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A Timing Model for the Intensity and Frequency Discrimination Functions

For a pure‐tone signal of intensity I and frequency f⩽1000 Hz, we attempt to arrive at the dependence of ΔI and Δf on I and f. Single fiber neural data for low frequency tones suggest that the pulse trains are approximately renewal process with interarrival times of the form IAT = I/f+X, where I is a geometrically distributed random variable with parameter p and X is a bounded random variable with E(X) = 0 and V(X) proportional to 1/f2. Because the distribution of IATs is almost perfectly multimodal, if the sample is reasonably large, it is usually possible to determine the value of I for each IAT. Since E(IAT) = 1/pf and E(IAT/I) = 1/f, p and f can be estimated from the sample in the obvious way. Using a d′ argument, we derive ΔP and Δf as functions of p and f. Assumptions are made relating p and the sample size to I and f, and from these assumptions are derived formulas relating ΔI and Δf to I and f. These predictions are compared with the existing data. Various theoretical problems are pointed out. [Th...