Aplicación del CBFM a geometrías en un único bloque 159

The 8192-sample impulse responses between loudspeaker and in-ear microphones can be further processed and equalised with respect to the free-field responses. As for the distal-region measurements, minimum phase inverse filters have been obtained from the free-field responses, which were then applied to the measured HRIRs [52]. In order to ac- quire the inverse filters, the left- and right-channel free-field responses are first windowed in the time domain by 200-point Hanning windows, the maximum of which are aligned with the absolute peaks of the responses. It is further observed that the responses before the 250th sample can be zeroed, which contain no meaningful data. These windowing and zeroing processes can disregard the unnecessarily long tails of the impulse responses, thus suppressing unwanted noise and reflection [see Fig. 3.12(a)]. Then, a 8192-point fast Fourier transform (FFT) is applied to the impulse responses to give magnitude and phase responses in the frequency domain. In order to prevent the final inverse filter from having a ‘ringing tail’ due to any excessively low amplitude in the high frequency range, the magnitude responses over 9.5 kHz have been flattened as depicted by the dashed lines in Fig. 3.12(b) [52]. Considering that the effective frequency range of the measure- ment is already limited by the microphone and loudspeaker responses, this equalisation process does not significantly influence the reliability of the measurement any further. The modified magnitude responses are recombined with the corresponding phase re- sponses, and these frequency responses are inverted, inverse-Fourier-transformed, and FFT-shifted. As shown in Fig. 3.12(c), the inverse filters at this stage are mixed-phased with non-causal responses. Finally, minimum phase inverse filters are acquired by taking

real cepstra using therceps function in Matlab 7.0 [see Fig. 3.12(d)].

The raw recordings of HRIRs are also windowed with 200-point Hanning windows and zeroed in the same way that the free-field responses are processed. These treated HRIRs are then convolved with the inverse filters acquired above. Finally, the data sequences from 200th to 455th points are only taken as 256-point equalised HRIRs.

In contrast to the post-processing for the distal-region data, it has not been possible to acquire usable inverse filters from the proximal-region free-field responses due to the limited and unreliable transducer responses at low frequencies. Therefore, no further process has been implemented in time-domain except that both HRIRs and free-field responses were windowed (200-sample Hanning window as above) and zeroed (until the 85th sample). On the other hand, in the frequency domain, the HRTFs obtained by FFT have been equalised by the free-field responses only in the magnitude responses [53].

Fig. 3.13 shows the distal-region HRIRs of subject SF at a few representative azimuth angles before and after the post-processing. In general, the impulse responses presented in this figure contain some known features of directional transfer functions: the greater interchannel differences in the attack times and the peak amplitudes at lateral angles

and the well-aligned and almost identical responses at 0◦ _{[27, 52, 55]. It is also observed}

that, after the equalisation, unwanted reflections and high-frequency noises have been relatively well controlled to result in smoother impulse responses.

The distal-region frequency domain responses shown in Fig. 3.14 can give clearer pictures of the impact of the post-processes including the free-field equalisation. (In Fig. 3.14, responses in full 8192-samples rather than the 256-sample truncated version are shown for discussion purpose.) First of all, the Hanning windows applied to both the free- field responses and the raw HRIRs effectively removed the high-frequency variability, particularly from the contralateral channels as shown in panels (c) through (d). In addition, flat and smooth responses at low frequencies have been also achieved, which can be directly attributed to the free-field equalisation. In both frequency responses before and after the post-processing, some well-known features of HRTFs can be clearly observed, which include the pinna notch at about 9 kHz [panels (a) and (b)] and the greater interaural level difference at higher frequencies [panels (c) through (f)] [27, 52, 55].

It is known that equalised HRTFs at 0◦ converge approximately to 0 dB at very low

frequencies, since the presence of the human head hardly affects the sound field in this range, thus giving responses nearly identical to the free-field responses [27]. However, in the current data shown in Figs. 3.14(b) [and 3.16(b)], such a convergence is not always observed, which perhaps resulted from the less satisfactory microphone responses in the very low frequency range. Considering this limited reliability at low frequencies particularly below 100 Hz, further post-processing such as bandpass filtering can be carried out depending on the nature of actual application.

In the time domain, it is difficult to observe differences between the distal- and the proximal-region HRIRs when the responses in Fig. 3.15 are compared to those in Fig. 3.13. (It is recalled that there is no equalised data for the proximal-region due to the absence of the inverse filtering process.) The time-domain features mentioned above for the distal-region HRIRs are also found in the proximal-region data in terms of the interchannel differences in attack times and amplitudes. However, in the frequency domain a clear contrast can be made as shown in Fig. 3.16, where the greater interaural level difference is observed for the proximal-region HRTFs than the distal-region. The increased ILD in the HRTFs measured at shorter distance is commonly reported in similar studies [53, 55], which have been explained well both in theory and numerical

simulations by the emphasised head-shadowing in the near-field. The difference between the distal- and the proximal-region HRTFs will be further discussed in relation to the characteristic curve in the following sections. Finally, it is noteworthy that HRIRs and HRTFs of the participants other than the subject SF were in common in showing the above discussed features, although they will not be presented here in detail.