Document Type : Research Paper


Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O.Box 546, Rafsanjan, Iran.


The duals of Gabor frames have an essential role in reconstruction of signals. In this paper we find a necessary and sufficient  condition for two Gabor systems $\left(\chi_{\left[c_1,d_1\right)},a,b\right)$ and $\left(\chi_{\left[c_2,d_2\right)},a,b\right)$ to form dual frames for $L_2\left(\mathbb{R}\right)$, where $a$ and $b$ are positive numbers and $c_1,c_2,d_1$ and $d_2$ are real numbers such that $c_1<d_1$ and $c_2<d_2$.


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