Density and Redundancy of the Noncoherent Weyl-Heisenberg Superframes
نویسنده
چکیده
In this paper I shall present the construction of Weyl-Heisenberg superframes and density results related to the noncoherent case. A superframe is a collection of r-frames F = ff i ; i 2 Ig H1, : : : , F r = ff i ; i 2 Ig Hr all having the same countable index set I such that F = ff i f r i ; i 2 Ig is a frame for the Hilbert spaceH = H1 Hr. For the Weyl-Heisenberg superframes we set H1 = = Hr = L (R), f l i = g l z;a;b(x) := zle 2 lg (x bl) and (z; a; b) 2 I := T r R. We study the density of superframes in the case is a subset of the r + 2 subgroup T r E ; . Our approach is inspired by a recent work of O.Christensen, B.Deng and C.Heil. In the special case of coherent WH superframes, we prove that its redundancy is given by 1= (where the lattice is = f(m ; n );m;n 2 Zg).
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