On the Construction of Finite Oscillator Dictionary

A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani, and Sochen in [3]. 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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