### Abstract

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, λ^{θ}n) = λφ(x, n), for any λ > 0, and some θ < 1. In the context of the model φ(x, n) = F_{0}[ g_{0}(x) (h_{0}(x) + k_{0}(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 (F_{0}, g_{0}, h_{0}, k_{0}) are possible candidates for interpolating empirical data. These two parametric families are given by the following expressions: φ_{1}(x, n) = A( x^{α} (x^{α′} + Kn^{ α′ θ}))^{ 1 (α - α′)}, φ_{2}(x, n) = A[x^{α}(x^{α′} - Kn^{ α′ θ})]^{ 1 (α + α′)}. Both of these expressions are in good agreement with a large array of partial masking data.

Original language | English (US) |
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Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Journal of Mathematical Psychology |

Volume | 24 |

Issue number | 1 |

DOIs | |

State | Published - Aug 1981 |

### ASJC Scopus subject areas

- Psychology(all)
- Applied Mathematics

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## Cite this

*Journal of Mathematical Psychology*,

*24*(1), 1-20. https://doi.org/10.1016/0022-2496(81)90033-X