Some Problems On Gabor Frames

The theory of frames for a Hilbert space plays a fundamental role in signal processing, image processing, data compression, robust data transmission and more. In the theory of frames, Gabor analysis is one of the extensive realms which need most to develop with thorough research. A basic question in Gabor analysis is to determine whether (g, a, b) is a frame, with respect to given g∈ L~2(R) and parameters a,b ∈ R. In this paper, we focus on these problems:1. We study the conditions under which (g, a, b) is a frame when g is a simple function with special properties.2. We investigate the necessary and sufficient conditions required for (X_E, a, b) to be a normalized tight Gabor frame or tight Gabor frame.