多个生成子生成的Gabor框架

Gabor frames generated by multiple generators

本文首先给出了由多个生成子生成的Gabor系成为Gabor框架(多Gabor框架)的几个充分条件.然后利用上述充分条件之一,构造出了一类多Gabor框架,它的生成子具有很好的时-频局部性质,此构造结果规避了Balian-Low定理的限制.另外,文中又给出了两种构造方案,通过这些方案可以对已有的多Gabor框架进行修正从而得到许多新的多Gabor框架.

Several sufficient conditions for a Gabor system generated by multiple generators to be a Gabor frame （MGF） are given. With one of them, this paper constructs a type of Gabor frames whose generators are well-localized in both the time and frequency domains. This circumvents the Balian-Low theorem. In addition, a general mathematical theorem is given which allows one to modify the existing MGF to get new ones.