Aliased polyphase sampling associated with the linear canonical transform

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].…”

Application of linear canonical transform correlation for detection of linear frequency modulated signals

“…In past decades, the FRFT has attracted much attention in the signal processing community [7][8][9]. As the generalisation of the FRFT, the LCT is at the initial stage to be utilised to analyse a signal processing system [10,11].…”

Reconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain

“…Signal reconstruction from its samples is an important signal processing operation, which is needed very frequently in several diverse areas, such as signal processing, communications, geophysics, radar and sonar and optics including optical signal processing [23][24][25]. As the LCT has recently been found, many applications in digital and optics signal processing and the sampling theorem expansions for the bandlimited or the timelimited continuous signal in the LCT domain have been studied from different angles in the literature [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. These sampling theorems establish the fact that a bandlimited or timelimited signal in the LCT domain can be completely reconstructed by a set of equidistantly spaced signal samples [26][27][28][29][30][31][32][33][34][35][36][37][38].…”

“…As the LCT has recently been found, many applications in digital and optics signal processing and the sampling theorem expansions for the bandlimited or the timelimited continuous signal in the LCT domain have been studied from different angles in the literature [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. These sampling theorems establish the fact that a bandlimited or timelimited signal in the LCT domain can be completely reconstructed by a set of equidistantly spaced signal samples [26][27][28][29][30][31][32][33][34][35][36][37][38]. However, there are a variety of applications in which the data are sampled in other ways, such as non-uniformly in time or through multichannel data acquisition [39][40][41][42][43][44][45][46][47][48][49][50][51][52]…”