Time-domain Characterization Of Multiwindow Gabor Frames On Discrete Periodic Sets

Due to its potential applications in signal processing, Gabor analysis in l2(Z) has interested many mathematicians. Recently, to analyze signals which appear periodical-ly but intermittently, Lian and Li investigated single-window Gabor systems on discrete periodic sets. On this basis, we focus on multiwindow Gabor systems on discrete peri-odic sets by using several windows instead of a single one, which may provide a more efficient way to deal with signals since we can choose window functions with different shape and support. The main results of this thesis is as follows:1. We characterize multiwindow Gabor systems to be frames and Riesz bases on discrete periodic sets; Some necessary or sufficient conditions for multiwindow Gabor systems to be frames are also established.2. We characterize two multiwindow Gabor systems to be dual frames on discrete periodic sets. For a given multiwindow Gabor frame, we derive all its Gabor duals, among which we obtain an explicit expression of the canonical Gabor dual and prove that its norm is smallest among all Gabor duals.3. We generalize multiwindow Gabor systems to the case of different sampling rates for each window, and provide a necessary and sufficient condition for multiwin-dow Gabor systems to be frames in this case. We also show the properties of the multi-window Gabor systems are essentially not changed by replacing the exponential kernel with other kernels.