Abstract
Compressed Sampling in Shift-Invariant Spaces Associated With FrFT
Highlights
F RACTIONAL FOURIER TRANSFORMATION (FrFT) is an extension of the ordinary Fourier transform (FT)
We propose sampling and compressed sampling methods under the generalized shift-invariant spaces associated with the FrFT
We proposed two compressed sampling methods combining the ideas of compressed sensing (CS) and sampling in the shift-invariant spaces (SISs)
Summary
F RACTIONAL FOURIER TRANSFORMATION (FrFT) is an extension of the ordinary Fourier transform (FT). Suppose the number and forms of the generators are known, how can we find coefficients of the generators from a known complete basis with a sufficient low sampling rate This question is a special case of sampling a signal in a union of subspaces [17,18,19]. We propose sampling and compressed sampling methods under the generalized shift-invariant spaces associated with the FrFT.
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