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Least-squares inverse filtering always involves consideration of the error. Under certain conditions the error will go to zero as the length of the filter tends to infinity. It is shown that the error will go to zero if either: (1) the waveform being inverted is minimum-phase, or (2) if the output is chosen to come after a sufficiently long time delay. If the waveform being inverted is not minimum-phase and if in addition the output is not chosen to be delayed, then the error will be finite and may be large.
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Claerbout et al. (1964) studied this question.
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