Multiwindow Gabor Frames On Periodic Subsets Of (?)

Gabor analysis is widely used in signal analysis, image processing and other information science as a time-frequency analysis method. Recently, to facilitate the analysis of signal which appears periodically but intermittently, Gabardo and Li studied the completeness of single-window Gabor systems in the periodic subsets of R and so on. On this basis, we use several windows instead of a single one, and focus on multiwindow Gabor systems in the periodic subsets of R, which can be more effective in signal processing by choosing window functions with different shapes and different supports.The main results of this thesis is as follows:1.We characterize the completeness of multiwindow Gabor systems in the peri-odic subsets of R, and derive a necessary and sufficient condition on periodic subsets admitting complete multiwindow Gabor systems.2.We obtain a necessary and sufficient condition for a multiwindow Gabor system to be a frame for its closed linear span. Based on this,we characterize a multiwindow Gabor system being a frame in the periodic subsets of R.3.We generalize multiwindow Gabor systems to the case of different sampling rates for each window, and give a characterization for such a multiwindow Gabor sys-tem to be a frame.We also show the properties of the multiwindow Gabor systems are essentially not changed by replacing the exponential kernel with other kernels.