Open AccessReconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain
Author(s) -
Wei Deyun,
Li Yuanmin
Publication year - 2014
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/iet-spr.2013.0240
Subject(s) - bandlimiting , signal reconstruction , algorithm , convolution (computer science) , mathematics , sampling (signal processing) , kernel (algebra) , basis function , frequency domain , signal processing , spectral leakage , iterative reconstruction , nonuniform sampling , multidimensional signal processing , context (archaeology) , transfer function , computer science , fourier transform , filter (signal processing) , fast fourier transform , artificial intelligence , computer vision , digital signal processing , mathematical analysis , quantization (signal processing) , discrete mathematics , artificial neural network , computer hardware , engineering , biology , paleontology , electrical engineering
The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. In this study, the authors address the problem of signal reconstruction from the multidimensional multichannel samples in the LCT domain. Firstly, they pose and solve the problem of expressing the kernel of the multidimensional LCT in the elementary functions. Then, they propose the multidimensional multichannel sampling (MMS) for the bandlimited signal in the LCT domain based on a basis expansion of an exponential function. The MMS expansion which is constructed by the ordinary convolution structure can reduce the effect of the spectral leakage and is easy to implement. Thirdly, based on the MMS expansion, they obtain the reconstruction method for the multidimensional derivative sampling and the periodic non‐uniform sampling by designing the system filter transfer functions. Finally, the simulation results and the potential applications of the MMS are presented. Especially, the application of the multidimensional derivative sampling in the context of the image scaling about the image super‐resolution is discussed.