Math @ Duke

Publications [#315773] of Ingrid Daubechies
Papers Published
 Daubechies, I; Landau, HJ; Landau, Z, Gabor TimeFrequency Lattices and the WexlerRaz Identity,
Journal of Fourier Analysis and Applications, vol. 1 no. 4
(January, 1994),
pp. 437478, Springer Nature, ISSN 10695869 [doi]
(last updated on 2019/05/24)
Abstract: Gabor timefrequency lattices are sets of functions of the form (Formula presented.) generated from a given function (Formula presented.) by discrete translations in time and frequency. They are potential tools for the decomposition and handling of signals that, like speech or music, seem over short intervals to have welldefined frequencies that, however, change with time. It was recently observed that the behavior of a lattice (Formula presented.) can be connected to that of a dual lattice (Formula presented.) Here we establish this interesting relationship and study its properties. We then clarify the results by applying the theory of von Neumann algebras. One outcome is a simple proof that for (Formula presented.) to span (Formula presented.) the lattice (Formula presented.) must have at least unit density. Finally, we exploit the connection between the two lattices to construct expansions having improved convergence and localization properties. © 1994, Birkhäuser Boston. All rights reserved.


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