New sampling formulae for the fractional Fourier transform
Signal Processing
Sampling of linear canonical transformed signals
Signal Processing
Eigenfunctions of linear canonical transform
IEEE Transactions on Signal Processing
Method for defining a class of fractional operations
IEEE Transactions on Signal Processing
The fractional Fourier transform and time-frequency representations
IEEE Transactions on Signal Processing
On generalized stable nonuniform sampling expansions involving derivatives
IEEE Transactions on Information Theory
Sampling rate conversion for linear canonical transform
Signal Processing
Sampling and discretization of the linear canonical transform
Signal Processing
IEEE Transactions on Signal Processing
Generalized prolate spheroidal wave functions associated with linear canonical transform
IEEE Transactions on Signal Processing
A fast algorithm for the linear canonical transform
Signal Processing
Speech recovery based on the linear canonical transform
Speech Communication
Multi-channel filter banks associated with linear canonical transform
Signal Processing
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Linear canonical transform (LCT) is an integral transform with four parameters a, b, c, d and has been shown to be a powerful tool for optics, radar system analysis, filter design, phase retrieval, pattern recognition, and many other applications. Many well-known transforms such as the Fourier transform, the fractional Fourier transform, and the Fresnel transform can be seen as special cases of the linear canonical transform. In this paper, new sampling formulae for reconstructing signals that are band-limited or time-limited in the linear canonical transform sense have been proposed. Firstly, the sampling theorem representation of band-limited signals associated with linear canonical transform from the samples taken at Nyquist rate is derived in a simple way. Then, based on the relationship between the Fourier transform and the linear canonical transform, the other two new sampling formulae using samples taken at half the Nyquist rate from the signal and its first derivative or its generalized Hilbert transform are obtained. The well-known sampling theorems in Fourier domain or fractional Fourier domain are shown to be special cases of the achieved results. The experimental results are also proposed to verify the accuracy of the obtained results. Finally, discussions about these new results and future works related to the linear canonical transform are proposed.