A precise knowledge of signal values and their statistical properties can be used to reduce the headroom requirements considerably. Investigations of the sample statistics of CD recordings, digital recordings, and "soft" clipped versions of digital recordings reveal that an appropriate use of nonlinear transfer characteristics gives only sporadic exceedings into the nonlinear range and thus distortions of only short durations which are inaudible. Using nonlinear transfer characteristics fit for peak signal values in advance by virtue of delay systems, the distortions can be reduced furthermore.
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