A set theoretic estimation approach is introduced for timescale modification of complex acoustic signals. The method determines a signal that meets, in a least-squared error sense, desired temporal and spectral envelope constraints that are inconsistent. These constraints are generalized within the set theoretic framework to include other signal characteristics such as instantaneous frequency and group delay. The approach can enhance acoustic signals consisting of closely-spaced sequential time components, and is applicable to biological, underwater, and music sound processing.