of detecting a signal of intensity x delayed τ msec relative to the offset of a noise
mask of intensity n.
P(x, n, τ) = P(x′, n′, τ) iff P(λx, μn, τ) = P(λx′, μn′, τ). (10)
Actually, the data suggest an even stronger hypothesis. To an excellent
approximation, the data appear to fall on a pencil of lines (see Figure 4). This
leads to the very strong conclusion
P(x, τ, n) = F(x/nε(τ)) (11)
for some strictly increasing function F, independent of delay. The question that we set forth above has thus been answered affirmatively.
It is of interest to seek dynamical systems which predict detection performance in accord with equation (11). Interestingly, our own efforts in this regard have proved unsatisfactory. Standard systems involving e.g. feedforward stages (as in gain control devices) appear to be incapable of performing in the desired manner. The apparent difficulty of this problem serves once again to emphasize the power of homogeneity laws abstracted here in (10), (11). We leave this issue unresolved as a challenge to the reader.
1. J. E. Hawkins and S. S. Stevens, "The masking of pure tones and of speech by white noise", J. Acoust. Soc. Amer. 22 ( 1950), 6-13.
2. G. J. Iverson and M. Pavel, "On the functional form of partial masking functions in psychoacoustics", J. Math. Psych. ( 1980) (submitted).
3. W. Jesteadt, C. C. Weir and D. M. Green, "Intensity discrimination as a function of frequency and sensation level", J. Acoust. Soc. Amer. 61 ( 1977), 169-177.
4. M. Pavel and G. J. Iverson, "Invariant characteristics of partial masking: Implications for mathematical models", J. Acoust. Soc. Amer. 69( 3) ( 1981).
5._____, Temporal properties of complete and partial forward masking, Mathematical Studies in Perception and Cognition, No. 81-2, New York University, Department of Psychology, 1981.
6. S. S. Stevens and M. Guirao, "Loudness functions under inhibition", Perception and Psychophysics 2 ( 1967), 459-465.
DEPARTMENT OF PSYCHOLOGY, NEW YORK UNIVERSITY, NEW YORK, NEW YORK, 10003