Extrapolation of Bandlimited Signals in Linear Canonical Transform Domain

Reversible image watermarking technique using LCWT and DGT

“…0 ( )is the LCT of ( ) [13][14][15][16][17][18], satisfying 0 0 − 0 0 . From the LCT domain the canonical convolution with matrix parameter is defined as [2,20] …”

Instantaneous frequency estimation based on the linear canonical transform

“…The classical Shannon sampling theory has been generalized to the LCT domain [19,20], the well known convolution and product theorem [21,22], the uncertainty principles [23] and the spectral analysis [12] are well investigated in the LCT domain. Recently, more results are derived and proposed associate with the ambiguity function [24], the Wigner-Ville distribution [25] and the extrapolation method [26] in the linear canonical transform domain. For the best of our knowledge, there are no paper published associated with the IF estimation in the LCT domain, it is therefore interesting and worthwhile to study the IF estimation methods based on the LCT.…”

A new convolution theorem associated with the linear canonical transform

“…Unfortunately, this claim is not true for the LCT. Therefore, by defining different forms of convolution operators (called canonical convolution operators in order to distinguish from the aforementioned convolution operator associated with the Fourier transform), a variety of convolution theorems for the LCT have been derived, see for example, Pei and Ding [11], Deng et al [5], Wei et al [22,23], Shi et al [15,16]. Pei and Ding [11] introduced a canonical convolution operator O A conv , which is denoted as…”

“…The form (7) is also quite simple with respect to that of Fourier transform. Furthermore, Shi et al [16] introduced a new canonical convolution structure for the LCT, and the canonical convolution operator Θ M is denoted as…”