## 1 Introduction
In a study by [PERSON] and [PERSON] [27], they used complex signals of mid-band (noise with a center frequency of 750 Hz) and high-band (noise with a center frequency of 2850 Hz) to find the effectiveness of ITD and ILD cues by measuring the ITD when there was an opposing ILD of 0, 1 or 2 dB in different reverberation conditions. In the present study, however, the first two harmonics of a 261-Hz tone are chosen as low-frequency components and its 7 th through 19 th odd harmonics are chosen as high frequency components of the test stimulus. As the effect of the ITD and ILD cues are of equal importance for mid-frequencies (783 Hz\(\sim\)1566 Hz) this range are discarded from the stimulus and instead, the ranges in which either of the ITD and ILD cues is mostly effective in lateralization are selected. Another reason why the second harmonic of the 261 Hz-tone, which would have been at 783 Hz, is not included in the low-frequency band of the sound stimulus is connected to the findings suggesting that humans may use different ITD-based sound lateralization strategies for different sound frequencies. For instance, based on data from the barn owl, gerbil, cat, and human, [PERSON] and [PERSON] [28] proposed a model in which two types of optimum coding strategy were apparent: In humans, for the lowest frequencies, the optimum strategy involves two distinct sub-populations, as for the classical case of the gerbil, whereas for the highest frequencies above 700 Hz a homogeneous distribution is optimal. Because 500 Hz appears to be the frequency where the transition from the classical strategy to a different strategy takes place, we prefer the former to avoid possible complications which might be caused by the involvement of two different ITD-coding strategies respectively for frequencies lower than 700 Hz and between 700 Hz and 1500 Hz. To impose location information to sound bursts, various studies conducted previously used arbitrary ITD and/or ILD values from available trading ratio tables [29] or the cue values extracted from the head-related transfer function (HRTF) [30, 31, 32]. The results of a study by [PERSON] et al. [33], in which they compared the localization performances of the subjects when they were presented with virtual sounds simulated by using individualized and generic HRTFs, showed that there was no clear advantage in using individualized HRTFs in this respect (under both echoic and anechoic conditions). Therefore, in the current study, we use the ITD and ILD values that are extracted from a generic HRTF dataset. In the current study, we present two main contributions in modeling roles of ITD and ILD in sound lateralization. First, we model the direction of arrival of a single tone separately for ITD and ILD cues in the form of phase and magnitude differences, which are extracted from the frequency domain characterization of the right and left HRTF responses. This avails us to monitor contribution of each cue in perceived lateralization change precisely, whereas in the literature common practice sets one of the ITD or ILD cue as the control signal and sets the other one to zero that results one cue to point the center. Second, we estimate the relative contribution of the ILD and ITD cues in sound lateralization using the diversity combination assumption for the integration of these cues based on the binary additive white-Gaussian noise channel model.