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There are three important points to draw from this paper.
Firstly, I have formulated causal non-stationary convolution and
combination and their adjoints in such a way that it is apparent that
the corresponding non-stationary recursive filters are true inverse
processes. If you think of causal non-stationary filtering as a
lower triangular matrix, then recursive inverse filtering applies
the inverse matrix.
The second important point is that recursive inverse-filtering with a
filter-bank consisting of minimum-phase two-point filters is
*unconditionally stable*, and as such it is totally safe to apply
in any circumstance.

However, the final point is that for a more general set of
minimum-phase filters, stability of non-stationary recursive
inverse-filtering is *not* guaranteed: use with care.

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Stanford Exploration Project

10/25/1999