A Pilot Study: Introduction of Time-domain
Segment to Intensity-based Perception Model ofHigh-frequency Vibration
Nan Cao1 , Hikaru Nagano1 , Masashi Konyo1 , Shogo Okamoto2
and Satoshi Tadokoro1
1

Graduate School of Information Sciences, Tohoku University,
6-6-01 Aramaki Aza Aoba, Aoba-ku, Sendai-shi, Miyagi, Japan.
2
Graduate School of Engineering, Nagoya University, Nagoya, Japan.

Abstract. The intensity of a high-frequency vibration is the primarycue to convey vibrotactile information perceived by the Pacinian system. However, the conventional intensity-based spectral power model is
not sufficient to interpret a relatively slow time-variant pattern of vibration such as amplitude-modulated (AM) vibrations. This paper introduced a time-domain segment to the intensity-based model such that along-term vibration pattern is divided into multiple short-term sinusoidal
vibrations that maintain the same energy. We expected that such shortterm segmentation could deliver the similar perception if the energy ofeach segment of the reproduced vibration is the same as the original
waveform even though the time-segmented reproduced waveform has a
step-wise envelope shape. We conducted a pilot psychophysical experiment in which the participants discriminated between the original AM
vibrations and the time-segmented vibrations by changing the segment
size from 1/6 to 1/2 of the AM period. The experiment is conductedunder different combinations of the carrier frequencies (300 Hz and 600
Hz) and envelope frequencies (15 Hz, 30 Hz, and 45 Hz) frequencies. The
results showed that the participants had low discrimination ratios (themean values are less than 0.6) at the segment size from 1/6 to 1/3 of theAM period and the participants could discriminate easily between the flat
sinusoidal vibration and the original AM vibration (the mean discrimination ratios are larger than 0.90) even if the energies of the two vibrations
were maintained. The results suggest that the time-segmented intensitybased model could reproduce perceptually-similar vibrations for AM vibrations at the segment size from 1/6 to 1/3 of the AM period.

1

Introduction

High-frequency vibration induced by scratching or tapping on surfaces was reported as the cues for roughness or hardness perception [?, ?, ?, ?]. Thus, transmitting high-frequency vibrations has been attempted for supporting telerobotic
surgery [?] and delivering realistic textures [?,?]. To mediate the relevant haptic
information under a limited communication bandwidth, we need to understandthe high-frequency vibration factor that plays the primary role in shaping tactile
perception.
The intensity of the high-frequency vibration (> 100 Hz), which is generally
defined as the integral of stimulus energy over time or spectral power summed
across all frequencies, has been focused as a primary cue to convey vibrotactile
information perceived by the Pacinian system [?, ?, ?, ?]. Makous et al. [?] foundthat the intensity model, which is a function of spectral power divided by threshold power, constitutes a measure of the ability to excite the Pacinian system.
Bensmaia et al. found the spectral model, which enhanced the ability of the intensity model with the spectral characteristics based on the psychophysical andneurophysiological findings [?]. Bensmaia et al. also applied the spectral model
to finely textured stimuli to infer the perceptual dissimilarity [?].
However, a missing argument for the intensity-based model is how the adequate duration is determined to integrate the energy of stimulus to account for
the relatively slow time-variant vibration patterns. For instance, Fig. 1 shows anexample of an equivalent energy-based waveform reproduction processes for generating similar stimulus with two different integral segments (broken blue lines),i.e., (a) long-term, and (b) short-term segment cases. Here, we assume that theoriginal stimulus is an amplitude-modulated high-frequency vibration (> 100Hz) that has a low-frequency temporal envelope (< 50 Hz) for both cases. In thelong-term segment case (a), the duration of the segment is long enough such thatthe energy on each segment constitutes a flat line at the same level. Thus, we
could reproduce an energy-equivalent waveform with a single constant sinusoidal
wave. On the other hand, in the short-term case (b), the segment duration isshorter than the envelope period such that the original stimulus is divided into
several segments and the energy on each segment changes in a step-wise manner.
Thus, the reproduced sinusoidal waveform could also have step-wise changes indisplacement. These two cases demonstrate that a reproduced waveform basedon the intensity-model depends on the segment duration of the power integral.
If the energy-equivalent waveforms as shown in Fig. 1 could be discriminated perceptually, it means the intensity-based model requires the suitable segment size of the power integration. Such a low-frequency component occurring in
high-frequency vibrations is highly expected to differentiate the tactile percept.
Several researchers reported that humans could detect the envelope of a highfrequency vibration modulated at low frequencies [?, ?, ?]. Bensmaia et al. also
reported that the high-frequency waveforms with equal power were difficult todiscriminate, especially after the function of the rapidly adapting (RA) channel
was minimized with the low-frequency adapting stimulus [?]. Therefore, we alsoneed to consider a possible implication of the RA system.
The present study introduces a time-domain segment to the intensity-based
perception model. In particular, we investigate the discriminability of the timesegmented reproduced waveform that has the same intensity as that of the original vibration on each segment, as a pilot study to determine the suitable segment size for the intensity-based modulation. This study targets the amplitudemodulated (AM) high-frequency vibrations (carrier frequency fc = 300 or 600

Time

Displacement
Displacement

EnergyTime

Energy

Displacement

Time

Time

Time

Fig. 1. The waveforms of the same segmental energy with different segment cases

Hz) that have relatively low envelope frequencies (fe =15, 30, or 45 Hz). These
low envelope frequencies are considered as the frequency range mainly perceived
by Meissner’s receptors.
Note, to simplify the experimental conditions and discussions, we incorporated several assumptions: (1) the original and reproduced vibrations have thesame carrier frequency, and (2) the stimulus energy is the general integral powerof vibration displacement in the time domain. Assumption (1) avoids the frequency dependence of the Pacinian system on the intensity-models, which wereincorporated with the human detection threshold [?] and the spectral characteristics [?]. Thus, we use the general integral power assumed in (2). In addition,
we also avoid the phase effects of segmentation by carefully selecting the segment size to be synchronized with the original waveform, not to generate otherperiodic vibrations.
We investigate the relationships between the time segment size and the discrimination performance through the psychophysical experiments. In the experiment, participants compare the reproduced stimuli using different segment sizes
with the original stimuli under different carrier and envelope frequencies. We also
confirm the effect of the carrier and envelope frequencies on the discriminability.

2

Proposed ModelIn this study, we introduce a time-domain segment to the energy model to represent the energy change in high-frequency vibrations. By using our model, we
simulate a perceptually-equal stimulus from an original vibration, and investigate the relationships between the time segment size and the discrimination
performance of stimuli among several carrier and envelope frequencies of stimuli.

Energy [μms]

0
-20

3
2
1
0

(a)

(b)

20
10
0

0

0.1
Time [s](c)0.2

Displacement [μm]Amplitude [μm] Displacement [μm]

20

20
0
-20

0

0.1
Time [s](d)0.2

Fig. 2. Method processes: (a) The original vibration signal is segmented into small
pieces of time sets using time segment size tp in the time domain. (b)The energies ofevery time set are calculated by Eq. 1; (c) The amplitude of each time set is calculated
based on the energy of the original data using Eq. 2. (d) The reproduced stimuli are
made using Eq. 3.

The original vibration v(t) is divided into segments by the time segment tp
as shown in Fig. 2(a). The dashed lines are the segment boundaries. Fig. 2(b)shows that the energy of the original signal P (n) of each segment is calculated
by integrating the displacement of the signal as follows:
Z (n+1)tp
2
P (n) =
v(t) dt.
(1)
ntp

As shown in Fig. 2(c), based on the calculated energy of the original signal, theamplitude of perceptually-similar vibration Ap (n) on each segment is calculated
as follows:Z
P 0 (n) =(n+1)tp2(Ap (n) sin(2πfc t + b(n))) dt,

(2)

ntp

where fc and b(n) are the carrier frequency of the original signals and the initial
phase of each segment, respectively; and the energy of the perceptually-similar
signal P 0 (n) is the same as that of the original vibration P (n). Finally, as shownin Fig. 2(d), the perceptually similar vibration v 0 (t) is determined byv 0 (t) = Ap (n) sin(2πfc t + b(n))(ntp < t < (n + 1)tp ).

(3)

In this paper, we adopt AM vibration as the original high-frequency vibrationv(t), which is represented asv(t) = ve (t)vc (t),(4)

ve (t) = 1 + sin(2πfe t + φ),(5)vc (t) = sin(2πfc t),(6)where fe and fc are the envelope and carrier frequencies of the AM vibration,
respectively; and φ is the envelope phase.

3

Experiment

We conduct the psychophysical experiments to investigate the relationships between the smoothness (the temporal resolution) of the energy change of vibrationand the discriminability of vibration. In the experiment, participants compare
the stimuli reproduced by the proposed model with the original stimuli under
different time segment sizes. In addition, comparisons are conducted among different carrier and envelope frequencies to investigate the effect of carrier andenvelope frequencies on the relationships between the time segment size and thediscrimination performance.
3.1

Stimuli

Reproduced vibrations using five types of segment sizes were reproduced froman original AM vibration. To avoid the reproduction of perturbed stimulus, weselected the time segment size tp that evenly divided the envelope period te . We
defined a segment ratio rs = tp /te ; thus, five types of time segment size tp were
decided based on the condition where in rs = 1/6, 1/5, 1/4, 1/3, and 1/2.
Six combinations of carrier frequency and envelope frequency were adopted
in the original AM vibration. The carrier frequency (fc ) of 300 Hz and 600
Hz respectively are used for the AM vibrations. In addition, we also adopted
three types of envelope frequencies: fc = 15, 30, and 45 Hz. These low envelope
frequencies are considered as the frequency range mainly perceived by Meissner’s
receptors while the stimuli are high frequencies which are as the frequency range
mainly perceived by Pacinian receptors.
For the selection of the stimuli, six original AM vibrations ((f c, f e) = (300, 15),(300, 30), (300, 45), (600, 15), (600, 30), and (600, 45)) and 30 reproduced vibrations (six original AM vibration × five segment number rs = 1/6, 1/5, 1/4, 1/3,
and 1/2) were used, with a total of 36 stimuli. The duration time of a stimulus is
800 ms. In the experiment, 30 conditions of the stimuli pairs were used, and eachcondition had an original AM vibration and a reproduced vibration generated
from the original vibration using a segment number rs .
To check the displacement profiles of 36 stimuli, we measured the displacement of the piezoelectric vibrator tip using the laser displacement sensor (LKH025, KEYENCE CORPORATION) as shown in Fig. 3. The displacement ismeasured without a finger press on the top of the actuator. Because of the large
pushing and pulling forces (800 N and 50 N, respectively) of the actuator, we
assume that the vibratory waveform will not change significantly between the(300, 15)

Displacement [μm]Carrier andenvelope freq.
(fc, fe) [Hz]Segment ratio (rs = tp/te)
Original

1/6

1/5

1/4

1/3

1/2

20
0
-20
0

Time [s]1/15(300, 30)

(300, 45)

(600, 15)(600, 30)

(600, 45)

Fig. 3. Measured displacement profile of stimuli.

preliminary measurement condition without a contact force and the experimental condition where participants press their fingers on the actuator with the
instructed force (0.5 N).
3.2

Participants

The participants were two females and seven males (aged from 20 to 28 years,
all right-handed). All participants had no motor or sensory limitations according
to their self-reports. Informed consent was obtained; however, the participants
were not aware of the experiment purpose.
3.3

Apparatus

The experimental apparatus is shown in Fig. 4. A tactile high-frequency vibrationis generated by a piezo actuator (PZ12-112, Matsusada Precision) and its pushingand pulling forces are 800 N and 50 N, respectively. The actuator contacts thefinger of the subject through an 8-mm diameter hole of the plate; the diameterof the contact part is 6 mm, as shown in Fig. 5. The actuator is connected toLaser displacement
sensorHand

Piezoelectric
vibrator
Load cell
Lab jack

Fig. 4. Experimental apparatus: a participant presses his index finger pad on the contact part of the actuator and rests his hand on the plate to stabilize the contact withthe actuator.

a load cell (LUR-A-100NSA1, Kyowa Electronic Instruments) to measure thecontact force which is 0.5 N between the actuator and a participant’s finger
pad. The load cell is connected to a lab jack that is used to change the heightof the actuator for adjusting the contact force between the contact part of theactuator and a participant’s finger. A computer generates the input signal tothe actuator though a USB audio interface (UR22mkII, Steinberg) and a piezo
driver (PZJRP6A, Matsusada Precision).

3.4

Procedure

Three alternative forced-choice paradigm is used for measuring the discrimination ratio between the reproduced and original vibration. We adopt 30 conditions (six original AM vibrations × five segment numbers) and 20 trials are
conducted for each condition. Therefore, each participant conducts a total of
600 trials.
At each trial, the participant receives three stimuli. The time interval between
the stimuli is 0.8 s. The order of the stimuli is randomized. Two stimuli are thesame as the original stimuli while the other one is a reproduced stimulus. After
receiving three stimuli, the participants attempt to identify the stimuli that isFig. 5. Contact part between the index finger pad and the piezo vibrator

different from others. After every 100 trials, the participants rest for five to ten
minutes.
Prior to the experiment, a double-sided adhesive is stuck around the holeof the plate. The participants are instructed to press the center part of theirindex finger pad on the hole to stick their finger around the hole and then relax
their hand on the plate. The lag jack that holds the actuator is lifted up slowly
through the hole on the plate to reach the finger pad. Its height is adjusted
until the expected contact force of 0.5 N between the finger and the actuator is
obtained. After every 100 trials, the double-sided adhesive is changed, and thecontact force is readjusted. Prior to the experiment, the participants complete
60 trials (two times of the 30 combinations) to familiarize themselves with theexperimental procedure.

4

Results

In Figs. 6(a)-(f), each figure showed the discrimination ratio between the original
AM vibration and its reproduced vibration under five conditions (one original
AM vibration × five segment ratios). For each type of the original AM vibration,
the discrimination ratio appears to be affected by segment ratio rs .
We analyzed the differences among the discrimination ratios and chance level
1/3. The Kolmogorov-Smirnov test was applied to 30 conditions (six original AM
vibrations × five segment ratios) for testing the normality of the distribution.
The result of the Kolmogorov-Smirnov test showed that all 30 conditions had
normal distributions. Therefore, we used the one-way ANOVA and post-hoc
analysis (the Tukey-Kramer test) for analyzing data.
Firstly, the results of one-way ANOVA and post-hoc analysis showed significant differences between the discrimination ratio at the segment ratio (rs = 1/2)
and chance level 1/3 with all six original AM vibrations (p < 1.0 × 10−7 ). It further showed that the conventional intensity-based model could not represent
perceptually-similar vibrations for original AM vibrations
Next, no significant difference appeared between the four segment ratios (rs =1/6, 1/5, 1/4, and 1/3) and chance level (p > 0.05) except the two conditions ((fc ,fe , rs ) = (300, 30, 1/4) and (600, 15, 1/3)). In addition, the discrimination ratios
at the four segment ratios (rs = 1/6, 1/5, 1/4, and 1/3) are significantly smaller
than that at rs = 1/2 in all original AM vibrations (p < 1.0 × 10−6 ). The participants mostly had low discrimination ratios, which were near the chance level,in the segment conditions except rs = 1/2. While the high-resolution envelope
step (rs = 1/6) showed the highest similarity among the six segment ratios, thelower-resolution (rs = 1/3) could deliver the sensation that was relatively similar
to the sensation of the original AM vibration.
The results suggest that the time-segmented intensity-based model could
reproduce perceptually-similar vibrations for the AM vibrations compared withthe conventional intensity-based model. Furthermore, we found that a small
segment number of the envelope period (rs = 1/3) could reproduce the similar
perception of the AM vibration.

5

Discussion

The first finding of this study is that the participants could discriminate easily
between the flat sinusoidal vibration (rs = 1/2) and the original AM vibration,even if the energy of the two vibrations were maintained. The mean discrimination rates for the rs = 1/2 case on each condition of the six types of original vibrations were higher than 0.9. On the other hand, other segment ratios(rs = 1/3, 1/4, 1/5, and 1/6) had relatively low mean discrimination ratios (<0.51) except the condition of (fc , fe , rs ) = (600, 15, 1/3) whose mean ratio is0.59. These suggest that the time-segmented intensity-based modulation possibly tends to reproduce similar stimuli at segment ratios (rs = 1/3, 1/4, 1/5,
and 1/6). These results are not surprising because several researchers have already reported that humans can detect the envelope of high-frequency vibrations
modulated at low frequencies [?, ?, ?]. However, the present study confirmed experimentally that the simple intensity-based model could not explain the slow
temporal change in the energy, and the time segment integral is one of the potential methods.
Note that our motivation is not to criticize the conventional models because
they intentionally avoided the effects of low-frequency components to assess the
Pacinian system [?] and several studies have already addressed the possible relationship between the envelope detection and the RA system [?, ?, ?].
The second interesting finding is that the segment size did not affect strongly
on the discrimination ratio. We had expected a trend where the discrimination
rates would increase when the segment ratio increases (segment duration decreases). However, the experimental results did not show the anticipated tendency. Surprisingly, even a single-step vibration (rs = 1/3) could reproduce thesimilar perception to some degree, except the (fc , fe ) = (600, 15) condition.
The results suggest that the envelope property of the AM vibration might beperceived with a relatively simple feature, such as a number of peaks of theenvelope, rather than the high resolution of the segmentation, when the energyof high-frequency vibration is maintained. A possible implication of this simple

0
1/6

Discrimination ratio

Discrimination ratio

0.5

1/5

1/4

1/3

0.5

0
1/6 1/5 1/4 1/3 1/2

Segment ratio

Segment ratio

(a)

(b)

(300,30)
1

0.5

0
1/6

(600,15)1

1/2

Discrimination ratio

Discrimination ratio(300,15)
1

1/5

1/4

1/3

(600,30)
1

0.5

0

1/2

1/6 1/5 1/4 1/3 1/2

Segment ratio(d)(300,45)Discrimination ratio

Discrimination ratio

Segment ratio
(c)
1

0.5

0
1/6

1/5

1/4

1/3

Segment ratio
(e)

1/2

(600,45)1

0.5

0
1/6 1/5 1/4 1/3 1/2

Segment ratio(f)Fig. 6. Relationships between the discrimination ratio and the segment ratio under
different combinations of the carrier and envelope frequency

feature detection is the function of the RA system that is activated corresponding to the onset and offset of skin deformation. If the time-segmented step-wisevibration can generate the similar skin deformation, the RA system could detect
the similar information.
An exceptional condition of (fc , fe , rs ) = (600, 15, 1/3) requires further investigation about the effects of segment duration. This condition had a relatively
higher mean discrimination rate (0.59). As shown in Fig. 3, both the rs = 1/3
and rs = 1/4 conditions have a similar single-step waveform but different durations. We need to investigate whether the difference could be explained by the
Pacinian or RA representations in the future.
One of the limitations of this study is that we applied a simple intensity-modelthat does not consider the frequency dependency of the Pacinian system [?,?,?].

In this study, such a dependency impacts on the results less because we used
the same carrier frequency combinations for the discrimination tests. To apply
the time-segment intensity-based model for general waveforms, the frequency
dependencies should be considered. Another limitation is the lack of participants.
We have a plan to increase the number of participants for investigations in the
future.

6Conclusion

This study introduced a time-domain segment to the energy-based perception
model to represent the temporal energy change in high-frequency vibration suchas amplitude-modulated (AM) vibrations. We conducted experiments in which
the participants performed the discrimination task between the original AM
vibration and the reproduced stimuli which has a different temporal energy resolution of the original AM vibration under 30 conditions (five segment sizes ×
six original vibrations). First, our results showed that the participants could
discriminate easily between the flat sinusoidal vibration (rs = 1/2) and the original AM vibration, even if the energy of the two vibrations were maintained.
Next, our results showed that the segment size did not significantly affect thediscrimination ratios at the segment size (rs = 1/3, 1/4, 1/5 and 1/6), and theparticipants had low discrimination rates (the mean values are less than 0.6).
These results suggest that the time-segmented intensity-based model could reproduce perceptually-similar vibrations (rs < 1/2) for the AM vibrations.

ACKNOWLEDGMENT
This work was partially supported by ImPACT Program Tough Robotics Challenge.