Aplicación del CBFM a geometrías en varios bloques 164

Having found that the HRTFs acquired in the current measurement are qualitatively comparable to those reported in the literature, the acquired HRIRs can be further pro- cessed to give characteristic curves. In order to obtain ITDs [see Fig. 3.17(a)], a 100-ms

pure tone signal at frequency, f is first modulated at an envelope frequency of 20 Hz

and zero-padded to give a target signal. Then, this signal is convolved with the post- processed HRIRs for a certain azimuth angle, producing synthesised binaural signals. (Post-processed HRIRs indicate the equalised HRIRs in case of the distal-region data, but the windowed HRIRs for the proximal-region.) The resolution of the final ITD depends on the sampling frequency, and the binaural signals can be oversampled at a higher sampling frequency which has been shown to give a smoother ITD curve. The peak of the cross-correlation function can be found for these interpolated signals to give the ITD, where it is necessary to correct the quasi-periodic ITDs by adding or subtract- ing multiple numbers of signal periods. On the other hand, ILD can be obtained simply

by comparing the magnitude responses of the HRTFs at the designated frequency f

as shown in Fig. 3.17(b). The ITDs and ILDs at this stage are true values reflecting the shape of subject’s head and torso and the distance from the loudspeaker. However, there can be a few data points away from the expected ‘trajectory’ of each interaural disparity, possibly due to the measurement error or the tolerance of the positioning er- ror. Therefore at the final stage, a curve fitting process has been additionally carried out to find smooth functions for the ITDs and the ILDs [see the last processes in Figs. 3.17(a) and (b)].

Figs. 3.18(a) and (b) show ITDs and ILDs at 600 Hz obtained from the distal-region HRIRs (Subject SF) where raw ITDs and ILDs have been fitted with polynomials at

the order of 11 (using Matlab 7.0 built-in functions,polyfit and polyval). The order of

curve-fitting has been set relatively high in order to make sure that no significant curve shape is lost. It is obvious that the features of the ITD and the ILD functions have been well preserved while irregular data points especially at lateral angles have been smoothed out. As expected from the average values found in previous studies in the

literature [27], the ITD ranges from ∼ −800µs to ∼ +800µs [40], and the ILD from

∼ −7.5 dB to∼+7.5 dB.

Combining ITD and ILD functions in Figs. 3.18(a) and (b) can give a characteristic curve

shown in Fig. 3.18(c) where it has been marked at every 10◦ _{of azimuth angle. Features}

discussed in section 2.2 can be found. Firstly, the two legs of the curve representing the frontal and the rear areas are not overlapped but are distinctive from each other, which implies that source localisation in the horizontal plane is even possible based only on the ITD and ILD information, but can be vulnerable to front-back confusion if there are

errors or noise in processing the binaural input signals. It is also apparent that sound sources at lateral angles can give similar combinations of ITD and ILD as there are more marks around the turning points of the characteristic curve in Fig. 3.18(c), which has been related to the more localisation error for these source positions in section 2.4. The characteristic curve shown in Fig. 3.18(c) is reasonably symmetric with respect to the origin where ITD and ILD are zero. However, it is noteworthy that the ITDs

and the ILDs are not necessarily identical for sound sources at 0◦ _{and 180}◦_{, which can}

be attributed partly to the asymmetry in the shape of head, but also to the random error in positioning the subject by the head-tracking device. (Remember that there were, inevitably, certain tolerances allowed for translational and rotational degrees of freedom. See section 3.2.2.) The characteristic curves obtained for all other subjects have similar

features to those as shown in Fig. 3.18(d), where the mismatch between 0◦ _{and 180}◦

can be found in most of the curves, and, depending on the subject, the shapes of the left and right ‘lobes’ of the characteristic curves have been found to be different from each other, again, due to the left-right asymmetry of the head. A detailed inspection of Fig. 3.18(d) illustrates that the width of the lobes and the degree of left-right asymmetry in individual curves may vary from subject to subject, and it is reasonable to say that the characteristic curve is as unique for each subject as the individual HRTFs at a single frequency.

In contrast to the distal-region results presented above, ITDs and ILDs obtained from the proximal-region HRIRs have been found to be mostly asymmetric with respect to the median plane as shown for the 600-Hz pure tone signal in Figs. 3.19(a) and (b) (subject SF). (The order of curve-fitting is 11 as was the case for the distal-region.)

Although ITD is relatively close to 0µs at 0◦ _{and 360} ◦ _{in Fig. 3.19(a) thanks to}

the initial alignment procedure inspecting the arrival times of the signals (see section

3.2.2), it is about 200µs at 180◦_{, far away from its ‘home’ position, when the subject}

faces backward. This mismatch severely disrupted the symmetry of the ITD curve,

broadening the positive peak at around 270◦_{. A similar observation can be made for the}

ILD function shown in Fig. 3.19(b), and it appears that there have been some systematic errors in the measurement which became more prominent in case of the proximal-region. As a result, the characteristic curve shown in Fig. 3.19(c) is significantly distorted, and

particularly, the shapes of the two turning points approximately at 90◦ and 270◦ appear

to be very different from each other. This distortion of the characteristic curve has been also found in the results for other subjects as illustrated in Fig. 3.19(d), which makes it difficult to determine whether the proximal-region characteristic curves are uniquely shaped for each person. The errors responsible for the distorted characteristic curves will be discussed in more detail in section 3.5.

Apart from the more prominent asymmetry resulting in the distorted curves, the proximal- region results are also distinguished from the distal-region data by the greater range of ILD. As clearly depicted in Fig. 3.19(b), the maximum of the absolute level difference is now about 12 dB, greater approximately by 5 dB than that for the distal-region. At- tributed to the increased influence of the head-shadowing at a shorter distance, this expanded ILD range is also reported in the literature [53, 55].