Some Simple Function Of Gabor Analysis

The theory of frames for a Hilbert space plays a fundamental role in signal processing, image processing, data compression, sampling theory and more, as well as being a fruitful area of research in abstract mathematics. In this paper, we mainly study a special type of frames-Weyl-Heisenberg frame. We will try to discuss the problem of when {ei2mbtg(t - na) : m, n Z} is a Weyl-Heisenberg frame for some real numbers a , b and simple function g L2(R) and give some new either necessary or sufficient conditions. In second chapter, the new approach reduces the problem under discussion in many cases to the problem of determining when certain sets cover the real line. In third chapter, we will discuss the connection between the problem under discussion and ABC problem.