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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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 |
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doaj-d31a62fa3cc244448ea569f841b05d732021-02-13T05:32:59ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002021-02-01181475710.22130/scma.2020.121704.75146666Gabor Dual Frames with Characteristic Function WindowMohammad Ali Hasankhani Fard0Department 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 $c_2<d_2$.https://scma.maragheh.ac.ir/article_46666_9834ce9dba37510565d183a06f8f5574.pdfframedual framegabor systemgabor frame |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Mohammad Ali Hasankhani Fard |
| spellingShingle |
Mohammad Ali Hasankhani Fard Gabor Dual Frames with Characteristic Function Window Sahand Communications in Mathematical Analysis frame dual frame gabor system gabor frame |
| author_facet |
Mohammad Ali Hasankhani Fard |
| author_sort |
Mohammad Ali Hasankhani Fard |
| title |
Gabor Dual Frames with Characteristic Function Window |
| title_short |
Gabor Dual Frames with Characteristic Function Window |
| title_full |
Gabor Dual Frames with Characteristic Function Window |
| title_fullStr |
Gabor Dual Frames with Characteristic Function Window |
| title_full_unstemmed |
Gabor Dual Frames with Characteristic Function Window |
| title_sort |
gabor dual frames with characteristic function window |
| publisher |
University of Maragheh |
| series |
Sahand Communications in Mathematical Analysis |
| issn |
2322-5807 2423-3900 |
| publishDate |
2021-02-01 |
| description |
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 $c_2<d_2$. |
| topic |
frame dual frame gabor system gabor frame |
| url |
https://scma.maragheh.ac.ir/article_46666_9834ce9dba37510565d183a06f8f5574.pdf |
| work_keys_str_mv |
AT mohammadalihasankhanifard gabordualframeswithcharacteristicfunctionwindow |
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1724271902861557760 |