Relationship between the shape of amplitude envelope and the hearing sensation of fluctuation on the simulated exhaust sound of motorbikes Nozomiko Yasui 1 Graduate School of Science and Engineering, Saitama University 255 Shimo-Okubo, Sakura-ku, Saitama City, Saitama 338-8570 Japan

ABSTRACT Previous studies showed that the procedure for estimating Fl uctuation St rength (FS) observing both constant fluctuation and deviation for time and amplitude approximately estimated the hearing sensation of fluctuation from tremolo played on the mandolin. Moreover, another one presented another procedure for estimating FS from the exhaust sound of various motorbikes by proposing new indexes about the shape of the amplitude envelope. However, the procedure targeted only the recorded exhaust sound of those motorbikes wasn't clarified the relationship between the shape and sensation hearing of fluctuation yet. Here, this paper explores acoustic characteristics that represent the shape of amplitude envelope and investigates the relationship between those characteristics and the sensation hearing of fluctuation. Investigations were carried out by using amplitude-fluctuated white noise which was designed to have various acoustic characteristics for the shape. Those white noises have characteristics of amplitude fluctuations in motorbikes. Then, the hearing sensation of fluctuation on those sounds was assessed and investigated the relationship between those characteristics and the sensation of hearing fluctuation. Results showed that those characteristics, especially the shape of the amplitude envelope on rising time, influence the hearing sensation of fluctuation.

1. INTRODUCTION

Modulated sounds elicit the sensation of hearing fluctuation. Previous studies represented the sensation of hearing fluctuation as Fl uctuation St rength (FS) by conducting psychoacoustical experiments [2,3]. FS is elicited for modulated sounds with a modulation frequency of up to around 20 Hz. The findings were that the FS from an Am plitude -M odulated br oad ba nd no ise (AM BBN) with a modulation frequency within 4-8 Hz is larger than that outside this range.

Another study computed FS from physical parameters of fluctuating sounds [3-8]. The FS estimated by extracting characteristics of the fluctuation from acoustic signals was confirmed to correspond approximately to the sensation of hearing fluctuation. The FS estimated using that procedure and commercial software for evaluating sound quality were found to represent the sensation of hearing fluctuation from an AM BBN [4, 8]. However, fluctuating sounds produced at constructions and/or traffics or musical instruments had not yet been investigated.

In a previous study, it was developed a procedure for estimating FS of a tremolo produced by irregular plucking of a mandolin [1]. It was found that the constant fluctuation of a tremolo elicited with only the average plucking rate and irregular fluctuation elicited with deviation for time and amplitude. In the procedure, FS was estimated using the extracted indexes for those fluctuations.

1 nyasui@mail.saitama-u.ac.jp

Moreover, another study presented another procedure for estimating FS from the exhaust sound of various motorbikes by proposing new indexes about the shape of the amplitude envelope [9]. In the procedure, it was added the characteristics for the shape of the amplitude envelope to the procedure for estimating FS. Multiple regression analysis was conducted to estimate FS using subjective evaluation results and indexes, where the indexes for the constant and irregular fluctuations were calculated from the procedure in previous studies [1] and the indexes for the shape such as acoustic power, normalized acoustic power, fluctuation depth for rising and falling, the slope for rising and falling, the duration for rising and falling and spectral centroid were newly calculated. It was shown that the procedure using specified features for shapes of the amplitude envelope on explosive sound correctly estimates FS for exhaust sounds with various shapes of the amplitude envelope.

However, the procedure targeted only the recorded exhaust sound of those motorbikes wasn't clarified the relationship between the shape and sensation hearing of fluctuation yet. Here, this paper explores acoustic characteristics that represent the shape of the amplitude envelope and investigates the relationship between those characteristics and the sensation hearing of fluctuation.

2. SUBJECTIVE EVALUATION EXPERIMENT

2.1. Method The aim of the subjective evaluation experiment is to obtain the subjective scores for the sensation of hearing fluctuation from amplitude-fluctuated white noises which were designed to have various acoustic characteristics for the shape. This study conducted a magnitude estimation experiment with six listeners in a soundproof room. In this study, the sound levels for those amplitude-fluctuated noises were measured in a soundproof room. A total of those subjects with an average of 23.5 years (21 to 36) took the experiment. 6 subjects(S 1 ~S 6 ) were male and 1 subject was female. A total of 18 noises were used as stimuli.

This experiment was conducted by the magnitude estimation method. Pairs of stimuli were presented to the listeners. A number (e.g., 100) representing the magnitude of fluctuation was assigned to the first stimulus on the pair. The listeners were asked to rate the magnitude of fluctuation for the second stimulus within each pair and compare it to this assigned number. For example, for a decrease in fluctuation by a factor of two, the listeners had to write the number 50 on an answer sheet. A stimulus amplitude-fluctuated by a sine wave of 8 Hz fluctuation frequency was chosen as the first stimulus of each pair.

The stimuli were presented to the listeners through a headphone. The headphone (MDR- CD900ST, Sony Marketing Inc.) was used for the evaluation. Before the experiment, each listener was allowed to adjust the acoustic sound level to one that best enabled him or her to listen to the amplitude-modulated sounds. The average level was about L A = 59.7 dB.

2.2. Stimuli Stimuli were a total of 21 white noise amplitude-fluctuated by various amplitude envelopesx with 3 fluctuation frequencies. Used fluctuation frequencies were 4, 8 20 Hz. 3 of those stimuli were synthesized using a sine wave as an amplitude envelope. The others were synthesized using various amplitude envelopes which were composed of three amplitude envelopes on rising and two types of one on falling. Used ones on rising were a linear line and those ones on falling were amplitude envelopes extracted from the motorbike’s exhaust sounds. The levels of acoustic power of the stimuli were equalized.

Those 18 fluctuated sounds (3 fluctuation frequency × 3 kinds of the amplitude envelope on rising × 2 types of the amplitude envelope on falling) were created under the under condition.

• Amplitude envelope on rising: linear line with 3 kinds of r atios of ri sing ti me (RRT) per one period. • Amplitude envelope on falling: one-period envelope extracted from exhaust sounds of the motorbike which is FTR (Honda Motor Co., Ltd.) and SEROW250 (Yamaha Motor Co., Ltd.) Used RRT were 0.1, 0.5 & 0.9. The overview of RRT is outlined in Fig.1.

Amplitude

Amplitude

Amplitude

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Figure 1: overview of RRT.

(a)RRT:0.1, Envelope on falling: FTR

(b)RRT:0.1, Envelope on falling: SEROW

Amplitude Time

(d)RRT:0.5, Envelope on falling: SEROW

(c)RRT:0.5, Envelope on falling: FTR

Amplitude Time

(e)RRT:0.9, Envelope on falling: FTR

(f)RRT:0.9, Envelope on falling: SEROW Figure 2: Amplitude envelopes per one period used in this study.

‘Amplitude Time

2.3. Procedure for synthesizing stimuli Amplitude-fluctuated noises with various amplitude envelopes were synthesized. Those noises were synthesized based on a procedure proposed in a previous study [1].

First, amplitude envelopes per one period were created by conjoining a linear line on rising time and envelopes extracted from the motorbike’s explosive sounds. The extracted envelope was obtained in 3 steps. In the first step, each explosive sound was extracted because the exhaust sound consists of various explosive sounds. Next step, the average amplitude envelope on those explosive sounds was extracted by full-wave rectification. Finally, the amplitude envelope on falling was obtained from the average envelope by removing the envelope prior to onset time. Those amplitude envelopes per one period are shown in Fig.2.

‘Amplitude Time

Amplitude Time

Amplitude envelope per one period

White noise

Conjoining amplitude envelope per one period

Amplitude-fluctuating white noise by using envelope conjoined as fluctuation wave

Amplitude-fluctuated

white noise

Figure 3: Procedure for synthesizing amplitude-fluctuated white noise.

Next, these waves were conjoined on each condition, so an amplitude envelope on amplitude- fluctuated white noise was obtained. Finally, a fluctuated noise was obtained by amplitude- fluctuating using a wave conjoined as a fluctuation wave. Figure 3 showed the procedure in the case of using an amplitude envelope (RRT:0.5, Envelope on falling: SEROW).

2.4. Result A result of each noise amplitude-fluctuated by sine wave on each fluctuation frequency is given in Fig. 4. The vertical axis represents the average evaluated magnitude of fluctuation. As can be seen from Fig. 4, it’s found that the magnitudes of fluctuation on S 3 ~ S 6 are different from one on S 1 and S 2 . S 1 ’s magnitudes of fluctuation are similar to past results [2,3]. So, the correlations among those subjects’ magnitude of fluctuation were investigated. As a result, a strong correlation was found between S 1 ’s magnitudes of fluctuation and S 2 ’s magnitudes of fluctuation (| r | < .99 ( n = 21)). Thus, the average of S 1 and S 2 ’s magnitudes of fluctuation were used in the analysis. The analysis of variance (ANOVA) was conducted for the result in the case of using a sine wave as an amplitude envelope. This ANOVA revealed an effect of kind of fluctuation frequency ( p < .05). To further examine the effect, post hoc analysis was made using Tukey’s multiple comparisons test. Tukey’s post hoc analysis showed that there are all differences among those magnitudes ( p < .05). As a result of this ANOVA, it’s shown that this experiment in the case of using sine wave obtained the same result as past studies [2,3].

Results of each noise amplitude-fluctuated by each motorbike’s amplitude envelope on each fluctuation frequency are given in Fig. 5. As can be seen from Fig. 5, it’s found that those magnitudes are a little different among fluctuation frequencies. So, the other ANOVA was conducted for the result in the case of using each motorbike’s amplitude envelope. Those ANOVA revealed a main effect of kind of fluctuation frequency ( p < .01). To further examine the effect of kind of fluctuation frequency, post hoc analysis was made using Tukey’s multiple comparisons test. Tukey’s post hoc analysis showed that there are differences between 4/8 and 20 Hz ( p < .01). Also, it showed that there is a difference between 0.1 of RRT and 0.9 of RRT in the case of using FTR’s envelope ( p < .05). In addition, it showed that there are differences between 0.1/0.5 of RRT and 0.9 of RRT in the case of using SEROW’s envelope ( p < .05). Next, So, the other ANOVA was conducted for all results of Fig. 5. Those ANOVA revealed a main effect of kind of fluctuation frequency (p < .01). It wasn't found the main effect of the kind of RRT and envelope on falling.

TT LALEKAKEROALARRKEROLERGREROALARAROLL

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Figure 4: Results of experiment in each fluctuation frequency (Envelope: sin wave).

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(b) Envelope on falling: SEROW Figure 5: Results of experiment in each fluctuation frequency. 3. DISUCUSSION

(a) Envelope on falling: FTR

It was found from Fig.5 that magnitude fluctuations of 4/8 Hz are larger than the magnitude fluctuation of 20 Hz on each amplitude envelope. As well as past studies [2,3], it was found that fluctuation frequency affects the sensation of hearing fluctuation even if a wave that is different from the sine wave is used as a fluctuation wave. Also, it was observed that the shape of rising/falling time is affected the sensation of hearing fluctuation because the averages of the magnitude on 0.9 of RRT are larger than the other ones in the case of 4 and 8 Hz of fluctuation frequency. So, the result shows that fluctuation frequency has a more potent effect on perceiving the sensation of fluctuation than the shape of rising/falling time. However, the number of subjects was small, so it needs to conduct an evaluation experiment to increase the number of subjects. 4. CONCLUSIONS

This study investigated the relationship between the shape of the amplitude envelope and the sensation of hearing fluctuation. Investigations were carried out by using amplitude-fluctuated white noise which was designed to have various acoustic characteristics for the shape. Those white noises have characteristics of amplitude fluctuations in motorbikes. Then, the hearing sensations of fluctuation on those sounds were assessed. The results revealed that the shape of the amplitude envelope per one period has a possibility of a favourable effect.

It plans to conduct the evaluation experiment increased the number of subjects and an evaluation experiment using other shapes of the amplitude envelope. 5. ACKNOWLEDGEMENTS

This study was partly supported by the Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (19K20613). 6. REFERENCES

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