Nonlinear decomposition filters with neural network elements

  • Authors:

  • Vairis Shtrauss

  • Affiliations:

  • Institute of Polymer Mechanics, University of Latvia, Riga, Latvia

  • Venue:
  • ICS'08 Proceedings of the 12th WSEAS international conference on Systems
  • Year:
  • 2008

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Abstract

The paper is devoted to finding ways for improving resolution and accuracy for decomposition of monotonic time- and frequency-domain multi-component signals. For solving the problem, a nonlinear decomposition filter is proposed operating with equally spaced data on a logarithmic time or frequency scale (geometrically spaced on linear scale), which is implemented as a parallel connection of several linear filters, which output signals are transformed by a nonlinear activation function, multiplied by weights and summed. One of the fundamental findings of this study is a square activation function, which ensures physically justified nonnegativity for the recovered distributions of time constants (DTC). It is found that the nonlinear decomposition filter under consideration transforms the Gaussian input noise into the nonnegative output noise with a specific probability distribution having the standard deviation and the mean proportional to the variance of input noise. For most practical cases when the standard deviation of input noise is small, the proposed solution considerably improves the noise immunity of algorithms. Enhancement in the resolution to compare with linear filters is demonstrated for the decomposition of a frequency-domain multi-component signal.