Gabor Dual Frames with Characteristic Function Window
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...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2021-02-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_46666_9834ce9dba37510565d183a06f8f5574.pdf |
| Summary: | 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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| ISSN: | 2322-5807 2423-3900 |