Finite Linear Combination Of Gabor Frames And Comparison Of Its Discriminant Method

As a generalization of the orthonormal basis,the frame can reconstruct the elements in the Hilbert space by the frame coefficients.It usually refers to a set of vectors that satisfy a certain characteristic in the Hilbert space.It plays an extremely important role in the development of wavelet analysis.With the development of wavelet analysis,the frame theory has been continuously enriched and perfected.The frame is widely used in many disciplines such as data compression,image processing,sampling theory and signal processing.The research on the frame for the space L2(R)generally focuses on the wavelet frame(affine frame),Fourier frame and Gabor frame.This thesis discusses some problems of Gabor frame.The first,it mainly states the research background of the frame,from Fourier transform to windowed Fourier transform,to wavelet analysis,until the emergence of the frame and its rapid development.The second is to lists some basic theorems and conclusions about the Gabor frame to be used in this thesis.This thesis focuses on two problems.The first one is to discuss whether a linear combination of any finite Gabor frames on L2(R)is a Gabor frame.For this problem,Consider the linear combination of two Gabor frames first,considering the combined frame bounds.Then consider the linear combination of any finite Gabor frames.The second problem is to compare the three discriminant methods(three sufficient conditions)commonly used in Gabor frame,this is the final content.First lists the three discriminant methods,and then gives some examples to compare the three methods.