Optimal bases of Gaussians in a Hilbert space: applications in mathematical signal analysis

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摘要

Arbitrary square-integrable (normalized) functions can be expanded exactly in terms of the Gaussian basis g(t;A) where A∈C. Smaller subsets of this highly overcomplete basis can be found, which are also overcomplete, e.g., the von Neumann lattice g(t;Amn) where Amn are on a lattice in the complex plane. Approximate representations of signals, using a truncated von Neumann lattice of only a few Gaussians, are considered. The error is quantified using various p-norms as accuracy measures, which reflect different practical needs. Optimization techniques are used to find optimal coefficients and to further reduce the size of the basis, whilst still preserving a good degree of accuracy. Examples are presented.

论文关键词:Time-frequency,Gabor analysis

论文评审过程:Received 22 November 1999, Revised 20 February 2000, Available online 3 August 2001.

论文官网地址:https://doi.org/10.1016/S0377-0427(00)00685-3