Some Issues On Continuous Mixed Gabor Frames And Super Gabor Frames

The multi-window Gabor frame is a kind of Gabor frames.Compared with single win-dow Gabor ones,multi-window Gabor frames process practical signals by the cooperation of time-frequency shifts of different window functions.A mixed multi-window Gabor frame is a generalization of a multi-window Gabor one,whose window functions enjoy different time-frequency shifts.It can process the practical signals with rich time-frequency information,and has potential application value.On the other hand,a super Gabor frame is also known as a vector-valued Gabor frame which is widely applied in mobile communication,satellite communication,local area network and so on.This thesis addresses mixed multi-window Gabor frames and their(weak)Gabor dual frames in the context of L~2(R),and uniqueness of super Gabor dual frames for super Gabor frames with irrational time-frequency product in the context of L~2(R,C~L).To be specific,we in our thesis1)establish a sufficient and necessary condition of mixed Gabor frames with integer-shift and characterize(weak)Gabor dual frames for these Gabor frames in the time domain;2)using a suitable Zak transform matrix,characterize(weak)Gabor duals for mixed Gabor frames with rational time-frequency product in the Zak transform domain;3)characterize uniqueness of super Gabor dual frames for super Gabor frames with irrational time-frequency product.Also some examples are provided to illustrate our main results.