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6.4.2 Loudness of Complex Noise
The loudness of spectrally complex noise, which includes band-pass noises, with multiple pass bands and center frequencies, is examined as a function of the effective duration of the ACF (τe). The center frequencies of two components of the complex noise were 2000 and 3000 Hz, so that the perceived pitch was centered on 1000 Hz due to the missing fundamental phenomenon as discussed in Section 6.2.2. To control the τe of the source signal, the bandwidth of each component noise was modified using a 2068 dB/octave sharp filter. Scale values for loudness obtained using the PCT were similar to those for single noise components centered on 1000 Hz. As with single noise components, loudness increases with the value of τe of the source signal, and the loudness of the complex noise with identical SPL is not constant within the critical band, 160 Hz.
This study examined the loudness of spectrally complex noise (Sato et al., 2001). The complex noises used consisted of multiple band-pass noises whose passband center frequencies were harmonics of a 1000-Hz fundamental. There were no correlations between the noise bands. The perceived pitch was centered on 1000 Hz, the “missing fundamental” of the noise bands. Perceptual judgments by listeners were compared with those for the single band-pass noise of 1000 Hz and 2000 Hz center frequencies in terms of the factors extracted from the ACF.
Source signals in the experiments included: (1) a complex noise stimulus with two band-pass noise components whose center frequencies were 2000 and 3000 Hz, and (2) a complex tone with pure-tone components of 2000 and 3000 Hz. All partial components had the same SPL, measured by taking the square root of the ACF of the recorded signal at the origin of the delay time, (0). To control the τe of the ACF of the complex noise, the bandwidths of each partial noise ( f) were changed to 0, 40, 80, 160, and 320 Hz with the cutoff slope of 2068 dB/octave. In the 0 Hz bandwidth condition only the slope component of the filter was used. Figure 6.17 shows the normalized ACF of complex noise with fundamental frequencies of 1000 Hz and that of a single noise component centered on 1000 Hz. As shown in Fig. 6.18a, all of the ACFs indicate the maximum peak at τ1 = 1.0 ms. Figure 6.18b and c show the measured φ1 and τe of the source signals as a function of the bandwidth.
Loudness judgments were performed using paired comparison tests (PCT). Pairwise comparisons were made using the complex tones and five complex noises ( f = 0, 40, 80, 160, 320 Hz). The same source signal was presented to both ears through headphones. The magnitude of the IACC was thus kept constant at unity. All stimuli were fixed at the same SPL at 74 dBA by measurement of (0). SPL was calibrated by using a dummy head with 1/2-inch condenser-type microphones at both ears. Input signals were digitized at 24 kHz sampling frequency. Fluctuation of the measured (0) for all stimuli were within ±0.06 dB when the duration of the signals was lengthened beyond 0.8 s; therefore, the stimulus duration was chosen at 1.0 s.
Four subjects with normal hearing ability were seated in the anechoic chamber and asked to judge which of two sound signals they perceived to be louder. The rise and fall times were 50 ms, and the silent interval between the stimuli was 0.5 s. Each
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Fig. 6.17 Normalized ACFs of complex multiband noises with fundamental frequencies of 1000 Hz (left-hand side) and single band-pass noises with 1000 Hz center frequency (right-hand side) for different passband bandwidths ( f). (a) f = 0 Hz. (b) f = 40 Hz. (c) f = 80 Hz. (d)f = 160 Hz. (e) f = 320 Hz
pair of stimuli was separated by an interval of 3.0 s, and the pairs were presented in random order. A single test session consisted of 15 pairs [N(N – 1)/2; N = 6] of stimuli and lasted about 1.5 minutes. Ten sessions were performed for each subject.
Forty responses (4 subjects × 10 sessions) to each stimulus were obtained. Consistency tests indicated that all subjects had a significant (p < 0.01) ability to
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a
b
c
Fig. 6.18 Measured factors extracted from the ACF of the source signal as a function of the bandwidth: , complex multiband noises with fundamental frequencies of 1000 Hz; , single band-pass noises of 1000 Hz center frequency. (a) τ1. (b) φ1. (c) τe
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discriminate loudness. The test of agreement also indicated that there was significant (p < 0.05) agreement among all subjects. Scale values for loudness were obtained by applying the law of comparative judgment. The relationship between the scale value of loudness and the bandwidth of each partial component of the complex noise with its fundamental frequency of 1000 Hz is shown in Fig. 6.19. The minimum loudness was observed for a bandwidth of 160 Hz. Loudness increased with increasing τe of the source signal within the bandwidth of 160 Hz, as shown in Fig. 6.19 for the complex noise. Analysis of the variance for the scale values of loudness showed that there were significant differences between the pairings of a complex tone and 160 Hz; 0 and 80 Hz; 0 and 160 Hz; 40 and 80 Hz; and 40 and 160 Hz. We find it remarkable that the pattern of the perceived loudnesses of single band-pass noises with 1000 Hz center frequencies and varying bandwidths closely resembled that of multiband complex noises with pseudo-fundamentals at 1000 Hz (compare Fig. 6.19 with Fig. 6.16c).
Fig. 6.19 Scale values of loudness as a function of the bandwidth for complex noises with fundamental frequencies of 1000 Hz. Different symbols indicate the scale values obtained with different subjects (four subjects)
All of the source signals used in this experiment had a fundamental frequency of 1000 Hz, and in fact the measured τ1 was 1.0 ms. In our preliminary experiment, a different set of subjects matched the pitch of the complex noise to 1000 Hz. The pitch of a complex tone consisting of the second and third harmonics corresponds to τ1 for fundamental frequencies below 1200 Hz. For missing fundamentals above 1200 Hz, the probability of accurate pitch matching rapidly decreases (see Section 6.2.3).
As shown in Fig. 6.20, the loudness of the sharply (2068 dB/octave) filtered single band-pass noise centered on 2000 Hz that was obtained by constant method is flat up to 160 Hz, although the τe increases as bandwidth decreases, as shown in Fig. 6.21. Thus, loudness may be described in relation to effective duration, τe, for fundamental frequencies below 1200 Hz, which is the upper limit of missing
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Fig. 6.20 Loudness of single band-pass noises centered at 2000 Hz obtained by the constant method comparing the 2000-Hz tone as a function of the bandwidth. Different symbols indicate the loudness obtained with different subjects (six subjects)
Fig. 6.21 Measured factor τe extracted from the ACF of the band-pass noise of 2000-Hz center frequency as a function of the bandwidth
fundamental percepts. In these experiments, we found that loudness for the complex noise with fundamental frequencies of 1000 Hz is similar to that of the single noise component centered on 1000 Hz. This is because both signals have the same τ1. Also, loudness increases with the increasing value of τe within the critical band of 1000 Hz. Loudness for the band-pass noise, centered on 2000 Hz, is not affected by the value of τe because of the limitation on the ACF model. It is worth noting we should take the spatial factors extracted from the IACF into consideration when estimating the perceived loudness of a sound in the context of a sound field (e.g., Edmonds and Culling, 2009).
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The sensation of temporal duration (DS) is introduced here. Every auditory event that is detected, including musical notes and speech sounds, has a perceived duration. Obviously, the sense of duration depends most directly on the physical signal duration, D. But apparent duration can be influenced by other acoustic factors as well. In terms of internal auditory representations, we show here that perceived duration also covaries with tone frequency and with its corresponding temporal factor in the ACF, τ 1, and consequently, with the pitch that is perceived (Ando et al., 2002).
This experimental study probed differences in the perception of duration for pure and complex tones for two frequencies (Saifuddin et al., 2002). The experiment used paired comparisons (PCT). Sound pressure level was fixed at 80 dBA throughout and all waveform amplitudes were ramped during onsets and offsets with rise/fall times of 1 ms, i.e., the time required to reach a threshold 3 dB below the steady level.
Perceived durations of the two-component complex tones (3,000 and 3,500 Hz) having a fundamental at 500 Hz were compared with those evoked by pure tones with frequencies of 500 or 3,000 Hz. Pairs of stimuli were presented randomly to obtain scale values for duration sensation (DS). Three signal durations, including rise/fall segments, were used for each of the stimuli: D = 140, 150, and 160 ms. There were thus 9 stimulus conditions and 36 pair-wise stimulus combinations. The source stimuli were presented in a darkened soundproof chamber from a single loudspeaker directly in front of the center of the seated listener’s head at a horizontal distance of 74 (±1) cm. Ten 22to 36-year-old subjects with normal hearing participated in the experiment. Each pair of stimuli was presented five times randomly within every session for each subject.
Observed scale values for the perceived durations of the nine stimuli are shown in Fig. 6.22. Whereas signal duration and stimulus periodicity had major effects on perceived duration, the number of frequency components (1 vs. 2) did not. Perceived durations of tones with the same periodicity (f, F0 = 500 Hz) were almost identical, whereas durations for pure tones of different frequencies (500 vs. 3000 Hz) differed significantly. This difference was approximately 10 ms (judging from equivalent scale values, the 500 Hz pure tone appeared about 10 ms longer than the 3,000 Hz tone). Thus, the perceived duration (DS) of the higher frequency pure tone (3000 Hz; τ 1 = 0.33 ms) was found to be significantly shorter (p < 0.01) than that of either the lower frequency pure tone (f = 500 Hz; τ 1 = 2 ms) or the complex tone (F0 = 500 Hz; τ 1 = 2 ms). Also, the scale values of duration sensation between the two pure tones: τ 1 = 2 ms (500 Hz) and 0.33 ms (3,000 Hz) are almost parallel, so that the effects of periodicity (τ 1) and signal duration (D) on the apparent duration (DS) are independent and additive. These relations are expressed in Equation (6.10), where S is the scale value of the perceived duration.
S = SL = fL(τ1,D) = fL(τ1) + fL(D) |
(6.10) |