The aim of this study is to determine the systems that preserve the minimum phase property in signal processing. The minimum phase signals are closely related to outer functions. A basic mathematical question that arises in geophysical imaging is to characterize the linear operators preserving the set of outer functions in Hardy spaces. It is shown that a bounded linear operator on the Hardy space HP, 1 < p < infinity, preserving the set of outer functions is necessarily a weighted composition operator. Moreover, an operator preserving the set of shifted outer functions is necessarily a weighted composition operator as well. These results complement work by Gibson and Lamoureux. (C) 2017 Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG).