References analysis of the Wikipedia article "Fractional Fourier transform" in the English version

arxiv.org

Somma, Rolando D. (2016). "Quantum simulations of one dimensional quantum systems". Quantum Information and Computation. 16: 1125–1168. arXiv:1503.06319v2.

De Bie, Hendrik (1 September 2008). "Fourier transform and related integral transforms in superspace". Journal of Mathematical Analysis and Applications. 345 (1): 147–164. arXiv:0805.1918. Bibcode:2008JMAA..345..147D. doi:10.1016/j.jmaa.2008.03.047. S2CID 17066592.

Fan, Hong-yi; Hu, Li-yun (2009). "Optical transformation from chirplet to fractional Fourier transformation kernel". Journal of Modern Optics. 56 (11): 1227–1229. arXiv:0902.1800. Bibcode:2009JMOp...56.1227F. doi:10.1080/09500340903033690. S2CID 118463188.

Klappenecker, Andreas; Roetteler, Martin (January 2002). "Engineering Functional Quantum Algorithms". Physical Review A. 67 (1): 010302. arXiv:quant-ph/0208130. doi:10.1103/PhysRevA.67.010302. S2CID 14501861.

Huang, Yichen (24 May 2011). "Entropic uncertainty relations in multidimensional position and momentum spaces". Physical Review A. 83 (5): 052124. arXiv:1101.2944. Bibcode:2011PhRvA..83e2124H. doi:10.1103/PhysRevA.83.052124. S2CID 119243096.

Tasca, DS; Walborn, SP; Souto Ribeiro, PH; Toscano, F (8 July 2008). "Detection of transverse entanglement in phase space". Physical Review A. 78 (1): 010304(R). arXiv:0806.3044. Bibcode:2008PhRvA..78a0304T. doi:10.1103/PhysRevA.78.010304. S2CID 118607762.

doi.org

Condon, Edward U. (1937). "Immersion of the Fourier transform in a continuous group of functional transformations". Proc. Natl. Acad. Sci. USA. 23 (3): 158–164. Bibcode:1937PNAS...23..158C. doi:10.1073/pnas.23.3.158. PMC 1076889. PMID 16588141.

Namias, V. (1980). "The fractional order Fourier transform and its application to quantum mechanics". IMA Journal of Applied Mathematics. 25 (3): 241–265. doi:10.1093/imamat/25.3.241.

Wiener, N. (April 1929). "Hermitian Polynomials and Fourier Analysis". Journal of Mathematics and Physics. 8 (1–4): 70–73. doi:10.1002/sapm19298170.

Almeida, Luís B. (1994). "The fractional Fourier transform and time–frequency representations". IEEE Trans. Signal Process. 42 (11): 3084–3091. Bibcode:1994ITSP...42.3084A. doi:10.1109/78.330368. S2CID 29757211.

Tao, Ran; Deng, Bing; Zhang, Wei-Qiang; Wang, Yue (2008). "Sampling and sampling rate conversion of band limited signals in the fractional Fourier transform domain". IEEE Transactions on Signal Processing. 56 (1): 158–171. Bibcode:2008ITSP...56..158T. doi:10.1109/TSP.2007.901666. S2CID 7001222.

Bhandari, A.; Marziliano, P. (2010). "Sampling and reconstruction of sparse signals in fractional Fourier domain". IEEE Signal Processing Letters. 17 (3): 221–224. Bibcode:2010ISPL...17..221B. doi:10.1109/LSP.2009.2035242. hdl:10356/92280. S2CID 11959415.

Bailey, D. H.; Swarztrauber, P. N. (1991). "The fractional Fourier transform and applications". SIAM Review. 33 (3): 389–404. doi:10.1137/1033097. (Note that this article refers to the chirp-z transform variant, not the FRFT.)

Candan, Kutay & Ozaktas 2000. Candan, C.; Kutay, M. A.; Ozaktas, H. M. (May 2000). "The discrete fractional Fourier transform" (PDF). IEEE Transactions on Signal Processing. 48 (5): 1329–1337. Bibcode:2000ITSP...48.1329C. doi:10.1109/78.839980. hdl:11693/11130.

Shi, Jun; Zhang, NaiTong; Liu, Xiaoping (June 2012). "A novel fractional wavelet transform and its applications". Sci. China Inf. Sci. 55 (6): 1270–1279. doi:10.1007/s11432-011-4320-x. S2CID 3772011.

Pellat-Finet, Pierre (15 September 1994). "Fresnel diffraction and the fractional-order Fourier transform". Optics Letters. 19 (18): 1388–1390. Bibcode:1994OptL...19.1388P. doi:10.1364/OL.19.001388. PMID 19855528.

Pellat-Finet, Pierre; Bonnet, Georges (15 September 1994). "Fractional order Fourier transform and Fourier optics". Optics Communications. 111 (1–2): 141. Bibcode:1994OptCo.111..141P. doi:10.1016/0030-4018(94)90154-6.

Sejdić, Ervin; Djurović, Igor; Stanković, LJubiša (June 2011). "Fractional Fourier transform as a signal processing tool: An overview of recent developments". Signal Processing. 91 (6): 1351–1369. Bibcode:2011SigPr..91.1351S. doi:10.1016/j.sigpro.2010.10.008. S2CID 14203403.

Walborn, SP; Lemelle, DS; Tasca, DS; Souto Ribeiro, PH (13 June 2008). "Schemes for quantum key distribution with higher-order alphabets using single-photon fractional Fourier optics". Physical Review A. 77 (6): 062323. Bibcode:2008PhRvA..77f2323W. doi:10.1103/PhysRevA.77.062323.

Pégard, Nicolas C.; Fleischer, Jason W. (2011). "Optimizing holographic data storage using a fractional Fourier transform". Optics Letters. 36 (13): 2551–2553. Bibcode:2011OptL...36.2551P. doi:10.1364/OL.36.002551. PMID 21725476.

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Fractional Fourier transform (English Wikipedia)

arxiv.org

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