A Fast Algorithm of Linear Canonical Transformation for Radar Signal Processing System

Abstract:

Linear canonical transformation is a new signal processing tools developing in recent years. As a unified multi-parameter linear integral transform, linear canonical transformation has its unique advantages when dealing with non-stationary signal. However, from the existing literatures, the basic theoretical system is not perfect, some of the theories associated with signal processing needs to be further established or strengthened, the research of linear canonical transformation has important theoretical significance and practical significance, but linear canonical transformation needs a lot of calculation, it is not like Fourier transform, fractional Fourier transform, Fresnel transform and scale operator, they have already been widely used in various fields of expertise, in order to reduce the amount of calculation, this paper puts forward a fast algorithm which uses duality theorem of linear canonical transformation to reduce the amount of calculation, it can quickly complete the operation when we use linear canonical transformation to process the signal during radar signal processing, the time for normal algorithm is 5s, the fast algorithm needs only 0.2s.

• Periodical: Advanced Materials Research (Volumes 1049-1050)
• Pages: 1245-1248
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1049-1050.1245
• Online since: October 2014
• Authors: Yan Xin Yu*, Chun Yang Wang, Yu Chen, Hong Yan Sun
• Keywords: Duality, Fractional Fourier Transform, Linear Canonical Transformation

References

[1] K. K. Sharma , S. D. Joshi. Signal separation using linear canonical and fractional Fourier transforms[J]. Opt. Communications, 2006, 265(2): 454-460.

DOI: 10.1016/j.optcom.2006.03.062

[2] T. Erseghe, P. Kraniauskas, G. Cariolaro. Unified fractional Fourier transform and sampling theorem[J]. IEEE Trans. Signal Process. 1999, 47 (12): 3419-3423.

DOI: 10.1109/78.806089

[3] L.M. Bernardo. ABCD matrix formalism of fractional Fourier optics[J]. Opt. Eng. 1996, 35(3): 732-740.

DOI: 10.1117/1.600641

[4] D.Y. Wei, Q.W. Ran, Y.M. Li. Generalized sampling expansion for bandlimited signals associated with the fractional Fourier transform [J]. IEEE Signal Processing Letters, (2010).

DOI: 10.1109/lsp.2010.2048642

[5] R. Torres, F.P. Pellat, Y. Torres. Fractional convolution, fractional correlation and their translation invariance properties[J]. Signal Process. 2010, 90(6): 1976-(1984).

DOI: 10.1016/j.sigpro.2009.12.016

[6] C. Candan, H.M. Ozaktas. Sampling and series expansion theorems for fractional Fourier and other transform [J]. Signal Process. 2003, 83 (11): 2455-2457.

DOI: 10.1016/s0165-1684(03)00196-8