This invention provides a process for purifying the crude aromatic dicarboxylic acids produced by oxidation of dialkyl aromatic hydrocarbons and for using the purified acids in the preparation of polyethylene terephthalate, polyethylene naphthalate and other polyesters. In one embodiment frequency-banded-noise samples, which collectively cover at least a portion of a spectrum, are sequentially generated at different points in time, and a baseline sound-pressure-level reading for each of the frequency banded noise samples is received. Also, the substrates may be formed with centerpieces that are recessed relative to the outer surfaces of the respective substrates. A control system for accomplishing the method is also disclosed. This permits analysis of the movement of the object to be performed by observing the proximities of the clusters.