Predictive Deconvolution: (Part 1)

Abstract

Predictive deconvolution is a method of separating two components of a convolved signal under the assumptions that one of them is amenable to reasonable prediction and the other is serially uncorrelated. It employs the theory of an optimum linear predictor and the hypothesis that prediction error filter is a whitening filter. Therefore, it removes the effect of a predictable component and the output of the prediction error filter is a good estimate of the serially uncorrelated component of the convolution.

Prediction formula based on various time-series models such as autoregressive (AR), moving average (MA) and ARMA are discussed. It is normally argued that predictive deconvolution requires one component of convolution to be autoregressive. This impression is corrected.

Computational aspects are discussed at some length. Many side-issues are discussed and the validity of the assumptions in some applications is also discussed.

This paper may be regarded as a companion paper to the author's earlier review paper on cepstral deconvolution [1].

Indexing terms:

• Linear prediction
• Wiener filter
• Autoregressive and moving average processes
• Time-series analysis
• Deconvolution
• Durbin's algorithm