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Limitations on the use of discrete linear models of continuous random processes

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Abstract

A continuous stationary signal possessing non-Gaussian higher order statistics cannot be correctly modelled by any discrete process based on passing independently and identically distributed noise through a linear filter. In particular, it is shown that at third order there exists no discrete skewed linear model with a discrete bispectrum that is the same as that obtained from the Nyquist samples of any continuous stationary process. The nature of the problem is elucidated and an alternative method for modelling the third order statistics of continuous stationary processes is proposed.

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Authors and Affiliations

  1. Defense Research Agency, 0T5 2JS, Portland, Dorset, UK

    A. T. Parsons

  2. Department of Applied Optics, Imperial College, University of London, UK

    M. L. Williams

Authors
  1. A. T. Parsons
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  2. M. L. Williams
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Supported by Defense Research Agency, Portland.

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Parsons, A.T., Williams, M.L. Limitations on the use of discrete linear models of continuous random processes. Circuits Systems and Signal Process 13, 403–410 (1994). https://doi.org/10.1007/BF01183738

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  • DOI: https://doi.org/10.1007/BF01183738

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