Estimating Characteristic Phase and Delay from Broadband Interaural Time Difference Tuning Curves

Characteristic delay and characteristic phase are shape parameters of interaural time difference tuning curves. The standard procedure for the estimation of these parameters is based on the measurement of delay curves measured for tonal stimuli with varying frequencies. Common to all procedures is the detection of a linear behavior of the phase spectrum. Hence a reliable estimate can only be expected if sufficiently many relevant frequencies are tested. Thus, the estimation precision depends on the given bandwidth. Based on a linear model, we develop and implement methods for the estimation of characteristic phase and delay from a single broadband tuning curve. We present two different estimation algorithms, one based on a Fourier-analytic interpretation of characteristic delay and phase, and the other based on mean square error minimization. Estimation precision and robustness of the algorithms are tested on artificially generated data with predetermined characteristic delay and phase values, and on sample data from electrophysiological measurements in birds and in mammals. Increasing the signal-to-noise ratio or the bandwidth increases the estimation accuracy of the algorithms. Frequency band location and strong rectification also affect the estimation accuracy. For realistic bandwidths and signal-to-noise ratios, the minimization algorithm reliably and robustly estimates characteristic delay and phase and is superior to the Fourier-analytic method. Bandwidth-dependent significance thresholds allow to assess whether the estimated characteristic delay and phase values are meaningful shape parameters of a measured tuning curve. These thresholds also indicate the sampling rates needed to obtain reliable estimates from interaural time difference tuning curves.