Nonstationary Super Gabor Frames

Super Gabor frames have been widely used in mobile communication network, satellite communication network and computer area network. But signal analysis with classical super Gabor frames leads to a fixed time-frequency resolution over the whole time-frequency plane. To overcome the limitations imposed by this rigidity, we propose a natural generalisation of super Gabor frames nonstationary —— super Gabor frames, which lead to a time-frequency resolution changing over time or frequency. They will be introduced in adaptive signal analysis by allowing for adaptivity of windows and lattice in either time or frequency. In this paper, we first give Walnut’s representation of the nonstationary super Gabor frame operator, which has been a central result in time-frequency analysis. Then we discuss the existence of a nonstationary super Gabor frame. Finally, we give a perturbation result for nonstationary super Gabor frames, and provide a method to construct nonstationary super Gabor frames. We will discuss respectively in time and frequency. The main work is as follows:1. We give the definition of nonstationary super Gabor frames, and obtain Walnut’s representation of frame operator.2. We provide a sufficient condition for the existence of a nonstationary super Gabor frame.3. We obtain a perturbation result of nonstationary super Gabor frames.4. We provide a method to construct nonstationary super Gabor frames with non-compactly supported windows.