Publication [5.1] of Tomás Oliveira e Silva

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T. Oliveira e Silva, P. Guedes de Oliveira, J. C. Príncipe and B. de Vries, "A Complex Pole Extension to the Gamma Filter," The INESC Journal of Research & Development, vol. 3, no. 1, pp. 35-41, Jan./Jun. 1992.


The paper proposes an extension to an existing structure, the gamma filter, substituting the real pole on the tap-to-tap transfer function by a pair of complex conjugate poles and a zero. The new structure is, like the gamma filter, an IIR filter with restricted feedback whose stability is trivial to check. While the gamma filter decouples the memory depth from the filter order for low pass signals the proposed structure decouples the memory depth and the central frequency from the filter order for band pass signals. The learning equations of the model parameters are presented and shown to introduce an adaptive O(p) complexity to the backpropagation algorithm, where p is the filter order. The error surface for a linear filter is investigated on a system identification context and the presence of local minima is confirmed.

BibTeX entry

  author = {Oliveira e Silva, T.} # { and } # {de Oliveira, P. {G}uedes} #
           { and } # {Pr{\'i}ncipe, J. {C}.} # { and } # {de Vries, B.},
  title = {A Complex Pole Extension to the {G}amma Filter},
  journal = {The INESC Journal of Research \& Development},
  year = {1992},
  volume = {3},
  number = {1},
  pages = {35--41},
  month = Jan # {/} # Jun