A class of Gabor frames with bounded compactly supported generator function

In this paper a class of Gabor frames with time shift parameter a>۰, frequency shift parameter b>۰ and bounded compactly supported generator function g such that supp\ g\subseteq\left[\left(k+۲\right)a-\frac{۲}{b},ka+\frac{۱}{b}\right] or supp\ g\subseteq\left[\left(k+۱\right)a-\frac{۱}{b},ka+\frac{۱}{b}\right], where k is an integer number is introduced. In particular, a sufficient condition on a function g\in C_c^+\left( \mathbb{R}\right) with supp\ g\subseteq\left[\left(k+۲\right)a-\frac{۲}{b},ka+\frac{۱}{b}\right] and positive decreasing derivative g^\prime on \left(ka-\frac{۱}{b},\left( k+۲\right)a \right), that make \left\{E_{mb}T_{na}g\right\}_{m,n\in\mathbb{Z}} into a Gabor frame, is given.

کلیدواژه ها:

Frame ، Dual frame ، Gabor system ، Gabor frame