An introduction to wavelets
New sampling formulae for the fractional Fourier transform
Signal Processing
Sampling of linear canonical transformed signals
Signal Processing
Compressed sensing of analog signals in shift-invariant spaces
IEEE Transactions on Signal Processing
A sampling theorem for shift-invariant subspace
IEEE Transactions on Signal Processing
B-spline signal processing. I. Theory
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Unified fractional Fourier transform and sampling theorem
IEEE Transactions on Signal Processing
Relations between fractional operations and time-frequencydistributions, and their applications
IEEE Transactions on Signal Processing
On simple oversampled A/D conversion in shift-invariant spaces
IEEE Transactions on Information Theory
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The fractional Fourier transform (FRFT), a generalization of the Fourier transform, has proven to be a powerful tool in optics and signal processing. Most existing sampling theories of the FRFT consider the class of band-limited signals. However, in the real world, many analog signals encountered in practical engineering applications are non-bandlimited. The purpose of this paper is to propose a sampling theorem for the FRFT, which can provide a suitable and realistic model of sampling and reconstruction for real applications. First, we construct a class of function spaces and derive basic properties of their basis functions. Then, we establish a sampling theorem without band-limiting constraints for the FRFT in the function spaces. The truncation error of sampling is also analyzed. The validity of the theoretical derivations is demonstrated via simulations.