Figure 7. Modulation-detection threshold is calculated as a function of modulation frequency.

Logistic fits to the function relating the area under the ROC curve to modulation depth are used to determine the modulation depth at which the single unit response reaches threshold at each individual modulation frequency. The logistic function accurately describes the data. Threshold is lowest around the best modulation frequency, and increases with both increasing and decreasing f_m relative to best modulation frequency. Responses of a single CT unit (BF = 5.25 kHz), at 10 dB above pure-tone threshold. A, temporal modulation transfer functions calculated from the vector strength of spike synchrony to the amplitude envelope as a function of f_m and m, as indicated in the figure legend. Filled symbols represent significant VS measurements (Rayleigh statistic > 13.8, P < 0.001), open symbols indicate non-significant VS. Colours identify modulation frequencies (5, 40, 75, 139, 260, 485, 905 Hz) at which further analyses are presented in B–D. Key shows modulation depth (m, %).;B, area under the receiver operating characteristic curve (AUC) as a function of f_m and m. Dashed line at 0.5 indicates the expected value for a signal indistinguishable from an unmodulated signal. Dashed line at 0.75 indicates the value taken as threshold for AM detection. Filled symbols indicate values above threshold, open symbols indicate values below threshold. C, AUC plotted as a function of m for each of the modulation frequencies highlighted in colour in panels A and B. Continuous lines indicate logistic functions fitted to the data. Dashed line at 0.75 indicates threshold. Filled symbols indicate values above threshold, open symbols indicate values below threshold. The m value at which each fitted function crosses this dashed line is taken as the threshold modulation depth (m_T) for that f_m. D, neural threshold for AM detection plotted as a function of f_m calculated from the responses in A–C. Colours correspond to the modulation frequencies highlighted in A and B, and fitted with logistic functions in C. For this unit, minimum threshold for AM detection is 3.7% at f_m= 139 Hz. At f_m= 905 Hz, threshold is not reached at any m.