Relationship between sampling and multirate filterbanks in the linear canonical transform domain

Abstract

Multirate filterbanks have found applications in speech processing, image processing, communications, and in the development of new sampling theorems. This paper explores the relationship between sampling theorems and multirate filterbanks in the linear canonical transform (LCT) domain. The sampling identity and the interpolation identity for bandlimited signals in the LCT domain are discussed and then employed to obtain a discrete-time implementation for bandlimited signals in the LCT domain from their multichannel samples. Furthermore, we relate the multichannel sampling for bandlimited signals in the LCT domain as well as the corresponding continuous-time LCT filterbank to the discrete-time LCT filterbank, which can lead to new sampling strategies for bandlimited signals in the LCT domain.

Discrete linear canonical wavelet transform and its applications

“…Especially, when choosing filter to be rbio1. 3 and A/B = 53, the proposed LCWT yields better results than the CVT for the MI, Q 0 , and Q W fusion metrics. Besides, the complexity and memory requirement of the 2D LCWT is much smaller than the CVT because of the fast algorithm we proposed here.…”

“…The linear canonical transform (LCT), the generalization of the Fourier transform (FT), the fractional Fourier transform (FrFT), the Fresnel transform and the scaling operations, has been found useful in many applications such as optics [1,2] and signal processing [3][4][5][6][7][8][9][10][11]. Higher concentration and lower sampling rate make the LCT more competent to resolve non-stationary signals.…”

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].…”