Reconstruction of digital spectrum from periodic nonuniformly sampled signals in offset linear canonical transform domain

Xu, Shuiqing; Chai, Yi; Hu, Youqiang; Jiang, Congmei; Li, Yang

doi:10.1016/j.optcom.2015.03.027

Cited by 31 publications

(17 citation statements)

References 29 publications

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“…For example, sampling theorems, convolution and correlation theorems, eigenfunctions, energy concentration problems, generalized prolate spheroidal wave functions, and spectral analysis of the OLCT have been derived extensively in previous studies. 2,[19][20][21][22][23][24] However, to the best of our knowledge, there are few results concerning the uncertainty principle for the OLCT. 2,25 In this paper, therefore, we complement it by deriving other different forms of uncertainty principle associated with the OLCT.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty principles associated with the offset linear canonical transform

Huo

Sun

Xiao

2018

Math Methods in App Sciences

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As a time‐shifted and frequency‐modulated version of the linear canonical transform (LCT), the offset linear canonical transform (OLCT) provides a more general framework of most existing linear integral transforms in signal processing and optics. To study simultaneous localization of a signal and its OLCT, the classical Heisenberg's uncertainty principle has been recently generalized for the OLCT. In this paper, we complement it by presenting another two uncertainty principles, ie, Donoho‐Stark's uncertainty principle and Amrein‐Berthier‐Benedicks's uncertainty principle, for the OLCT. Moreover, we generalize the short‐time LCT to the short‐time OLCT. We likewise present Lieb's uncertainty principle for the short‐time OLCT and give a lower bound for its essential support.

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Section: Introductionmentioning

confidence: 99%

Uncertainty principles associated with the offset linear canonical transform

Huo

Sun

Xiao

2018

Math Methods in App Sciences

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“…It performs an affine mapping of the time frequency distribution of the signal because it has additional degrees of freedom [31,32]. So, the LCT is more flexible and suitable for processing nonstationary signals, particularly in the linear frequency modulated (LFM) signals [33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Gear Fault Diagnosis in Variable Speed Condition Based on Multiscale Chirplet Path Pursuit and Linear Canonical Transform

Zhang

Chai

et al. 2018

Complexity

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The vibration signals analysis is a very effective and reliable method for detecting the gear failures. Because the vibration signals acquired from the gear in the variable speed condition often contain more useful fault information, the analysis of the gear vibration signals during the variable speed condition has been a hot research topic. In this paper, a method based on the multiscale chirplet path pursuit (MSCPP) and the linear canonical transform (LCT) has been applied to diagnose the gear fault in the variable speed condition for the first time. First, by using the MSCPP method to estimate the instantaneous meshing frequency, the suitable signal segment approximation to the acceleration or deceleration process can be selected. Then, because the LCT is a novel and efficient nonstationary signals analysis tool, the optimal LCT spectrum of the selected signal has been attainted to diagnose the gear faults based on the properties of the LCT. In addition, the simulations and the experimental evaluation are provided to verify the effectiveness of the proposed method.

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“…We also analyze the evolution of spatial information along the longitudinal direction and show that the spherical reference surfaces should be equally spaced with respect to the fractional Fourier transform order. Our results are relevant to work on both sampling and fast computation of light fields propagating through quadratic-phase systems [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Optimal representation and processing of optical signals in quadratic-phase systems

Arık

Özaktaş

2016

Optics Communications

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a b s t r a c tOptical fields propagating through quadratic-phase systems (QPSs) can be modeled as magnified fractional Fourier transforms (FRTs) of the input field, provided we observe them on suitably defined spherical reference surfaces. Non-redundant representation of the fields with the minimum number of samples becomes possible by appropriate choice of sample points on these surfaces. Longitudinally, these surfaces should not be spaced equally with the distance of propagation, but with respect to the FRT order. The non-uniform sampling grid that emerges mirrors the fundamental structure of propagation through QPSs. By providing a means to effectively handle the sampling of chirp functions, it allows for accurate and efficient computation of optical fields propagating in QPSs.

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Reconstruction of digital spectrum from periodic nonuniformly sampled signals in offset linear canonical transform domain

Cited by 31 publications

References 29 publications

Uncertainty principles associated with the offset linear canonical transform

Uncertainty principles associated with the offset linear canonical transform

Gear Fault Diagnosis in Variable Speed Condition Based on Multiscale Chirplet Path Pursuit and Linear Canonical Transform

Optimal representation and processing of optical signals in quadratic-phase systems

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