Open Access
Linear Canonical Transform and Its Implication
Deng Bing,Tao Ran +1 more
TLDR
The definition of LCT and some special cases are given at first, followed by its properties as listed, and the discrete linear canonical transform is introduced.Abstract:
As an emerging tool for signal processing,the linear canonical transform(LCT) proves itself to be more general and flexible than the Fourier transform as well as the fractional Fourier transform.So it can slove problems that can't be dealt with well by the latter.In this paper,the definition of LCT and some special cases are given at first,followed by its properties as listed.Besides,the discrete linear canonical transform is introduced.The implication of LCT is illustrated finally,displaying(LCT's) potentials and capabilities in the field of signal processing.read more
Citations
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Journal ArticleDOI
Uncertainty Principles for Wigner-Ville Distribution Associated with the Linear Canonical Transforms
TL;DR: In this paper, the uncertainty principle for Wigner-Ville distribution and ambiguity function associate with the linear canonical transform was obtained and the -dimensional cases were investigated in detail based on the proposed Heisenberg uncertainty principle of the linear Canonical Transform.
Journal ArticleDOI
New Integral Transforms for Generalizing the Wigner Distribution and Ambiguity Function
Zhichao Zhang,Mao-Kang Luo +1 more
TL;DR: New integral transforms that can be regarded as the generalization of LCWD, LCAF, WDL, and AFL are introduced and shown to be useful and effective in filter design in the LCT domain for the separation of multi-component signals and detection of linear frequency-modulated (LFM) signals.
Journal ArticleDOI
Sliding Discrete Linear Canonical Transform
Yan-Nan Sun,Bing-Zhao Li +1 more
TL;DR: This paper introduces a scheme for the single-point DLCT, which can effectively calculate a single or a few linear canonical spectra, and presents two methods to assess performance with regard to computational complexity and precision and to show the correctness of the derived results.
Journal ArticleDOI
Linear Canonical Wigner Distribution Based Noisy LFM Signals Detection Through the Output SNR Improvement Analysis
TL;DR: A mathematical theory foundation of the output signal-to-noise ratio (SNR) improvement, an output SNR inequality relation between the traditional WD and the CICFWD for a general noisy signal, and how to solve this inequality to come out LCT free parameters is formulated.
Journal ArticleDOI
Tighter uncertainty principles for linear canonical transform in terms of matrix decomposition
TL;DR: This study discusses the lower bound of uncertainty product of complex signals in two LCT domains through using this matrix's rotation orthogonal decomposition mainly and formulates two kinds of lower bounds, which are tighter than the existing ones proposed respectively by Xu et al and Dang et al.
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