Optimized orthonormal wavelet filters with improved frequency separation

  • Authors:
  • Henrique Mohallem Paiva;Roberto Kawakami Harrop Galvão

  • Affiliations:
  • Mectron Engenharia, Indústria e Comércio S/A, Av. Brigadeiro Faria Lima, 1399, São José dos Campos, SP, Brazil;Instituto Tecnológico de Aeronáutica, Divisão de Engenharia Eletrônica, Praça Marechal Eduardo Gomes, 50, São José dos Campos, SP, Brazil

  • Venue:
  • Digital Signal Processing
  • Year:
  • 2012

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Abstract

This paper proposes an optimization-based method to design orthonormal wavelet filters with improved frequency separation. The proposed approach adopts a parameterization of orthogonal filter banks which ensures that the resulting wavelets have at least two vanishing moments. The filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to cut-off sharpness. In comparison with standard orthonormal filters, the proposed method is shown to provide better trade-off between frequency selectivity and time resolution. For illustration, the optimized filters are employed in an application example involving the use of a wavelet-packet system identification scheme. As a result, the identification errors are smaller than those obtained by using a non-optimized filter with the same length.