Convolution and correlation theorems for the offset fractional Fourier transform and its application

AEU - International Journal of Electronics and Communications

Volumn 70, Issue 2, 2016, Pages 138-150

  Goel, Navdeep ^a   Singh, Kulbir ^b  

^a PUNJABI UNIVERSITY   (India)

^b THAPAR UNIVERSITY   (India)

Author keywords

Convolution theorem; Correlation theorem; Multiplicative filter; Offset fractional Fourier transform

Indexed keywords

FAST FOURIER TRANSFORMS; FREQUENCY MODULATION; SIGNAL PROCESSING; TIME DOMAIN ANALYSIS;

BAND-LIMITED SIGNAL; CONVOLUTION THEOREMS; DESIGN METHOD; EFFECT OF TIME; FRACTIONAL FOURIER TRANSFORMS; ITS APPLICATIONS; MODULATION PARAMETERS; MULTIPLICATIVE FILTER;

CONVOLUTION;

EID: 84953635908     PISSN: 14348411     EISSN: 16180399     Source Type: Journal    
DOI: 10.1016/j.aeue.2015.10.009     Document Type: Article

References (37)

1. S.C. Pei, and J.J. Ding Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms J Opt Soc Am A 20 3 2003 522 532
2. S.C. Pei, and J.J. Ding Eigenfunctions of Fourier and fractional Fourier transforms with complex offsets and parameters IEEE Trans Circuits Syst I 54 7 2007 1599 1611
3. J.W. Goodman Introduction to Fourier optics 2005 McGraw-Hill New York
4. J.W. Goodman International trends in optics 1991 Academic Press New York
5. F.G. Stremler Introduction to communication systems 1982 Addison-Wesley Massachusetts
6. 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 5 2005 917 927
7. A. Akan, and E. Onen A discrete fractional Gabor expansion for multi-component signals Int J Electron Commun 61 5 2007 279 285
8. S.C. Pei, and J.J. Ding Relations between fractional operations and time-frequency distributions, and their applications IEEE Trans Signal Process 49 8 2001 1638 1655
9. L.B. Almeida The fractional Fourier transform and time-frequency representations IEEE Trans Signal Process 42 11 1994 3084 3091
10. H.M. Ozaktas, Z. Zalevsky, and M.A. Kutay The fractional Fourier transform with applications in optics and signal processing 2001 Wiley New York
11. T.Z. Xu, and B.Z. Li Linear canonical transform and its applications 2013 Science Press Beijing, China
12. A.K. Singh, and R. Saxena On convolution and product theorems for FRFT Wirel Pers Commun 65 01 2012 189 201
13. H.M. Ozaktas, B. Barshan, D. Mendlovic, and L. Onural Convolution, filtering, and multiplexing in fractional Fourier domains and their relationship to chirp and wavelet transforms J Opt Soc Am A 11 2 1994 547 559
14. O. Akay, and G.F. Boudreaux-Bartels Fractional convolution and correlation via operator methods and application to detection of linear FM signals IEEE Trans Signal Process 49 5 2001 979 993
15. D. Mendlovic, Y. Bitran, R.G. Dorsch, and A.W. Lohmann Optical fractional correlation: experimental results J Opt Soc Am A 12 8 1995 1665 1670
16. D. Mendlovic, H.M. Ozaktas, and A.W. Lohmann Fractional correlation Appl Opt 34 2 1995 303 309
17. R. Torres, P. Pellat-Finet, and Y. Torres Fractional convolution, fractional correlation and their translation invariance properties Signal Process 90 6 2010 1976 1984
18. A. Borsellino, and T. Poggio Convolution and correlation algebras Kybernetik 13 2 1973 113 122
19. M. Moshinsky, and C. Quesne Linear canonical transformations and their unitary representations J Math Phys 12 1971 1772 1783
20. L. Almeida Product and convolution theorems for the fractional Fourier transform IEEE Signal Process Lett 4 1 1997 15 17
21. A. Zayed A convolution and product theorem for the fractional Fourier transform IEEE Signal Process Lett 5 4 1998 101 103
22. B. Deng, R. Tao, and Y. Wang Convolution theorem for the linear canonical transform and their applications Sci China Ser F: Inf Sci 49 5 2006 592 603
23. D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan A convolution and product theorem for the linear canonical transform IEEE Signal Process Lett 16 10 2009 853 856
24. D. Wei, Q. Ran, and Y.-M. Li A convolution and correlation theorem for the linear canonical transform and its application Circuits Syst Signal Process 31 1 2012 301 312
25. D. Wei, Q. Ran, and Y.-M. Li Multichannel sampling expansion in the linear canonical transform domain and its application to superresolution Opt Commun 284 23 2011 5424 5429
26. Q. Xiang, and K. Qin Convolution, correlation, and sampling theorems for the offset linear canonical transform Signal Image Video Process 8 3 2014 433 442
27. D. Wei, Q. Ran, and Y. Li New convolution theorem for the linear canonical transform and its translation invariance property Optik - Int J Light Electron Opt 123 16 2012 1478 1481
28. J. Shi, Y. Chi, and N. Zhang Multichannel sampling and reconstruction of bandlimited signals in fractional Fourier domain IEEE Signal Process Lett 17 11 2010 909 912
29. J. Shi, X. Liu, X. Sha, and N. Zhang Sampling and reconstruction of signals in function spaces associated with the linear canonical transform IEEE Trans Signal Process 60 11 2012 6041 6047
30. J. Shi, X. Liu, and N. Zhang Generalized convolution and product theorems associated with linear canonical transform Signal, Image Video Process 8 5 2014 967 974
31. J. Shi, X. Sha, X. Song, and N. Zhang Generalized convolution theorem associated with fractional Fourier transform Wirel Commun Mob Comput 14 13 2014 1340 1351
32. A.M. Mathai Jacobians of matrix transformations and functions of matrix arguments 1997 World Scientific Singapore
33. C. Candan, M.A. Kutay, and H.M. Ozaktas The discrete fractional Fourier transform IEEE Trans Signal Process 48 5 2000 1329 1337
34. D. Wei, and Q. Ran Multiplicative filtering in the fractional Fourier domain Signal Image Video Process 7 3 2013 575 580
35. N. Goel, and K. Singh Modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics Int J Appl Math Comput Sci 23 3 2013 685 695
36. N. Goel, and K. Singh Modified correlation theorem for the linear canonical transform with representation transformation in quantum mechanics Signal Image Video Process 08 02 2014 595 601
37. S.S. Fan, B.Z. Li, and T.Z. Xu A two-channel perfect reconstruction filter bank associated with the linear canonical transform Int J Electron Lett 2 2 2014 72 82