TY - JOUR

T1 - On the functional form of partial masking functions in psychoacoustics

AU - Iverson, Geoffrey J.

AU - Pavel, M.

N1 - Funding Information:
This work was supported by National Science Foundation Grants 77-16984 and 79-24526 to New York University. We are grateful to J. C. Falmagne for his encouragement of this research, and his many comments on a previous draft of this manuscript. Requests for reprints should be sent to G. J. Iverson, Department of Psychology, Northwestern University, Evanston, Ill. 60201.

PY - 1981/8

Y1 - 1981/8

N2 - Partial masking of pure tones is often investigated in terms of matching functions which record the intensity φ(x, n) of an unmasked tone which matches, in perceived loudness, a tone of intensity x embedded in a flat, broadband noise of intensity n. Empirically, the following property of "shift invariance" is observed to hold for these matching functions: φ(λx, λθn) = λφ(x, n), for any λ > 0, and some θ < 1. In the context of the model φ(x, n) = F0[ g0(x) (h0(x) + k0(n))] which expresses the idea that the effect of a noise mask is to control the gain of a pure tone signal in a multiplicative fashion, shift invariance proves to be an extremely powerful theoretical constraint. Specifically, we show that only two parametric families of functions (F0, g0, h0, k0) are possible candidates for interpolating empirical data. These two parametric families are given by the following expressions: φ1(x, n) = A( xα (xα′ + Kn α′ θ)) 1 (α - α′), φ2(x, n) = A[xα(xα′ - Kn α′ θ)] 1 (α + α′). Both of these expressions are in good agreement with a large array of partial masking data.

AB - Partial masking of pure tones is often investigated in terms of matching functions which record the intensity φ(x, n) of an unmasked tone which matches, in perceived loudness, a tone of intensity x embedded in a flat, broadband noise of intensity n. Empirically, the following property of "shift invariance" is observed to hold for these matching functions: φ(λx, λθn) = λφ(x, n), for any λ > 0, and some θ < 1. In the context of the model φ(x, n) = F0[ g0(x) (h0(x) + k0(n))] which expresses the idea that the effect of a noise mask is to control the gain of a pure tone signal in a multiplicative fashion, shift invariance proves to be an extremely powerful theoretical constraint. Specifically, we show that only two parametric families of functions (F0, g0, h0, k0) are possible candidates for interpolating empirical data. These two parametric families are given by the following expressions: φ1(x, n) = A( xα (xα′ + Kn α′ θ)) 1 (α - α′), φ2(x, n) = A[xα(xα′ - Kn α′ θ)] 1 (α + α′). Both of these expressions are in good agreement with a large array of partial masking data.

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U2 - 10.1016/0022-2496(81)90033-X

DO - 10.1016/0022-2496(81)90033-X

M3 - Article

AN - SCOPUS:39149084864

VL - 24

SP - 1

EP - 20

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

SN - 0022-2496

IS - 1

ER -