Study Of Some Questions For Wilson Frame And Gabor Frame

Frame usually refers to satisty certain characteristics of a set of vectors in Hilbert space. Frame is the extention of the orthonormal basis, and plays an important part in the development of wavelet analysis. It is widely used in signal processing, image processing, data compression, sampling theory and many other disciplines. Along with wavelet analysis, frame theory is progressing rapidly.Much research focuses on the Gabor frames and Wavelet frames (affine frames). However, the study of Wilson is very little. This thesis is mainly to study Wilson frame, and discusse some of the problems for Gabor frame. The thesis is divided into three chapters.Chapter 1 briefly introduces the background of Fourier analysis, wavelet analysis and the frame.Chapter 2 Firstly, obtains the Wilson frame identity. Secondly, Several Sufficient Conditions in Time-domain and Frequency-domain are given. Finally, The necessary Conditions for Wilson frame and a necessary and sufficient condition for Wilson When Wilson tight frame are established.Chapter 3 Presents a new criterion for Gabor frame in L2(R), and illustrates the new criterion is more advantage than the original one.