As we will see, there is an infinite number of time functions with any given spectrum.
Spectral factorization is a method of finding the one time function which is also minimum phase.
The minimum-phase function has many uses. It, and it alone, may be used for feedback filtering. It will arise frequently in wave propagation problems of later chapters. It arises in the theory of prediction and regulation for the given spectrum. It determines the minimum amount of dispersion in viscous wave propagation which is implied by causality.