INTERNACIONALIZACIÓN Y FUNDAMENTO DE DERECHOS

Before presenting the results of the model simulations, it is worth first discussing the results of subjective listening tests reported in the literature. There have been a large number of studies to measure human performance in locating a sound source, and some of them carried out more than several hundreds of trials, analysing them to attain the

associated statistics. Since the conditions of those experiments are diverse (as well as the analysis methods), a direct comparison is not easy to make between the localisation performances described by different studies. However, it is still meaningful to examine those subjective experiments that used similar stimuli in relatively consistent circum- stances. Among such comparative studies, Blauert [4] summarised a couple of previous experiments in the 1960’s and 70’s, and suggested that listeners can locate a sound source in the front and back more accurately than at lateral positions, which are rather classical data, but still agree well with those of recent experiments.

In Table 5.1, a few subjective experiments considered to be relevant to the current study have been listed in terms of their methodologies and source signal specifications. A main improvement in recent subjective experiments is the way listeners indicate the source location: in the studies summarised by Blauert [4], listeners were asked to move a

loudspeaker to the positions which they believe are 0◦_{, 90}◦_{, 180}◦ _{and 270}◦_{. However, in}

the majority of experiments performed in recent years, listeners wear an electromagnetic device that automatically reads the angular position to which their heads are directed. Undoubtedly, the latter method is fast and accurate in some ways, but there are concerns about systematic errors associated with, for example, spontaneous eye movement [39] and less mobility in indicating the rear source.

Stimuli Duration Direction Response protocol

Blauert [4] White noise pulse 100 ms Horizontal Alignment of a loudspeaker Makous and Middle-

brooks [38] Noise of random- phase flat-amplitude spectrum, 40∼50 dBSL 150 ms Horizontal Vertical

Head movement monitored by electromagnetic device Carlile et al. [39] Broadband white

noise, 70 dB

150 ms Horizontal Vertical Recanzone et al. [77] Gaussian noise,

30±2 dBSL

200 ms Horizontal

Current model Gaussian noise,

60∼80 dB at ear

entrance

100 ms Horizontal n/a

Table 5.1: Conditions of previous subjective experiments of sound localisation.

In Fig. 5.15, the listening test data from Blauert [4], Carlile et al. [39] and Makous and Middlebrooks [38] have been reproduced. For the purpose of comparison, some modifications have been made so that a positive localisation error may represent the

centroid of response angles greater than the target angle throughout the range of 0◦ _∼

360◦. In addition, horizontal data were unavailable in Makous and Middlebrooks [38],

and so the experimental results for a source at +5◦ _{elevation have been taken.}

For the frontal positions, the mean responses in the listening test data seem to agree with

each other, to some extent, up to about 130◦_{[see Fig. 5.15(a)]. Then, some discrepancies}

start to emerge and grow, and at 180◦_{, the data in Blauert [4] seem to diverge from the}

other available data reported by Carlile et al. [39] and Makous and Middlebrooks [38]. The latter two data sets show a similar tendency such that the localisation error turns

rapidly from positive to negative for the target locations around 90◦_{, where a similar}

observation can be made for the responses around 270◦ _{reported by Carlile et al. [39].}

It is remarkable that the localisation performance at 180◦ _{in Blauert [4] is much better}

than that in Carlile et al. [39] and in Makous and Middlebrooks [38] (if some extrapo- lation of data is allowed), which is demonstrated not only by Fig. 5.15(a) but also by Fig. 5.15(b) in terms of the standard deviation. Considering that their experiments have been carried out with fairly similar source signals, such a significant discrepancy for a sound source at the rear position can be probably ascribed to the method used to report the source location. In author’s opinion, it is uncertain which listening test data reflect the true statistics of human performance in sound localisation, since there are insufficient target locations in the report by Blauert [4], while the results in Carlile et al. [39] and Makous and Middlebrooks [38] could be vulnerable to the measurement error associated with, for example, listener’s use of eye movement.

It is also noteworthy that, despite some partial agreements noticed and discussed above, no pair of the three subjective experiments showed a satisfactory match with each other. This seems to imply that it is difficult to obtain any collective and conclusive statistics regarding human sound localisation ability by means of subjective experiments.

Having reviewed the results of the subjective listening tests reported in the literature, the current pattern-matching model can be adjusted to reflect the performance of human listeners in the task of sound localisation, in terms of the errors and the variances. For

a source signal identical to that employed to establish the template EI00

T, the pattern-

matching process without the internal error n(i, t, τ, α) gives a perfect localisation of

target sound sources, which is, however, undesirable. If a running noise is considered to be the source signal instead of the frozen noise used for the template, some errors can be incurred by the current model in the localisation task, but the range of the judgement errors and variances were found to be much less than those shown by the statistics for human subjects. Accordingly, the influence of the noise mask has been investigated by

controlling the parameter σn in Eq. (5.4) in an attempt to adjust the accuracy of the

current model.

Fig. 5.16 shows statistics of the current model with different values ofσn for the target

locations only in the right hemisphere. Both mean error and standard deviation of the model predictions increase in absolute value as more noise is added to the EI-patterns in each auditory frequency band independently. From Fig. 5.16(a), it is shown that

the mean error increases until a certain target position depending on the value of σ_n,

then starts to decrease as the source position approaches 90◦_{. Interestingly, the sign of}

the mean error switches from negative to positive around 90◦_{, which implies that the}

actual target position. In addition, there are two prominent maxima in the standard

deviation, where the first is located between 30◦ _{and 45}◦_{, again, depending on the value}

of σn, while the second is always found at 90◦. The greater variance for the target

locations near 90◦ can be understood in relation to the higher correlation observed for

pairs of EI-patterns in that region as shown in Fig. 5.7. It is also noticeable that the

standard deviation at 90◦ _{is particularly high compared to the adjacent target locations,}

which is possibly attributed to the side-effect of resolving the front-back confusion for

all other target angles except for 90◦_{. Nevertheless, it is not clear how the first peak}

of the standard deviation in the frontal hemisphere can be linked to the aspects of the pattern-matching procedure used in the current model.

Superimposed on the subjective experimental results reported in the literature, the line- connected dots in Fig. 5.17(a) represent the mean responses of 500 model predictions,

where the internal noise parameter σn = 0.12 has been found to give statistics most

similar to those of subjective test results. Although the agreement between the sim- ulation results and the published listening test data is not perfect, it is interesting to see that the current model gives predictions which are at least qualitatively consistent with the nature of the localisation tasks performed by human subjects. For example, the mostly positive errors for the target locations in the right frontal hemisphere have

been reasonably simulated where the sudden sign change near 90◦_{, in case of the test}

data reported by Carlile et al. [39] and Makous and Middlebrooks [38], has been also predicted well.

In terms of the standard deviation of the sound source judgements, the agreement be- tween the model predictions and the results of the listening tests is noticeable for the

target location at 90◦ _{and 270}◦ _{and those in the frontal area. For other target loca-}

tions, however, the simulation results appear to be misleading for the estimation of the variance in actual listening tests, where the variances for the rear target positions are

particularly low. Finally, the raw predictions of the current model for σn = 0.12 are

shown in Fig. 5.18 where the front-back confusion and the greater variabilities around lateral target positions are clearly observed.

To summarise, the localisation of broadband noise sources has been compared between the model simulation and the published listening test data. Some degree of agreement has been found between the two results especially in terms of the mean errors of the judgements, but there were also inconsistencies that are particularly prominent in the standard deviation. A further adjustment of the current model can be attempted by,

for example, considering a non-uniform noise maskn(i, t, τ, α) that reflects the probable

signal-to-noise ratio in neural process depending on the ITD and/or the ILD. However, it is not clear that any improvement made by such a manipulation would be confirmed

by subjective test results, which tend to involve many psychological factors other than actual hearing process, often giving inconsistent results from experiment to experiment, as partly shown by the previous studies discussed above.