Figure 1. ITD statistics of natural stimulus.

(A) Estimation of ITD mean and standard deviation over time in broadband signals filtered by human head-related impulse responses (HRIRs) and modeled cochlear filters. (1) Example HRIRs from sound emitted from speakers located at −15 degrees and recorded with microphones positioned in each ear (obtained from a publicly available LISTEN dataset). Traces show example impulse responses in the right (red) and left (blue). (2) A broadband signal was convolved with HRIRs from right (red) and left (blue) ears for each direction. (3) Convolved signals were then filtered using parameters analogous to human cochlear filters. Example of signal passed through a cochlear filter with a frequency band centered on 1000 Hz for the left (blue) and right (red) ears. (4) The instantaneous phase of the resulting signals on the left and right ears was computed. Top, instantaneous phase over time for the left (blue) and right (red) signals shown in 3. Bottom, instantaneous phase differences (IPD, in radians) and instantaneous time differences (ITD, in microseconds) between left and right signals. (5) Histogram of instantaneous IPD and ITD, illustrating their variability over time for the example signal shown in 3. (B) ITD mean (left) and standard deviation (right) over time, as a function of frequency and azimuth. Plots represent median values across subjects (N = 51), fit by spline curves, and color coded for each frequency. The derivative of the curves on the left was used to calculate ITD rate of change (ITDrc) across azimuth. The ITD variability (ITDv) was computed as the standard deviation of the ITD distribution over time. (C) Left, information of ITD cues as a function of frequency and azimuth, quantified by the median square root of ITD Fisher information (√FI_ITD) across subjects (azimuth was converted to ITD to obtain the estimate of the ITD statistics as a function of frequency and ITD, matching the stimulus metrics and model parameters used in our study). √FI_ITD statistic closely approximates ITDrc/ITDv. Right, the interquartile range of √FI_ITD across subjects shows low inter-individual variability. Black lines on each panel indicate the π-limit across frequency, beyond which ITD cues become ambiguous for narrowband sounds. (D) This study tests the hypothesis that over evolutionary and/or ontogenetic time scales the human brain became adapted to natural ITD statistics, such that stimuli that are more informative about sound source location would be distinctively encoded.

Figure 1—figure supplement 1. Basis of ITD statistics and consistency across conditions.

(A) ITDrc (left) and ITDv (right) as a function of ITDs corresponding to azimuth locations from −90° to 90°, averaged across subjects, for three example signals: a 500 Hz tone (yellow) and two signals combining 500 Hz and 523 Hz (red), and 500 Hz and 723 Hz (blue). 523 Hz and 723 Hz were chosen to demonstrate the effect of combining signals lying, respectively, within and outside the bandwidth of a cochlear filter with a center frequency of 500 Hz. The ITD statistics were estimated using the same method described in Figure 1, by convolving each of these signals with impulse responses from the left and right ears, then filtering using parameters analogous to human cochlear at 500 Hz center frequency. This procedure was applied across all other locations and subjects in the reported dataset. Note that ITDrc is similar for the three signals, indicating no significant effect of frequency interference on this statistic. However, while ITDv is near zero across azimuth locations for 500 Hz alone (yellow) and 500 + 723 Hz (blue), it increases from front to periphery when neighboring frequencies within a single cochlear filter are combined (500 + 523 Hz; red). Hence, unlike ITDrc, ITDv depends on interference between neighboring frequencies within cochlear filter ranges. (B) ITD statistics are consistent across broadband signals. ITDrc (left) and ITDv (right) computed using white noise (the broadband noise used to estimate ITD statistics in Figure 1) and a distinct broadband signal (first second of the chorus section of the popular song Alive, by Pearl Jam; bottom) displayed similar patterns. (C) ITD statistics are consistent across acoustic environments. ITDrc (left) and ITDv (right) computed from impulse responses recorded in human-head shaped manikins inside two different types of environment - anechoic chambers (top) and reverberant office spaces (bottom). We used the first 2.5 ms of impulse responses (corresponding mostly to the direct click reaching the ears, avoiding echo components in the reverberant office).