Vector Dynamic Sampling Problem And Special Affine Fourier Transform Phase Recovery Problem

The special affine Fourier transform is generalized by the Fourier transform,the study of phase retrieval in the special affine Fourier transform domain of discrete windows is of great significance in both theory and application.In this paper,and the phase retrieval problem in discrete windowed special affine Fourier transform domain are discussed,and the corresponding results are obtained.Moreover,we also study the dynamic sampling problem in l2(Z)(d)space and vector translation invariant space.In the first chapter,we first introduce the status and development process of the phase retrieval problem and dynamic sampling problem in detail,and then give the relevant basic knowledge needed in this paper.In the second chapter,we discussed the problem of phase retrieval in discrete windowed special affine Fourier transform domain,i.e.,the problem of recovering a signal from the magnitudes of discrete windowed special affine Fourier transform.Firstly,we provide some appropriate conditions under which discrete windowed special affine Fourier transform allows phase retrieval.Then we proved the above conditions can be weaken for non-vanishing signals.Finally,the results of the numerical simulations demonstrate that our theoretical analysis is reasonable,and provide some directions for future work.In the third chapter,we study the dynamic sampling problem.We attempt to reconstruct sequences and functions in dynamical systems through space-time tradeoffs.These sequences and functions can be mathematically described as l2(Z)(d)and vector shift-invariant spaces.We first give a sufficient and necessary condition under which c?l2(zd)(d)can be recovered by its spatial and temporal samples.To illustrate our main results,we give a concrete example to show that the necessary and sufficient conditions in the main results are feasible.Finally,we study the problem of dynamic sampling in vector shift-invariant spaces.