Shift-Invariant and Sampling Spaces Associated With the Fractional Fourier Transform Domain
Shift-invariant spaces play an important role in sampling theory, multiresolution analysis, and many other areas of signal and image processing. A special class of the shift-invariant spaces is the class of sampling spaces in which functions are determined by their values on a discrete set of points. One of the vital tools used in the study of sampling spaces is the Zak transform. The Zak transform is also related to the Poisson summation formula and a common thread between all these notions is the Fourier transform.
Keywords: Fractional fourier transform ; fractional Zak transform ; Poisson summation formula ; reproducing kernels ; sampling spaces ; semi-discrete convolution ; shift-invariant spaces ; Band-Limited Signals ; Unmatched Filter Properties ; Pulse-Shaping Filters ; Wavelet Subspaces ; Theorem ; Reconstruction ; Formulas ; Conversion ; Splines ; Shannon
Record created on 2012-04-19, modified on 2016-08-09