## 2 Experimental Methodology
### Stimulation  
The time and level differences were extracted between the left and right channels at a given frequency using the discrete Fourier transform (DFT) of the impulse response sequences from a previously recorded HRTF database [34]. The DFT of a single channel HRTF impulse response \(l_{\theta}^{c}(n)\) at frequency index \(k_{i}\) is given as,  
\[H_{\theta}^{c}(k_{i})=\frac{1}{N}\sum_{n=0}^{N-1}h_{\theta}^{c}(n)e^{\frac{-2 \pi k_{i}\pi}{N}}, \tag{1}\]  
where the HRTF \(h_{\theta}^{c}(n)\) is defined for channel \(c\), left or right, at azimuth angle \(\theta\), and \(k_{i}\) is the frequency index that corresponds to \(k_{i}=\left\lfloor\frac{f_{i}}{f_{s}}+0.5\right\rfloor\) at frequency \(f_{i}\) with sampling frequency \(f_{s}\). Magnitude ratio and phase difference of the right, \(H_{\theta}^{r}\), and the left, \(H_{\theta}^{l}\), channels at frequency \(f_{i}\) are respectively computed as,  
\[\alpha_{\theta}(k_{i}) =\frac{|H_{\theta}^{r}(k_{i})|}{|H_{\theta}^{l}(k_{i})|}, \tag{2}\] \[\phi_{\theta}(k_{i}) =arg(H_{\theta}^{r}(k_{i}))-arg(H_{\theta}^{l}(k_{i})). \tag{3}\]  
Then, the power ratio of \(\alpha_{\theta_{1}}^{2}\) at azimuth \(\theta_{1}\) and the phase difference of \(\phi_{\theta_{2}}\) at azimuth \(\theta_{2}\) are used to define a sound stimulus with the right and left channels as,  
\[s^{r}(t;\alpha_{\theta_{1}},\phi_{\theta_{2}}) =\frac{1}{9}\sum_{i=1}^{9}\alpha_{\theta_{1}}(k_{i})sin(2\pi f_{ i}t+\frac{1}{2}\phi_{\theta_{2}}(k_{i})), \tag{4}\] \[s^{l}(t;\alpha_{\theta_{1}},\phi_{\theta_{2}}) =\frac{1}{9}\sum_{i=1}^{9}\frac{1}{\alpha_{\theta_{1}}(k_{i})} sin(2\pi f_{i}t-\frac{1}{2}\phi_{\theta_{2}}(k_{i})), \tag{5}\]  
Figure 1: Frequency spectrum of the TL stimulus sound, \(s^{c}(t;\alpha_{30},\phi_{30})\), showing the relative magnitudes (spectral amplitudes in arbitrary units) of the pure tones used in the stimuli. where the azimuth angles \(\theta_{1}\) and \(\theta_{2}\) respectively refer to the ILD and ITD cues. It should be noted that the formulated sound stimulus was flexible to set the ILD and ITD cues from different azimuth angles. The duration of the sound signals was set to 200 ms and a Hanning window of 50 ms for onset and 50 ms for offset was used to eliminate the onset/offset effects of the rise and fall of the stimuli on the perceived lateralization through its envelope ITD. In the experiments, the stimuli sounds were presented to the participants in pairs of sound bursts consisting of a reference sound and a probe sound with a 200 msec gap between them. The reference sound was the first sound of the stimulus pair and contained interaural time and level cue information of azimuth \(\theta\). That is, the \(\alpha\) and \(\phi\) values were set to azimuth \(\theta\) and the reference sound was defined as, \(s^{c}(t;\alpha_{\theta},\phi_{\phi})\), at channel \(c\). The probe sound was the second sound of the stimulus pair. Probe sounds are defined under three conditions based on time and level cues they use. These conditions are time-only (TO), level-only (LO), and time-level (TL). The TO probe sound uses the ILD information from azimuth \(\theta\) and the ITD information from azimuth (\(\theta\pm 10^{\circ}\)). Then, the resulting TO stimulus can be given as: \(s^{c}(t;\alpha_{\theta},\phi_{\theta\pm 10^{\circ}})\). The LO probe sound uses the ITD information from azimuth \(\theta\) and the ILD information from azimuth (\(\theta\pm 10^{\circ}\)). Then, the resulting LO stimulus can be given as: \(s^{c}(t;\alpha_{\theta\pm 10^{\circ}},\phi_{\theta})\). The TL probe sound uses both of the ITD and ILD information from azimuth (\(\theta\pm 10^{\circ}\)). Hence, the resulting TL stimulus can be given as: \(s^{c}(t;\alpha_{\theta\pm 10^{\circ}},\phi_{\theta\pm 10^{\circ}})\).