ozaktas, “Exact relation between continuous and discrete linear canonical transforms,” IEEE Signal Process. Lett. 16, 727-730 (2009).

[CrossRef]

J. J. Healy and J. T. Sheridan, “Sampling and discretization of the linear canonical transform,” Signal Process. 89, 641-648 (2009).

[CrossRef]

A. Cortes, I. Velez, and J. F. Sevillano, “Radix rk FFTs: matricial representation and SDC/SDF pipeline implementation,” IEEE Trans. Signal Process. 57, 2824-2839 (2009).

[CrossRef]

J. Zhao, R. Tao, and Y. Wang, “Sampling rate conversion for linear canonical transform,” Signal Process. 88, 2825-2832 (2008).

[CrossRef]

A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Trans. Signal Process. 56, 2383-2394 (2008).

[CrossRef]

U. Gopinathan, G. Situ, T. J. Naughton, and J. T. Sheridan, “Noninterferometric phase retrieval using a fractional Fourier system,” J. Opt. Soc. Am. A 25, 108-115 (2008).

[CrossRef]

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[PubMed]

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[CrossRef]

B.-Z. Li, R. Tao, and Y. Wang, “New sampling formulae related to linear canonical transform,” Signal Process. 87, 983-990 (2007).

[CrossRef]

S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,” IEEE Trans. Signal Process. 55, 111-119 (2007).

[CrossRef]

T. J. Lundy and J. Van Buskirk, “A new matrix approach to real FFTs and convolutions of length 2k,” Computing 80, 23-45 (2007).

[CrossRef]

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145-167 (2006).

[CrossRef]

H. M. Ozaktas, A. Koç. I. Sari, and M. Alper Kutay, “Efficient computation of quadratic-phase integrals in optics,” Appl. Opt. 31, 35-37 (2006).

[CrossRef]

A. Stern, “Sampling of linear canonical transformed signals,” Signal Process. 86, 1421-1425 (2006).

[CrossRef]

B. Deng, R. Tao, and Y. Wang, “Convolution theorems for the linear canonical transform and their applications,” Sci. China Ser. F, Inf. Sci. 49, 592-603 (2006).

[CrossRef]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[CrossRef]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

[CrossRef]
[PubMed]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[CrossRef]

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[CrossRef]

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. Am. A 22, 917-927 (2005).

[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Fast numerical algorithm for the linear canonical transform,” J. Opt. Soc. Am. A 22, 928-937 (2005).

[CrossRef]

L. Onural, “Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations,” Opt. Eng. (Bellingham) 43, 2557-2563 (2004).

[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Stuttgart) 114, 251-265 (2003).

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[CrossRef]

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[CrossRef]

H. M. Ozaktas, A. Koç. I. Sari, and M. Alper Kutay, “Efficient computation of quadratic-phase integrals in optics,” Appl. Opt. 31, 35-37 (2006).

[CrossRef]

B. Barshan, M. Alper Kutay, and H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32-36 (1997).

[CrossRef]

H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagt, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141-2150 (1996).

[CrossRef]

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145-167 (2006).

[CrossRef]

B. Barshan, M. Alper Kutay, and H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32-36 (1997).

[CrossRef]

H. O. Bartelt, K.-H. Brenner, and A. W. Lohmann, “The Wigner distribution function and its optical production,” Opt. Commun. 32, 32-38 (1980).

[CrossRef]

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A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Trans. Signal Process. 56, 2383-2394 (2008).

[CrossRef]

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145-167 (2006).

[CrossRef]

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of complex Fourier series,” Math. Comput. 19, 297-301 (1965).

[CrossRef]

A. Cortes, I. Velez, and J. F. Sevillano, “Radix rk FFTs: matricial representation and SDC/SDF pipeline implementation,” IEEE Trans. Signal Process. 57, 2824-2839 (2009).

[CrossRef]

B. Deng, R. Tao, and Y. Wang, “Convolution theorems for the linear canonical transform and their applications,” Sci. China Ser. F, Inf. Sci. 49, 592-603 (2006).

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[CrossRef]

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145-167 (2006).

[CrossRef]

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[CrossRef]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[CrossRef]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[CrossRef]

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[CrossRef]

J. J. Healy and J. T. Sheridan, “Sampling and discretization of the linear canonical transform,” Signal Process. 89, 641-648 (2009).

[CrossRef]

J. J. Healy and J. T. Sheridan, “Cases where the linear canonical transform of a signal has compact support or is band-limited,” Opt. Lett. 33, 228-230 (2008).

[CrossRef]
[PubMed]

J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “An additional sampling criterion for the linear canonical transform,” Opt. Lett. 33, 2599-2601 (2008).

[CrossRef]
[PubMed]

J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “An additional sampling criterion for the linear canonical transform,” Opt. Lett. 33, 2599-2601 (2008).

[CrossRef]
[PubMed]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[CrossRef]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

[CrossRef]
[PubMed]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[CrossRef]

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. Am. A 22, 917-927 (2005).

[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Fast numerical algorithm for the linear canonical transform,” J. Opt. Soc. Am. A 22, 928-937 (2005).

[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Stuttgart) 114, 251-265 (2003).

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145-167 (2006).

[CrossRef]

S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,” IEEE Trans. Signal Process. 55, 111-119 (2007).

[CrossRef]

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93, 216-231 (2005).

[CrossRef]

A. Nelleri, J. Joseph, and K. Singh, “Digital Fresnel field encryption for three-dimensional information security,” Opt. Eng. (Bellingham) 46, 045801 (8 pages) (2007).

[CrossRef]

J. E. Ward, D. P. Kelly, and J. T. Sheridan, “Three-dimensional speckle size in generalized optical systems with limiting apertures,” J. Opt. Soc. Am. A 26, 1858-1867 (2009).

[CrossRef]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[CrossRef]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

[CrossRef]
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A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Trans. Signal Process. 56, 2383-2394 (2008).

[CrossRef]

H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagt, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141-2150 (1996).

[CrossRef]

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

B.-Z. Li, R. Tao, and Y. Wang, “New sampling formulae related to linear canonical transform,” Signal Process. 87, 983-990 (2007).

[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

A. Nelleri, J. Joseph, and K. Singh, “Digital Fresnel field encryption for three-dimensional information security,” Opt. Eng. (Bellingham) 46, 045801 (8 pages) (2007).

[CrossRef]

F. Oktem and H. M. Ozaktas, “Exact relation between continuous and discrete linear canonical transforms,” IEEE Signal Process. Lett. 16, 727-730 (2009).

[CrossRef]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[CrossRef]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

[CrossRef]
[PubMed]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[CrossRef]

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[CrossRef]

F. Oktem and H. M. Ozaktas, “Exact relation between continuous and discrete linear canonical transforms,” IEEE Signal Process. Lett. 16, 727-730 (2009).

[CrossRef]

A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Trans. Signal Process. 56, 2383-2394 (2008).

[CrossRef]

H. M. Ozaktas, A. Koç. I. Sari, and M. Alper Kutay, “Efficient computation of quadratic-phase integrals in optics,” Appl. Opt. 31, 35-37 (2006).

[CrossRef]

B. Barshan, M. Alper Kutay, and H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32-36 (1997).

[CrossRef]

H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagt, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141-2150 (1996).

[CrossRef]

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

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[CrossRef]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

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[CrossRef]

A. Cortes, I. Velez, and J. F. Sevillano, “Radix rk FFTs: matricial representation and SDC/SDF pipeline implementation,” IEEE Trans. Signal Process. 57, 2824-2839 (2009).

[CrossRef]

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[CrossRef]

J. E. Ward, D. P. Kelly, and J. T. Sheridan, “Three-dimensional speckle size in generalized optical systems with limiting apertures,” J. Opt. Soc. Am. A 26, 1858-1867 (2009).

[CrossRef]

U. Gopinathan, G. Situ, T. J. Naughton, and J. T. Sheridan, “Noninterferometric phase retrieval using a fractional Fourier system,” J. Opt. Soc. Am. A 25, 108-115 (2008).

[CrossRef]

J. J. Healy and J. T. Sheridan, “Cases where the linear canonical transform of a signal has compact support or is band-limited,” Opt. Lett. 33, 228-230 (2008).

[CrossRef]
[PubMed]

J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “An additional sampling criterion for the linear canonical transform,” Opt. Lett. 33, 2599-2601 (2008).

[CrossRef]
[PubMed]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[CrossRef]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

[CrossRef]
[PubMed]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

A. Cortes, I. Velez, and J. F. Sevillano, “Radix rk FFTs: matricial representation and SDC/SDF pipeline implementation,” IEEE Trans. Signal Process. 57, 2824-2839 (2009).

[CrossRef]

J. Zhao, R. Tao, and Y. Wang, “Sampling rate conversion for linear canonical transform,” Signal Process. 88, 2825-2832 (2008).

[CrossRef]

B.-Z. Li, R. Tao, and Y. Wang, “New sampling formulae related to linear canonical transform,” Signal Process. 87, 983-990 (2007).

[CrossRef]

B. Deng, R. Tao, and Y. Wang, “Convolution theorems for the linear canonical transform and their applications,” Sci. China Ser. F, Inf. Sci. 49, 592-603 (2006).

[CrossRef]

J. E. Ward, D. P. Kelly, and J. T. Sheridan, “Three-dimensional speckle size in generalized optical systems with limiting apertures,” J. Opt. Soc. Am. A 26, 1858-1867 (2009).

[CrossRef]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[CrossRef]

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[CrossRef]

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