7.2 Apparent Source Width (ASW) |
127 |
We shall clearly show differences in the three temporal factors, τ e, τ 1, and φ1, extracted from the ACF as a function of the incident angle of elevation. According to the model described in Section 5.1, localization in the median plane Lmedian is grouped with monaural, temporal sensations because it appears to be based on factors extracted from the autocorrelation function:
Lmedian = SL = fL (te, t1, f1) |
(7.2) |
Like other perceptual attributes based on ACF factors, we expect sound localization in the median plane to exhibit “left hemisphere specialization.”
The amplitudes of the transfer functions for sound incident from the median plane to the ear entrances as measured by Mehrgardt and Mellert (1977) were transformed into equivalent autocorrelation functions (ACFs). The following steps obtain the ACFs from these transfer functions:
1.Data sets were obtained from the figures from the Mehrgardt and Mellert paper using an optical image reader (scanner), with 300 data points each.
2.Amplitude as a function of frequency in the logarithmic scale was obtained.
3.Each amplitude in decibel scale was converted to a corresponding real number, and the ACF was calculated by inverse Fourier transform after passage through an A-weighted filter.
Examples of the NACF are shown in Fig. 7.2. There is a certain degree of correlation between both τn and τn+i, φn and φn+i, where τn and φn are the delay time and amplitude, respectively, of the n-th peak of the NACF. Thus, τ1 and φ1 can be representatives for sets of τn and φn. Examples of plotting the amplitude of the ACF on a logarithmic scale as a function of the delay time are shown in Fig. 7.3. A straight line can fit the envelope of the decay of the ACF in the logarithmic scale, and τe was easily obtained from the delay at which the envelope drops below −10 dB. The value (0) is not considered as a cue for sound localization here. Three factors extracted from the NACF are shown in Fig. 7.4. The value of τ1 for incident angles from 0◦ to 45◦ is almost the same, but τe for incident angle of 45◦ (τe = 3.1 ms) is much larger than that at 0◦ (τe = 2.1 ms). The value of τ1 for incident angle of 180◦ is different from those for the above two angles, however, the φ1 is relatively small.
Obviously, the angle in the median plane can be distinguished by the three monaural temporal factors τ1, φ1, and τe. These factors, therefore, may play an important role in the perception of localization in the median plane.
7.2 Apparent Source Width (ASW)
We shall show that apparent source width (ASW) may be described in terms of factors extracted from the IACF.
128 |
7 Spatial Sensations of Binaural Signals |
Fig. 7.2 Examples of the NACF of different incident angles in the median plane, 0◦, 45◦, and 180◦
7.2 Apparent Source Width (ASW) |
129 |
Fig. 7.3 Examples of the effective duration extracted from the NACF envelope (in logarithm) for different incident angles in the median plane, 0◦, 45◦, and 180◦
130 |
7 Spatial Sensations of Binaural Signals |
Fig. 7.4 Three-dimensional illustration plotted for three factors, φ1, τ1, and τe, which may distinguish different incident angles in the median plane. Numbers in the circles indicate incident angle in degrees
7.2.1 Apparent Width of Bandpass Noise
For sound fields passing sounds with predominately low frequencies, the interaural correlation function IACF has no sharp peaks in the interaural delay range of less than 1 ms, and the width of the major IACF peak, WIACC, becomes “wider.” The WIACC of band-pass noise may calculated theoretically using the following equation (Ando, 1998),
WIACC(δ) |
≈ |
4 |
cos−1 |
1 − |
δ |
(7.3) |
ω |
IACC |
where ωc = 2π(f1 + f2), and f1 and f2 are the lower and upper frequencies of an ideal filter. For the sake of simplicity, δ is defined as 10% of the maximal value of the interaural correlation function IACF, i.e. δ = 0.1(IACC).
The scale value of the ASW was obtained by the PCT with 10 subjects (Sato and Ando, 1996). In order to control the value of WIACC, the center frequency of the 1/3-octave band-pass noise was changed as 250, 500, 1, and 2 kHz. The value of IACC was adjusted by controlling the sound pressure ratio between reflections (ξ =
±54◦) and the direct sound (ξ = 0◦). To avoid effects of the listening level on the ASW (Keet, 1968), the total SPL at the ear canal entrances of all sound fields was kept constant at a peak of 75 dBA. Subjects judged which of two sound sources they perceived to be wider.