Novel uncertainty relations associated with fractional Fourier transform

doi:10.1088/1674-1056/19/1/014203

Abstract In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform (FRFT) domains, are presented and three theorems on the uncertainty principle in FRFT domains are also developed. Theorem 1 gives the bounds of two spreads in two FRFT domains. Theorem 2 shows the uncertainty relation between two group delays in two FRFT domains. Theorem 3 presents the crossed uncertainty relation between one group delay and one spread in two FRFT domains. The novelty of their results lies in connecting the products of different physical measures and giving their physical interpretations. The existing uncertainty principle in the FRFT domain is only a special case of theorem 1, and the conventional uncertainty principle in time-frequency domains is a special case of their results. Therefore, three theorems develop the relations of two spreads in time-frequency domains into the relations between two spreads, between two group delays, and between one spread and one group delay in FRFT domains.

Keywords: fractional Fourier transform (FRFT) uncertainty principle time-frequency spreads group delay

Received: 21 August 2008
Revised: 23 November 2008
Accepted manuscript online:

PACS:	03.65.Ta	(Foundations of quantum mechanics; measurement theory)
	02.30.Nw	(Fourier analysis)
	02.30.Uu	(Integral transforms)
	03.65.Db	(Functional analytical methods)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60473141) and the Natural Science Foundation of Liaoning Province of China (Grant No. 20062191).

Cite this article:

Xu Guan-Lei(徐冠雷), Wang Xiao-Tong(王孝通), and Xu Xiao-Gang(徐晓刚) Novel uncertainty relations associated with fractional Fourier transform 2010 Chin. Phys. B 19 014203

[1]	Exampleh V, Ozaktas M and Aytur O 1995 Signal Process. 46 119
[2]	Tao R, Qi L and Wang Y 2004 Theory and Application of the Aroctional Fourier Transform (Beijing: Tsinghua University Press) p23 (in Chinese)
[3]	Yuan L 2008 Chin. Phys. B 17 170
[4]	Namias V 1980 J. Inst. Math. Appl. 25 241
[5]	McBride A C and Kerr F H 1987 IMA J. Appl. Math. 39 159
[6]	Bo W R G, Ping Z L, Ren H P, Sheng Y L and Wu W K 2003 Chin. Phys. 12 610
[7]	Jian X H, Zhang C M and Zhao B C 2007 Acta Phys. Sin. 56 824 (in Chinese)
[8]	Shinde S and Vikram G M 2001 IEEE Trans. Signal Processing 49 2545
[9]	Mustard D 1991 J. Austral. Math. 33 180
[10]	Chen T L, Lü B D and Wu P 2005 Chin. Phys. 14 1130
[11]	Namias V 1980 J. Inst. Math. Appl. 25 241
[12]	Selig K K 2001 Tech. Rep. [Online]. Available: http://www-lit.ma.tum.de/veroeff/quel/010.47001.pdf
[13]	Chen T L, Lü B D and Wu P 2005 Acta Phys. Sin. 54 658 (in Chinese)
[14]	Zayed A I 1996 IEEE Signal Processing Lett. 3 310
[15]	Deng W J, Xu Y H and Liu P 2003 Acta Phys. Sin. 52 2961 (in Chinese)
[16]	Shu F W and Shen Y G 2007 Chin. Phys. 16 2497
[17]	Hu S Q and Zhao R 2005 Chin. Phys. 14 1477
[18]	Chen B X, Li M and Zhang A J 2007 Acta Phys. Sin. 56 4535 (in Chinese)
[19]	Jiang X J, Lin Z Q, Zhou S L and Zhu J 2006 Acta Phys. Sin. 55 5824 (in Chinese)
[20]	Yang X P and Zhai H T 2005 Acta Phys. Sin. 54 1578 (in Chinese)
[21]	Ma R Q, Li Y F and Shi J 2008 Acta Phys. Sin. 57 4083 (in Chinese)
[22]	Xia L L, Li X C and Wang X J 2009 Acta Phys. Sin. 58 28 (in Chinese)
[23]	Li Y F, Ma R Q and Shi J 2008 Acta Phys. Sin. 57 5593 (in Chinese)

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