Convolution, correlation, and sampling theorems for the offset linear canonical transform

Signal, Image and Video Processing

Volumn 8, Issue 3, 2014, Pages 433-442

  Xiang, Qiang ^a,b   Qin, KaiYu ^a  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b SOUTHWEST UNIVERSITY FOR NATIONALITIES   (China)

Author keywords

Convolution theorem; Correlation theorem; Linear canonical transform; Multiplicative filtering; Offset linear canonical transform; Sampling theorem

Indexed keywords

CONVOLUTION; SIGNAL PROCESSING; TIME DOMAIN ANALYSIS;

BAND-LIMITED SIGNAL; CONVOLUTION THEOREMS; DESIGN METHOD; FREQUENCY MODULATED; LINEAR CANONICAL TRANSFORM; PRACTICAL METHOD; SAMPLING THEOREMS; UNIFORM SAMPLING;

MATHEMATICAL TRANSFORMATIONS;

EID: 84894272411     PISSN: 18631703     EISSN: 18631711     Source Type: Journal    
DOI: 10.1007/s11760-012-0342-0     Document Type: Article

References (22)

1. Pei S. C., Ding J. J.: Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms. J. Opt. Soc. Am. A 20(3), 522-532 (2003).
2. Stern A.: Sampling of compact signals in the offset linear canonical domain. Signal Image Video Process. 1(4), 359-367 (2007).
3. Pei S. C., Ding J. J.: Eigenfunctions of Fourier and fractional Fourier transforms with complex offsets and parameters. In: IEEE Trans. Circuits Syst. I 54(7), 1599-1611 (2007).
4. Abe S., Sheridan J. T.: Optical operations on wave functions as the Abelian Subgroups of the special affine Fourier transformation. Opt. Lett. 19(22), 1801-1803 (1994).
5. Moshinsky M., Quesne C.: Linear canonical transformations and their unitary representations. J. Math. Phys. 12(8), 1772-1783 (1971).
6. Pei S. C., Ding J. J.: Relations between fractional operations and time-frequency distributions, and their applications. In: IEEE Trans. Signal Process. 49, 1638-1655 (2001).
7. Sharma K. K., Joshi S. D.: Signal separation using linear canonical and fractional Fourier transforms. Opt. Commun. 265(2), 454-460 (2006).
8. Almeida L. B.: The fractional Fourier transform and time-frequency representations. In: IEEE Trans. Signal Process. 42(11), 3084-3091 (1994).
9. James D. F. V., Agarwal G. S.: The generalized Fresnel transform and its applications to optics. Opt. Commun. 126(5), 207-212 (1996).
10. Ozaktas H. M., Zalevsky Z., Kutay M. A.: The Fractional Fourier Transform with Applications in Optics and Signal Processing. Wiley, New York (2000).
11. Akay O., Boudreaux B. G. F.: Fractional convolution and correlation via operator methods and application to detection of linear FM signals. In: IEEE Trans. Signal Process. 49, 979-993 (2001).
12. Torres R., Pellat F. P., Torres Y.: Fractional convolution, fractional correlation and their translation invariance properties. Signal Process. 90, 1976-1984 (2010).
13. Almeida L. B.: Product and convolution theorems for the fractional Fourier transform. In: IEEE Trans. Signal Proc. Lett. 4, 15-17 (1997).
14. Zayed A. I.: A product and convoution theorems for the fractional Fourier transform. In: IEEE Trans. Signal Proc. Lett. 5, 101-103 (1998).
15. Deng B., Tao R., Wang Y.: Convolution theorems for the linear canonical transform and their applications. Sci. China (Ser. E Information Science) 49(5), 592-603 (2006).
16. Wei D. Y., Ran Q. W., Li Y. M., Ma J., Tan L. Y.: A convolution and product theorem for the linear canonical transform. In: IEEE Signal Process. Lett. 16(10), 853-856 (2009).
17. Wei, D. Y., Ran, Q. W., Li, Y. M.: A convolution and correlation theo- rem for the linear canonical transform and its application. Circuits Syst. Signal Process. (2011). doi: 10. 1007/s00034-011-9319-4.
18. Zayed A. I.: Function and Generalized Function Transformations. CRC, Boca Raton, FL (1996).
19. Candan C., Ozaktas H. M.: Sampling and series expansion theorems for fractional Fourier and other transform. Signal Process. 83(11), 2455-2457 (2003).
20. Erseghe T., Kraniauskas P., Cariolaro G.: Unified fractional Fourier transform and sampling theorem. In: IEEE Trans. Signal Process. 47(12), 3419-3423 (1999).
21. Li B. Z., Tao R., Wang Y.: New sampling formulae related to linear canonical transform. Signal Process. 87(5), 983-990 (2007).
22. Stern A.: Sampling of linear canonical transformed signals. Signal Process. 86(7), 1421-1425 (2006).