Reconstruction of band-limited signals from multichannel and periodic nonuniform samples in the linear canonical transform domain

Wei, Deyun; Ran, Qiwen; Li, Yuanmin

doi:10.1016/j.optcom.2011.05.010

Cited by 28 publications

(45 citation statements)

References 40 publications

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“…tomography, or due to factors that impinge on our ability to sample regularly, such as jitter, or dropped packets. A number of papers have addressed this issue for a variety of special cases [18,27,31,33,35]. For example, in [31], Tao et al discussed two factors that affect the quality of reconstruction.…”

Section: Nonuniform Samplingmentioning

confidence: 99%

Sampling and Discrete Linear Canonical Transforms

Healy

Özaktaş

2016

Springer Series in Optical Sciences

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A discrete linear canonical transform would facilitate numerical calculations in many applications in signal processing, scalar wave optics, and nuclear physics. The question is how to define a discrete transform so that it not only approximates the continuous transform well, but also constitutes a discrete transform in its own right, being complete, unitary, etc. The key idea is that the LCT of a discrete signal consists of modulated replicas. Based on that result, it is possible to define a discrete transform that has many desirable properties. This discrete transform is compatible with certain algorithms more than others.

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Section: Nonuniform Samplingmentioning

confidence: 99%

Sampling and Discrete Linear Canonical Transforms

Healy

Özaktaş

2016

Springer Series in Optical Sciences

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“…Comparing to the FRFT with one extra degree of freedom and FT without a parameter, the LCT is more flexible and has been found many applications in optics, radar system analysis, signal separation, phase retrieval, pattern recognition, filter design and many others [4,[8][9][10][11][12][13][14][15][16]. As a generalisation of FT and FRFT, the relevant theory of LCT has been developed including the convolution theorem [13][14][15][16], uncertainty principle [17,18], sampling theory [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] and so on; this can enrich the theoretical framework of the LCT and advance the application of the LCT.…”

Section: Introductionmentioning

confidence: 99%

Filterbank reconstruction of band‐limited signals from multichannel samples associated with the LCT

Wei

2017

IET signal process.

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The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. This study addresses the problem of filterbank implementation for multichannel sampling in the LCT domain. First, the interpolation and sampling identities in the LCT domain are derived by the properties of LCT. The interpolation identity is the key result of the current study, which establishes the equivalence of two signal processing operations. One of these uses continuous-timedomain filters, whereas the other uses discrete processing. Then, applying the interpolation identity, the particularly efficient filterbank implementation for derivative sampling, periodic non-uniform sampling and multichannel sampling are obtained in the LCT domain. Moreover, the authors present filterbank implementation using polyphase structures in LCT domain. Furthermore, the simulations are carried out to verify the effectiveness of the results and the potential applications of the multichannel sampling are also presented. Finally, combining the sampling and interpolation identity, they explore the relationship between the multichannel sampling and the filterbank in the LCT domain.

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“…Sampling is fundamental and significant in signal processing and communications because it provides a bridge between continuous and discrete signals. Sampling theorems for a deterministic signal bandlimited in the LCT domain have been extensively studied in the literature [11,18,22,26,[28][29][30][31]. In the real world, however, some random character is inherent in physical signals, and thus, it is much more convenient to model processes as random signals in many practical situations [1,9].…”

Section: Introductionmentioning

confidence: 99%