Some Weyl-Heisenberg frame bound calculations

A.J.E.M. Janssen

doi:10.1016/0019-3577(96)85088-9

Some Weyl-Heisenberg frame bound calculations

A.J.E.M. Janssen

Control Systems

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Abstract

We calculate for several g ¿ L²(R) and for integer values of 1/ab the frame bounds and, when possible, the minimum energy dual functions °¿ for the set of time-frequency translates of g corresponding to the lattice parameters a, b. For this we use a recently derived expression for frame bounds and biorthogonal functions in terms of translates of g corresponding to the complementary lattice with parameters 1/b, 1/a.

Original language	English
Pages (from-to)	165-183
Number of pages	19
Journal	Indagationes Mathematicae. New Series
Volume	7
Issue number	2
DOIs	https://doi.org/10.1016/0019-3577(96)85088-9
Publication status	Published - 1996

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abstract = "We calculate for several g ¿ L2(R) and for integer values of 1/ab the frame bounds and, when possible, the minimum energy dual functions °¿ for the set of time-frequency translates of g corresponding to the lattice parameters a, b. For this we use a recently derived expression for frame bounds and biorthogonal functions in terms of translates of g corresponding to the complementary lattice with parameters 1/b, 1/a.",

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AB - We calculate for several g ¿ L2(R) and for integer values of 1/ab the frame bounds and, when possible, the minimum energy dual functions °¿ for the set of time-frequency translates of g corresponding to the lattice parameters a, b. For this we use a recently derived expression for frame bounds and biorthogonal functions in terms of translates of g corresponding to the complementary lattice with parameters 1/b, 1/a.

U2 - 10.1016/0019-3577(96)85088-9

DO - 10.1016/0019-3577(96)85088-9

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JO - Indagationes Mathematicae. New Series

JF - Indagationes Mathematicae. New Series

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IS - 2

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