کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4589743 1334903 2015 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Gabor orthonormal bases generated by the unit cubes
ترجمه فارسی عنوان
گابور پایگاه های ارگانیک تولید شده توسط مکعب واحد
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We consider the problem in determining the countable sets Λ in the time-frequency plane such that the Gabor system generated by the time-frequency shifts of the window χ[0,1]dχ[0,1]d associated with Λ forms a Gabor orthonormal basis for L2(Rd)L2(Rd). We show that, if this is the case, the translates by elements Λ of the unit cube in R2dR2d must tile the time-frequency space R2dR2d. By studying the possible structure of such tiling sets, we completely classify all such admissible sets Λ of time-frequency shifts when d=1,2d=1,2. Moreover, an inductive procedure for constructing such sets Λ in dimension d≥3d≥3 is also given. An interesting and surprising consequence of our results is the existence, for d≥2d≥2, of discrete sets Λ with G(χ[0,1]d,Λ)G(χ[0,1]d,Λ) forming a Gabor orthonormal basis but with the associated “time”-translates of the window χ[0,1]dχ[0,1]d having significant overlaps.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 269, Issue 5, 1 September 2015, Pages 1515–1538
نویسندگان
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