Discrete linear canonical txransform of finite chirps

Qing Yun Lee; Bing Zhao Li; Qi Yuan Cheng

doi:10.1016/j.proeng.2012.01.549

Discrete linear canonical txransform of finite chirps

Qing Yun Lee, Bing Zhao Li^*, Qi Yuan Cheng

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Conference article › peer-review

5 Citations (Scopus)

Abstract

Linear canonical transformation (LCT) as an Fourier transform and fractional fourier transform's generalization, is an effective tool for non-stationary signals and has more flexibility, chirp signal can be looked as a typical nonstationary signal. In this letter, we derived closed-form expressions for the DLCT of a finite chirp. It is shown that the DLCT of a finite chirp is zeros at some points, and the number of zeros is related to chirp rate a, the parameter of DLCT α%, and the root of unity N. And if we choose proper DLCT parameters, the finite chirp is again a finite chirp or the original chirp except for a coefficient.

Original language	English
Pages (from-to)	3663-3667
Number of pages	5
Journal	Procedia Engineering
Volume	29
DOIs	https://doi.org/10.1016/j.proeng.2012.01.549
Publication status	Published - 2012
Event	2012 International Workshop on Information and Electronics Engineering, IWIEE 2012 - Harbin, China Duration: 10 Mar 2012 → 11 Mar 2012

Keywords

Discrete linear canonical transform (DLCT)
Finite chirp
Gauss sum
Jacobi symbol

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10.1016/j.proeng.2012.01.549

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title = "Discrete linear canonical txransform of finite chirps",

abstract = "Linear canonical transformation (LCT) as an Fourier transform and fractional fourier transform's generalization, is an effective tool for non-stationary signals and has more flexibility, chirp signal can be looked as a typical nonstationary signal. In this letter, we derived closed-form expressions for the DLCT of a finite chirp. It is shown that the DLCT of a finite chirp is zeros at some points, and the number of zeros is related to chirp rate a, the parameter of DLCT α%, and the root of unity N. And if we choose proper DLCT parameters, the finite chirp is again a finite chirp or the original chirp except for a coefficient.",

keywords = "Discrete linear canonical transform (DLCT), Finite chirp, Gauss sum, Jacobi symbol",

author = "Lee, {Qing Yun} and Li, {Bing Zhao} and Cheng, {Qi Yuan}",

year = "2012",

doi = "10.1016/j.proeng.2012.01.549",

language = "English",

volume = "29",

pages = "3663--3667",

journal = "Procedia Engineering",

issn = "1877-7058",

publisher = "Elsevier B.V.",

note = "2012 International Workshop on Information and Electronics Engineering, IWIEE 2012 ; Conference date: 10-03-2012 Through 11-03-2012",

}

TY - JOUR

T1 - Discrete linear canonical txransform of finite chirps

AU - Lee, Qing Yun

AU - Li, Bing Zhao

AU - Cheng, Qi Yuan

PY - 2012

Y1 - 2012

N2 - Linear canonical transformation (LCT) as an Fourier transform and fractional fourier transform's generalization, is an effective tool for non-stationary signals and has more flexibility, chirp signal can be looked as a typical nonstationary signal. In this letter, we derived closed-form expressions for the DLCT of a finite chirp. It is shown that the DLCT of a finite chirp is zeros at some points, and the number of zeros is related to chirp rate a, the parameter of DLCT α%, and the root of unity N. And if we choose proper DLCT parameters, the finite chirp is again a finite chirp or the original chirp except for a coefficient.

AB - Linear canonical transformation (LCT) as an Fourier transform and fractional fourier transform's generalization, is an effective tool for non-stationary signals and has more flexibility, chirp signal can be looked as a typical nonstationary signal. In this letter, we derived closed-form expressions for the DLCT of a finite chirp. It is shown that the DLCT of a finite chirp is zeros at some points, and the number of zeros is related to chirp rate a, the parameter of DLCT α%, and the root of unity N. And if we choose proper DLCT parameters, the finite chirp is again a finite chirp or the original chirp except for a coefficient.

KW - Discrete linear canonical transform (DLCT)

KW - Finite chirp

KW - Gauss sum

KW - Jacobi symbol

UR - http://www.scopus.com/inward/record.url?scp=84863362541&partnerID=8YFLogxK

U2 - 10.1016/j.proeng.2012.01.549

DO - 10.1016/j.proeng.2012.01.549

M3 - Conference article

AN - SCOPUS:84863362541

SN - 1877-7058

VL - 29

SP - 3663

EP - 3667

JO - Procedia Engineering

JF - Procedia Engineering

T2 - 2012 International Workshop on Information and Electronics Engineering, IWIEE 2012

Y2 - 10 March 2012 through 11 March 2012

ER -

Discrete linear canonical txransform of finite chirps

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Keywords

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