Multichannel sampling expansion in the linear canonical transform domain and its application to superresolution

FFT multichannel interpolation and application to image super-resolution

“…, g M (nT ) of the output signals The study of GSE has been extended in various directions. Cheung [10] introduced GSE for real-valued multidimensional signals associated with Fourier transform, while Wei, Ran and Li [11,12] presented the GSE with generalized integral transformation, such as fractional Fourier transform (FrFT) and linear canonical transform (LCT). Some new sampling models in FrFT domain, such as shift-invariant spaces model [13] and multiple sampling rates model [14] were discussed.…”

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

“…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.…”

“…It is central in almost any domain because it provides the link between the continuous physical signals and the discrete domain. As the LCT has recently been found many applications in signal processing, the sampling theorem expansions for the LCT of compact functions in time domain or LCT domain have been derived from different perspectives [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. In particular, the uniform sampling expansions for the band-limited signal in the LCT domain were derived using different methods [21][22][23][24][25][26]; the spectral analysis and reconstruction of a uniform sampled signal band-limited in the LCT domain are presented [23].…”

“…All above-mentioned sampling theorems associated with the LCT are considered as uniform sampling schemes [21][22][23][24][25][26]. However, in some practical engineering applications, more will be encountered in other ways such as non-uniform sampling [32][33][34][35][39][40][41] or multichannel sampling [34][35][36][37][38][42][43][44][45][46][47][48]. In many practical applications, periodic non-uniform sampling and multichannel sampling schemes for band-limited signal in the LCT domain are frequently introduced [32][33][34][35][36][37][38], such as flexible interleaving/ multiplexing analogue-to-digital (A/D) converter for band-limited signal in the LCT domain [35], the orthogonal frequency division multiplexing system based on the LCT for time-frequencyselective channels or multi-input-multi-output (MIMO) systems [8,9], the application in the context of the image super-resolution [37,38] or digital flight control [36].…”

“…The filterbanks interpolation and reconstruction technique have been explored for band-limited signals in the FT domain [49,51]. Recently, multichannel sampling theory and its applications have been addressed in the LCT domain [35][36][37][38]. However, the filterbanks interpolation and reconstruction associated with polyphase structure for multichannel sampling in the LCT domain has never been presented before.…”