New sampling formulae for non-bandlimited signals associated with linear canonical transform and nonlinear Fourier atoms

被引：50

作者：

Liu, Yue-Lin ^{[1
]}

Kou, Kit-Ian ^{[1
]}

Ho, Io-Tong ^{[1
]}

机构：

[1] Univ Macau, Dept Math, Taipa, Peoples R China

来源：

SIGNAL PROCESSING | 2010年 / 90卷 / 03期

关键词：

Sampling theorem; Linear canonical transform; Non-bandlimited signal; Generalized sinc function; Parameter M-Hilbert transform; THEOREM;

D O I：

10.1016/j.sigpro.2009.09.030

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

The sampling theory is basic and crucial in engineering sciences. On the other hand, the linear canonical transform (LCT) is also of great power in optics, filter design, radar system analysis and pattern recognition, etc. The Fourier transform (FT), the fractional Fourier transform (FRFT), Fresnel transform (FRT) and scaling operations are considered as special cases of the LCT. In this paper, we structure certain types of non-bandlimited signals based on two ladder-shape filters designed in the LCT domain. Subsequently, these non-bandlimited signals are reconstructed from their samples together with the generalized sinc function, their parameter M-Hilbert transforms or their first derivatives and other information provided by the phase function of the nonlinear Fourier atom which is the boundary value of the Mobius transform, respectively. Simultaneously, mathematical characterizations for these non-bandlimited signals are given. Experimental results presented also offer a foundation for the sampling theorems established. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：933 / 945

页数：13

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