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Proceedings Paper

Study on sampling of continuous linear system based on generalized Fourier transform
Author(s): Huiguang Li
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Paper Abstract

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

Paper Details

Date Published: 2 September 2003
PDF: 10 pages
Proc. SPIE 5253, Fifth International Symposium on Instrumentation and Control Technology, (2 September 2003); doi: 10.1117/12.521532
Show Author Affiliations
Huiguang Li, Yanshan Univ. (China)


Published in SPIE Proceedings Vol. 5253:
Fifth International Symposium on Instrumentation and Control Technology
Guangjun Zhang; Huijie Zhao; Zhongyu Wang, Editor(s)

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