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9 Applications (II) – Speech Reception in Sound Fields |
Fig. 9.14 Examples of the ACF analyzed. The locations of sources and listeners are shown in fig. 9.12. (a) Source location at seat position B. (b) Source location at seat position B
the short time interval centered on the time, when (τe)min of the source signal was obtained. Figure 9.14 illustrates examples of the running ACF of source locations 2 and 6 at seat position B. A difference can be observed in the measured ACF due to the different transmission characteristics of the sound field.
Next, in order to find a relationship between the scale value and physical factors obtained by the measurement, a multiple regression analysis was made. The perceptual distance between the sound fields of a and b with respect to each factor was estimated in the following manner.
9.3.1 Perceptual Distance due to Temporal Factors
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Dτ1 = |log(τ1)a−log(τ1)b| |
(9.8) |
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Dφ1 = |log(φ1)a−log(φ1)b| |
(9.9) |
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t1 |
a |
t1 |
b |
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D t1 = |
log |
−log |
(9.10) |
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[ t1]p |
[ t1]p |
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9.3 Effects of Sound Fields on Perceptual Dissimilarity |
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195 |
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Tsub |
a |
Tsub |
b |
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DTsub = log |
−log |
(9.11) |
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[Tsub]p |
[Tsub]p |
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where D t1 andDTsub are the distances due to the normalized values with the most preferred [ t1]p and [Tsub]p, respectively. These preferred values are calculated by Equations (3.4) and (3.6) using (τe)min instead of (τe). The distances of temporal factors Dτ1 , Dφ1 , D t1 , and DTsub were calculated using logarithmic values.
9.3.2 Perceptual Distance due to Spatial Factors
DLL = |(LL)a−(LL)b| |
(9.12) |
DIACC = |(IACC)a−(IACC)b| |
(9.13) |
DτIACC = |(τIACC)a−(τIACC)b| |
(9.14) |
DWIACC = |(WIACC)a−(WIACC)b| |
(9.15) |
In the multiple regression analysis, the distance of dissimilarity for multiple physical factors is combined linearly, so that the total distance is given by
D = DL+DR = a DLL+b Dτ 1+c Dφ1+d DIACC+e DτIACC +f DWIACC +g D t1+h DTsub (9.16)
where DL = b’Dτ1 + c’Dφ1 + g’D t1 + h’DTsub , DR = a’DLL + d’DIACC + e’DτIACC + f’DWIACC and a’, b’, c’, d’, e’, f’, g’, and h’ are coefficients, which may be obtained by a stepwise regression method.
Prior to the multiple regression analysis, correlation coefficients between factors were figured out as listed in Table 9.6. Concerning the value of WIACC, it is a significant factor for determining the ASW, if source signals with different fre-
Table 9.6 Correlation coefficients between physical factors obtained by the acoustic measurements
|
DLL |
Dτ1 |
Dφ1 |
DIACC |
DτIACC |
DWIACC |
D t1 |
DTsub |
DLL |
1.00 |
−0.26 |
−0.30 |
0.41 |
0.56 |
0.21 |
−0.10 |
0.28 |
Dτ1 |
|
1.00 |
0.42 |
0.08 |
−0.18 |
−0.23 |
0.13 |
−0.34 |
Dφ1 |
|
|
1.00 |
0.38 |
−0.28 |
−0.04 |
0.23 |
−0.29 |
DIACC |
|
|
|
1.00 |
0.54 |
0.26 |
0.15 |
0.03 |
DτIACC |
|
|
|
|
1.00 |
0.59 |
−0.05 |
0.04 |
DWIACC |
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|
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|
|
1.00 |
−0.02 |
−0.11 |
D t1 |
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|
|
|
|
1.00 |
−0.25 |
DTsub |
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|
1.00 |
p < 0.01; p < 0.05.
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9 Applications (II) – Speech Reception in Sound Fields |
quency ranges are applied (Ando et al., 1999). However, it was eliminated from the analysis, due to the fact that the single source signal was used in this experiment. The same is true for the factor Wφ(0), fortunately. Results of the table show that
DWIACC , DLL and DIACC highly correlated with DτIACC (correlation coefficients with were 0.59, 0.56, and 0.54, respectively). Thus, τ1, φ1, τ1ACC, t1, and Tsub were
selected as a representative of these factors. The resulting distance of dissimilarity D is given by,
D ≈ DL + DR = aDτ1 + bDφ1 + cDτIACC + dD t1 + eDTsub |
(9.17) |
where DL = aDτ1 + bDφ1 + dD t1 + eDTsub , DR = cDτIACC , and coefficients obtained are a ≈ 1.91, b ≈ 3.37, c ≈ 7.59, d ≈ 0.37, and e ≈3.90 (Table 9.7).
Figure 9.15 shows the relationship between measured scale values of dissimilarity obtained at each seat position and calculated values of dissimilarity. The correlation coefficients between them at each seat position were 0.92 (p < 0.01) at seat position A, 0.79 (p < 0.01) at seat position B, 0.90 (p < 0.01) at seat position C, and 0.84 (p < 0.01) at seat position D. The total correlation coefficient between scale
Table 9.7 Partial regression coefficients for significant factors obtained by multiple regression analysis with normalized partial regression coefficients
|
Dτ1 |
Dφ1 |
DτIACC D t1 DTsub |
||
Normalized partial coefficients |
0.10 |
0.15 |
0.69 |
0.08 |
0.17 |
p value |
<0.02 |
<0.01 |
<0.01 |
<0.01 |
<0.05 |
|
|
|
|
|
|
Fig. 9.15 Relationships between calculated scale values by Equation (9.17) and scale values of dissimilarity judgments at each seat position (r = 0.84; p < 0.01). The locations of listeners are shown in Fig. 9.12. • , values obtained at seat position A (r = 0.92; p < 0.01); ◦ , values obtained at seat position B (r = 0.79; p < 0.01); , values obtained at seat position C (r = 0.90; p < 0.01); , values obtained at seat position D (r = 0.84; p < 0.01)
9.3 Effects of Sound Fields on Perceptual Dissimilarity |
197 |
values of dissimilarity and calculated values of dissimilarity for all seats was 0.84 (p < 0.01).
In summary, the significant factors that influenced dissimilarity judgment in the existing hall were:
1.Temporal factors τ1 and φ1 extracted from the ACF at the minimum effective duration (τe)min of the signal. These factors correspond to the percepts of pitch and pitch salience.
2.The spatial factor τIACC extracted from the IACF at (τe)min that corresponds to the perception of spatial diffuseness and envelopment.
3.Temporal factors of the sound field, t1 and Tsub i.e. the times of early reflections and later reverberations, respectively.