Interpretation and identification of minimum phase reflection coefficients

Abstract

If the acoustic reflection coefficient is minimum phase, then the causality condition can be used to reconstruct its phase from its magnitude. Such reconstructions are useful when environmental conditions obscure the phase, which is vital to understanding the dynamics of the reflecting object. However, the reconstructions are usually impossible because one cannot be sure that the reflection coefficient is minimum phase. The present work addresses this difficulty by formulating a time-domain description of the minimum phase condition and by identifying classes of submerged objects that always create minimum phase reflection coefficients. Numerical examples are used to confirm the analytical findings and to illustrate their applicability to objects that reflect sound with a wide range of magnitudes.