@article { author = {Hasankhani Fard, Mohammad Ali}, title = {Gabor Dual Frames with Characteristic Function Window}, journal = {Sahand Communications in Mathematical Analysis}, volume = {18}, number = {1}, pages = {47-57}, year = {2021}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2020.121704.751}, abstract = {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