In the case of wideband (aperiodic) signals, the classical signal and noise measures used to characterize stochastic resonance do not work because their way of distinguishing signal from noise fails. In a study published earlier (L. B. Kish, 1996), a new way of measuring and identifying noise and aperiodic (wideband) signals during strongly nonlinear transfer was introduced. The method was based on using cross-spectra between the input and the output. According to the study, in the case of linear transfer and sinusoidal signals, the method gives the same results as the classical method and in the case of aperiodic signals it gives a sensible measure. In this paper we refine the theory and present detailed simulations which validate and refine the conclusions reached in that study. As neural and ion channel signal transfer are nonlinear and aperiodic, the new method has direct applicability in membrane biology and neural science (S.M. Bezrukov and I. Vodyanoy, 1997).