Study of an Optimal Example for the Balian–Low Theorem
نویسندگان
چکیده
We analyze the time-frequency concentration of the Gabor orthonormal basis G(f,1,1) constructed by Høholdt, Jensen, and Justesen. We prove that their window function f has near optimal time and frequency localization with respect to a non-symmetric version of the Balian-Low Theorem. In particular, we show that if (p, q) = (3/2,3), then R |t||f(t)|dt < ∞, and R |γ|| b f(γ)|dγ < ∞, for 0 < ǫ ≤ 3/2, but that both integrals are infinite if ǫ = 0.
منابع مشابه
An Optimal Example for the Balian-Low Uncertainty Principle
We analyze the time-frequency concentration of the Gabor orthonormal basis G(f, 1, 1) constructed by Høholdt, Jensen, and Justesen. We prove that their window function f has near optimal time and frequency localization with respect to a non-symmetric version of the Balian-Low Theorem. In particular, we show that if (p, q) = (3/2, 3), then R |t| |f(t)|dt < ∞ and R |γ| | b f(γ)|dγ < ∞, for 0 < ≤ ...
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