Fast communication: Generalized entropic uncertainty principle on fractional Fourier transform

Authors:
Xu Guanlei;Wang Xiaotong;Xu Xiaogang
Affiliations:
Dalian Naval Academy, Department of Navigation, Dalian of China 116018, China and Dalian Naval Academy, Institute of Photoelectric Technology, Dalian of China 116018, China;Dalian Naval Academy, Department of Navigation, Dalian of China 116018, China and Dalian Naval Academy, Institute of Photoelectric Technology, Dalian of China 116018, China;Dalian Naval Academy, Department of Automatization, Dalian of China 116018, China and Dalian Naval Academy, Institute of Photoelectric Technology, Dalian of China 116018, China
Venue:
Signal Processing
Year:
2009

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Abstract

The entropic uncertainty principle is an element in information theory and plays an important role in signal processing. Based on the relations between the original function and the definition of the fractional Fourier transform (FRFT), two novel entropic uncertainty principles in FRFT domains, in which one is Shannon entropy uncertainty principle and the other is Renyi entropy uncertainty principle, are derived, which are associated with the FRFT parameters. In addition, the extended Renyi entropy uncertainty principle for multiple functions and discrete entropy uncertainty principle are explored as well. These inequalities disclose the relations between the bounds and the transform parameters and sampling periods.