Dynamical sampling associated with the special affine Fourier transform

Abstract

In this paper, we study the dynamical sampling of sequence spaces and shift-invariant spaces in the special affine Fourier transform domains. We present a method for recovering the signals in sequence spaces and shift-invariant spaces from their dynamical sampling values. Moreover, in the special affine Fourier transform domains, we give a characterization for stable reconstruction of signals in sequence spaces and shift-invariant spaces. Finally we give a concrete example to elucidate our main results. Our results extend original ones in the Fractional Fourier transform domains and the Fourier transform domains.