On the Construction of Finite Oscillator Dictionary |
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| Authors: | Rongquan Feng Zhenhua Gu Zilong Wang Kai Zhou |
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| Institution: | 1. LMAM , School of Mathematical Sciences, Peking University , Beijing , China;2. School of Mathematical Sciences , Suzhou University , Suzhou , China;3. State Key Laboratory of Integrated Service Networks , Xidian University , Xi'an , China;4. KLMM, AMSS , Chinese Academy of Sciences , Beijing , China |
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| Abstract: | A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani, and Sochen in 3
Gurevich , S. ,
Hadani , R. ,
Sochen , N. (2008). The finite harmonic oscillator and its applications to sequences, communication and radar. IEEE Trans. Inform. Theory 54(9):4239–4253.Crossref], Web of Science ®] , Google Scholar]]. In this paper, closed formulae of the finite split oscillator dictionary 𝔖 s are revisited by a simple proof, the structure of nonsplit tori of the group SL(2, 𝔽 p ) is studied, and an explicit algorithm for computing the finite nonsplit oscillator dictionary 𝔖 ns is described. |
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| Keywords: | DFT Finite harmonic oscillator Torus Weil representation |
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