Exact jnd functions for a generalized McGill-Goldberg counting model
William S. Hellman, Rhona P. Hellman · The Journal of the Acoustical Society of America · 1987
In an earlier work [W. S. Hellman and R. P. Hellman, J. Acoust. Soc. Am. Suppl. 1 79, S34 (1986)], a generalization of the McGill-Goldberg counting model was presented. It was demonstrated that loudness functions, consistent with experiments, could be determined from intensity jnd functions that obeyed both the power-function near miss and Weber's law. The central formula for the model is the integral relation N(I)1/2 = (h/2)∫dI /[IJ(I)] + a, where h and a are constants, and N(I) and J(I) are the neural count and input jnd functions, respectively. Following McGill and Goldberg, the model was developed using a first-order approximation for the jnd induced change ΔN. To determine just how appropriate the first-order approximation might be, the results of boot-strapping the model are shown. That is, given the derived neural-count functions, the “exact” associated jnd functions are generated. For a power-function near miss as original input, an “exact” jnd function that exhibits a low-intensity deviation from power-function behavior is obtained. When the input jnd function obeys Weber's law, it is found that the boot-strapped jnd function is constant over a wide range of intensities. These results are compatible with psychophysical data. [Work partially supported by the Rehabilitation Research and Development Service of the VA.]