Sampling of linear canonical transformed signals
Signal Processing
New sampling formulae related to linear canonical transform
Signal Processing
Sampling and discretization of the linear canonical transform
Signal Processing
Uncertainty principles for linear canonical transform
IEEE Transactions on Signal Processing
On uncertainty principle for the linear canonical transform of complex signals
IEEE Transactions on Signal Processing
On Sampling of Band-Limited Signals Associated With the Linear Canonical Transform
IEEE Transactions on Signal Processing
B-spline signal processing. I. Theory
IEEE Transactions on Signal Processing
The Zak transform and sampling theorems for wavelet subspaces
IEEE Transactions on Signal Processing
Relations between fractional operations and time-frequencydistributions, and their applications
IEEE Transactions on Signal Processing
Two Channel Paraunitary Filter Banks Based on Linear Canonical Transform
IEEE Transactions on Signal Processing
On sampling in shift invariant spaces
IEEE Transactions on Information Theory
Perturbation of Regular Sampling in Shift-Invariant Spaces for Frames
IEEE Transactions on Information Theory
Extrapolation of Bandlimited Signals in Linear Canonical Transform Domain
IEEE Transactions on Signal Processing
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The linear canonical transform (LCT) has proven to be a powerful tool in optics and signal processing. Most existing sampling theories of this transform were derived from the LCT band-limited signal viewpoint. However, in the real world, many analog signals encountered in practical engineering applications are non-bandlimited. The purpose of this paper is to derive sampling theorems of the LCT in function spaces for frames without band-limiting constraints. We extend the notion of shift-invariant spaces to the LCT domain and then derive a sampling theorem of the LCT for regular sampling in function spaces with frames. Further, the theorem is modified to the shift sampling in function spaces by using the Zak transform. Sampling and reconstructing signals associated with the LCT are also discussed in the case of Riesz bases. Moreover, some examples and applications of the derived theory are presented. The validity of the theoretical derivations is demonstrated via simulations.