## 1 Introduction
Several studies [11; 12; 13; 14] concluded that the reverberation between 20 ms and 80 ms (early reflection parts) affected the degree of externalization; increasing the reverberation to durations of longer than 80 ms-100 ms did not increase externalization further. [PERSON] et al. [15] characterized the statistical distribution of short-term binaural cues, i.e., ILDs and ITDs, in critical bands as a function of source-listener distances and investigated the impact of the sizes of these distributions (ILD and ITD fluctuations) on perceived externalization. The results of their study showed that the degree of externalization decreased substantially by compressing the ILD fluctuations of binaural speech signals containing mid- to high-frequency components (above 1 kHz). In contrast, the perceived externalization of low-pass-filtered speech sounds remained unaffected by the compression of ILD fluctuations. Therefore, the size of ILD fluctuations could be utilized as an indicator of the externalization of reverberant sound sources at mid- to high-frequencies. [PERSON] et al. [13] pointed  
Figure 1: Illustration of the setup of BRIR measurements. out that the binaural reverberation was important for externalization, while the monaural reverberation (identical reverberation in both ears) was not sufficient to externalize a virtual sound image well, especially for frontal sound sources. This finding revealed that the reverberation-related monaural cues, i.e., direct-to-reverberant energy ratio (DRR), might by useful for perceived externalization [16], but not as relevant as the reverberation-related binaural cues, i.e., ILD fluctuations and interaural coherence (IC). Furthermore, [PERSON] et al. [14] investigated the relative influence of reverberation in contralateral versus ipsilateral ear signals on externalization of a 45\({}^{\circ}\) sound source. The results indicated that the reverberation at the contralateral ear had more influence on perceived externalization than that at the ipsilateral ear; the degree of externalization remained almost unchanged by removing the reverberation in the ipsilateral ear signal. However, it is still unclear how this effect changes as a source moves from lateral to frontal incidence angles. [PERSON] et al. [17] studied the role of spectral details in BRIRs on perceived externalization. The magnitude spectra in the direct and reverberant part of BRIRs were smoothed by using gammatone filters with different bandwidths. The results of their study indicated that the spectral details in the direct part of BRIRs were essential for perceived externalization, while reducing the spectral details in the reverberant part of BRIRs did not affect externalization noticeably. This conclusion differs from the informal results obtained by [PERSON] and [PERSON] [8], where the degree of externalization was not substantially reduced by smoothing the magnitude spectra of HRTFs. It should be noted that the experiment in [8] was conducted under the free-field condition. Based on the two studies (cf. [8; 17]) mentioned above, it could be concluded that the spectral details in the direct sound are important for perceived externalization of virtual sound sources when reverberation is present. However, relatively little is known about whether the spectral details in direct parts of ipsilateral and contralateral ear signals have the same influence on perceived externalization. Other cues, e.g., dynamic cues caused by head or source movements, visual cues, etc., also play an important role in perceived externalization. Since they were not related to the present study, the details of these cues regarding externalization were not discussed in this paper. Readers can refer to some recent studies [18; 19; 20; 21; 22] for detailed information. This study aimed to investigate the influence of (a) smoothing the magnitude spectra of direct parts and (b) removing the reverberation, in contralateral and ipsilateral ear signals on perceived externalization. In the studies of [PERSON] et al. [13] and [PERSON] et al.