Open AccessApplication of linear canonical transform correlation for detection of linear frequency modulated signals
Author(s) -
Li Yuanchao,
Zhang Feng,
Li Yanbin,
Tao Ran
Publication year - 2016
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
ISSN - 1751-9683
DOI - 10.1049/iet-spr.2015.0041
Subject(s) - autocorrelation , fractional fourier transform , mathematics , algorithm , operator (biology) , chirp , ambiguity function , fourier transform , unitary operator , linear map , unitary state , signal processing , computer science , mathematical analysis , fourier analysis , hilbert space , statistics , optics , physics , waveform , telecommunications , pure mathematics , radar , repressor , law , laser , chemistry , biochemistry , political science , transcription factor , gene
Linear canonical transform (LCT), which can be deemed to be a generalisation of the fractional Fourier transform, has been used in several areas, including signal processing and optics. Motivated by the operator theory, a new unitary operator associated with the LCT is introduced. This new operator generalises the unitary fractional operator which is proposed by Akay et al . recently. Via operator manipulations, the authors also derive a new definition, the LCT correlation operation, and present an alternative and efficient implementation of it. It is shown that the proposed LCT autocorrelation corresponds to radial slices of the ambiguity function in the ambiguity plane. On the basis of this relationship, an application of the fast LCT autocorrelation for detection and parameter estimation with respect to the chirp rates of linear frequency modulated signals corrupted by noise is proposed. Finally, the validity of the proposed method is verified by simulation results.