Multiple reflections are predictable. It is the unpredictable part of a signal, the prediction residual, that contains the primary information. The output of the filter (1,-f1, -f2) is the unpredictable part of the input. This filter is a simple example of a ``prediction-error" (PE) filter. It is one member of a family of filters called ``error filters."
The error-filter family are filters with one coefficient constrained to be unity and various other coefficients constrained to be zero. Otherwise, the filter coefficients are chosen to have minimum power output. Names for various error filters follow:
prediction-error (PE) filter gapped PE filter with a gap of 2 interpolation-error (IE) filter a gapped IE filter
A program for computing all the error filters
will be presented after we examine a collection of examples.