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- W3102146249 abstract "Let g be a totally positive function of finite type, that is, ĝ(ξ)=∏ν=1M(1+2πiδνξ)−1 for δν∈R, δν≠0, and M≥2, and let α,β>0. Then the set {e2πiβltg(t−αk):k,l∈Z} is a frame for L2(R) if and only if αβ<1. This result is a first positive contribution to a conjecture of Daubechies from 1990. Until now, the complete characterization of lattice parameters α, β that generate a frame has been known for only six window functions g. Our main result now yields an uncountable class of window functions. As a by-product of the proof method, we also derive new sampling theorems in shift-invariant spaces and obtain the correct Nyquist rate." @default.
- W3102146249 created "2020-11-23" @default.
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- W3102146249 date "2013-04-15" @default.
- W3102146249 modified "2023-10-16" @default.
- W3102146249 title "Gabor frames and totally positive functions" @default.
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- W3102146249 doi "https://doi.org/10.1215/00127094-2141944" @default.
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