References
- A. Bhandari and A. I. Zayed, Shift-invariant and sampling spaces associated with the fractional Fourier transform domain, IEEE T. Signal Process. 60(4) (2012), 1627-1637. https://doi.org/10.1109/TSP.2011.2177260
- C. Candan and H. M. Ozaktas, Sampling and series expansion theorems for fractional Fourier and other transforms, Signal Process. 83(11) (2003), 2455-2457. https://doi.org/10.1016/S0165-1684(03)00196-8
- O. Christensen, Frames and bases, an introductory course, Birkhauser, Boston, 2008.
-
A. G. Garcia, G. Perez-Villalon, and A. Portal, Riesz bases in
$L^2$ (0; 1) related to sampling in shift-invariant spaces, J. Math. Anal. Appl. 308(2) (2005), 703-713. https://doi.org/10.1016/j.jmaa.2004.11.058 - J. R. Higgins, Sampling theory in Fourier and signal analysis, Volume 1: Foundations, Oxford University Press, USA, 1996.
- A. J. Jerri, Shannon Sampling Theorem - Its Various Extensions and Applications - Tutorial Review, Proceedings of the IEEE 65(11) (1977), 1565-1596. https://doi.org/10.1109/PROC.1977.10771
- J. M. Kim and K. H. Kwon, Sampling expansion in shift invariant spaces, Int. J. Wavelets Multiresolut. Inf. Process. 6(2) (2008), 223-248. https://doi.org/10.1142/S021969130800232X
- V. A. Kotelnikov, On the transmission capacity of the 'ether' and of cables in electrical communications, Izd Red Upr Svyazzi RKKA Translated from the Russian by V. E. Katsnelson, Appl. Numer. Harmon. Anal., Modern sampling theory, Birkhauser Boston, Boston, MA, 2001. (1933), 27-45.
- A. C. McBride and F. H. Kerr, On Namias's Fractional Fourier Transforms, IMA J. Appl. Math. 39(2) (1987), 159-175. https://doi.org/10.1093/imamat/39.2.159
- V. Namias, The fractional order Fourier transform and its application to quantum mechanics, IMA J. Appl. Math. 25(3) (1980), 241-265. https://doi.org/10.1093/imamat/25.3.241
- E. Sejdic, I. Djurovic and L. Stankovic, Fractional Fourier transform as a signal processing tool An overview of recent developments, Signal Process. 91(6) (2011), 1351-1369. https://doi.org/10.1016/j.sigpro.2010.10.008
- C. E. Shannon, Communication in the presence of noise, Proc. IRE 37 (1949), 10-21.
- J. Shi, W. Xiang, X. Liu, and N. Zhang, A sampling theorem for the fractional Fourier transform without band-limiting constraints, Signal Process. 98 (2014), 158-165. https://doi.org/10.1016/j.sigpro.2013.11.026
- R. Tao, B. Deng, W. Q. Zhang and Y. Wang, Sampling and Sampling Rate Conversion of Band Limited Signals in the Fractional Fourier Transform Domain, IEEE T. Signal Process. 56(1) (2008), 158-171. https://doi.org/10.1109/TSP.2007.901666
- R. Torres, P. Pellat-Finet and Y. Torres, Sampling Theorem for Fractional Bandlimited Signals: A Self-Contained Proof. Application to Digital Holography, IEEE Signal Proc. Let. 13(11) (2006), 676-679. https://doi.org/10.1109/LSP.2006.879470
- M. Unser, Sampling - 50 years after Shannon, Proceedings of the IEEE 88(4) (2000), 569-587. https://doi.org/10.1109/5.843002
- E. T. Whittaker, On the functions which are represented by the expansions of the interpolation theory, Proc. Royal. Soc. Edinburgh 35 (1915), 181-194. https://doi.org/10.1017/S0370164600017806
- A. I. Zayed, On the relationship between the Fourier and fractional Fourier transforms, IEEE Signal Proc. Let. 3(12) (1996), 310-311. https://doi.org/10.1109/97.544785
- A. I. Zayed, A convolution and product theorem for the fractional Fourier transform, IEEE Signal Proc. Let. 5(4) (1998), 101-103. https://doi.org/10.1109/97.664179