IEEE TRANSACTIONS ON HAPTICS, VOL. 4, NO. 4, OCTOBER-DECEMBER 2011
`
`229
`
`Design and Evaluation of Identifiable
`Key-Click Signals for Mobile Devices
`
`Hsiang-Yu Chen, Jaeyoung Park, Steve Dai, and Hong Z. Tan, Senior Member, IEEE
`
`Abstract—As touch based input becomes more popular in mobile devices, there is an increasing need for haptic feedback on key-less
`input surface. Four experiments were conducted to design and evaluate identifiable emulated key-click signals using a piezoelectric
`actuator. Experiments I and II assessed the information transmission capacity for the amplitude, frequency, and number of cycles of
`raised cosine waveforms used to drive the piezo actuators under fixed- and roving-background conditions, respectively. Experiment III
`estimated the total information transfer for all three parameters. The results were used to reduce the number of stimulus alternatives in
`the key-click signal set with the goal to achieve perfect identification performance. Experiment IV verified that up to 5 to 6 identifiable
`key-click signals could be achieved with the experimental setup. The present study outlines an information theoretic approach to
`conducting identification experiments to guide the design of and to evaluate a perfectly identifiable stimulus set. The methodology can
`be applied to other applications in need of perceptually identifiable stimulation patterns.
`
`Index Terms—Mobile applications, haptic feedback, key click, human information processing.
`
`Ç
`
`1 INTRODUCTION
`
`HAPTIC interactions have become increasingly popular in
`
`consumer products in the last decade. Applications
`include, but are not limited to, touch screens, PDAs, and cell
`phones. Haptic interaction refers to both manual input to a
`device and haptic feedback provided by the device. With
`sensing technologies, mobile devices can receive manual
`inputs through pressure-sensitive touch screens with or
`without individual keys. Most mobile devices also provide
`touch feedback in the form of vibration alerts, a useful and
`discreet feature especially when the device is in silent mode.
`At
`the same time, keyboards on mobile devices are
`disappearing to make room for larger display screens and
`thinner profiles, yet many people find it disconcerting to
`type on a surface with only visual but no haptic feedback.
`As touch screen technology gains popularity, the need has
`risen for key-click feedback signals that serve as confirma-
`tion of key presses, especially when the user’s eyes are busy
`with other tasks. The idea of “active click” was first
`introduced by Fukumoto and Sugimura [2] where a
`vibrotactile actuator attached to the back of a touch panel
`generated a click-like vibrating pulse whenever the screen
`was tapped by a finger. Since then, several technologies
`have been implemented to generate haptic feedback. For
`example, Chang and O’Sullivan used a multifunction
`transducer [3]; Brewster’s group adopted C2 tactors in
`
`. H.-Y. Chen is with the Motorola Corporation, 600 US Hwy 45,
`Libertyville, IL 60048. E-mail: nelly.hychen@gmail.com.
`. J. Park and H.Z. Tan are with the Haptic Interface Research Laboratory at
`Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907.
`E-mail: {park183, hongtan}@purdue.edu.
`. S. Dai is with the Materials Science and Engineering Center, Sandia
`National Laboratories, PO Box 5800, MS 0959, Albuquerque, NM 87185.
`E-mail: sxdai@sandia.gov.
`
`Manuscript received 20 July 2010; revised 29 Mar. 2011; accepted 12 Apr.
`2011; published online 16 May 2011.
`Recommended for acceptance by H. Kajimoto.
`For information on obtaining reprints of this article, please send e-mail to:
`toh@computer.org, and reference IEEECS Log Number TH-2010-07-0037.
`Digital Object Identifier no. 10.1109/ToH.2011.21.
`
`most of their studies [4], [5]; and Lee et al. utilized a
`solenoid actuator to create feedback for a stylus [6]. In
`addition, piezoelectric actuators have been used in several
`applications involving handheld mobile devices [7], [8], [9],
`[10], [11], [12], [13], [14].
`The present study focuses on the design and evaluation of
`haptic signals generated by a piezoelectric actuator that
`emulates key-click sensations. Our study is different from
`previous research on “tacton” [15] or “haptic icons” [16] in
`that we focus on signals that emulate key clicks, as opposed
`to any vibrotactile signals that may make up a tactile
`vocabulary. Our efforts also differ from those of earlier work
`on haptic devices for sensory substitution (e.g., [17]; see also
`[18] for a review) in that we use signals with an intuitive
`meaning (key clicks) instead of abstract signals that require
`extensive user training of a specific coding scheme (e.g.,
`tactile aids for individuals with hearing impairments).
`Finally, instead of searching for signals that feel “pleasant”
`(e.g., [7]), our aim is to design a set of identifiable signals that
`can be used with different functions on a mobile device. We
`use the term “identifiable signals” to refer to a set of
`distinctive stimulus alternatives that can be easily identified
`in isolation (i.e., identification) as opposed to in comparison
`with other stimuli (i.e., discrimination). Instead of a
`relatively high level of identification (e.g., above 80 percent
`correct), we aimed to reach a near 100 percent identification
`accuracy. In many applications such as a belt with haptic
`waypoint information [19], a vest displaying haptic commu-
`nication signals [20], or a mobile device with haptic alerts
`[15], recognition accuracy needs to be near perfect instead of
`being just “good enough” because the cost of misidentifica-
`tion can be high. In mobile applications, identifiable key
`clicks can enable eye-free operations when the user is unable
`to look at or see the device.
`The problem of designing a set of perceptually identifiable
`signals for a given actuator has been studied in various
`contexts in the past. The common theme is to map the physical
`
`1939-1412/11/$26.00 ß 2011 IEEE
`
`Published by the IEEE CS, RAS, & CES
`
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`parameter values for driving the actuator to perception, so
`that different sensations can be achieved by judicious
`selections of these parameter values. These identifiable
`signals can then be encoded for a specific application. For
`example, Geldard [21] studied the use of vibrotactile
`frequency, amplitude, duration, locus in space, and wave
`complexity in encoding speech elements with an array of
`tactors. After discarding frequency (for interacting with
`intensity perception) and wave complexity (for being non-
`discriminable), a total of 45 (3 amplitudes  3 durations  5
`loci on the chest) vibrotactile signals were created, each
`representing an English alphabet letter, a single-digit
`number, or a short word (e.g., “of,” “the,” “in,” “and”). One
`participant was able to receive 38 words per minute with this
`system. Maclean and colleagues have conducted extensive
`studies characterizing the relation between physical para-
`meters and perceptual dimensions using a multidimensional
`scaling technique (MDS) [11], [16], [22]. In [22], these
`researchers used the MDS solution space to demonstrate
`and measure the perceptual distinctiveness of periodic
`vibrotactile signals varying in its waveform. In another study
`on the design of the tactile equivalent of ring tones for mobile
`devices, Brown et al. [15] mapped location, rhythm, and
`roughness parameters to vibrotactile alerting signals to
`indicate time-until-appointment (30, 15, 5 min), type of alert
`(meeting, lecture, tutorial), and importance (low, medium,
`high), respectively. Performance in terms of percent-correct
`scores and information transfer (IT) were reported.
`The present study addresses similar questions as these
`previous investigations: What are the key physical para-
`meters that affect perception in a predictable way? For each
`parameter, how many levels can be correctly identified
`without error? When multiple parameters vary in a signal
`set, by how much does the identification of each parameter
`level deteriorate? More importantly, how to reduce the
`number of levels per parameter so that identification of
`signals varying in multiple parameters remains perfect?
`Various methods have been employed to study these
`questions. In Geldard’s work [21], discrimination experi-
`ments were carried out to measure the just noticeable
`difference (JND) within each parameter range. The results
`indicated that there were about 15-17 JNDs for amplitude
`over a reference amplitude range of 20 to 400 microns, and
`25 JNDs for duration over a reference duration range of 0.1
`to 2.0 s. With no further explanation, the author claimed that
`for practical purposes, three levels of amplitude, three levels
`of duration, and five loci on the chest could be included in
`the signal set. The selection of the parameter levels would
`have been more convincing if the author had conducted
`absolute identification experiments to measure the max-
`imum number of identifiable signals, or the “channel
`capacity,” of each parameter [23]. MacLean and colleagues
`[11], [16], [22] used the MDS technique to discover the
`perceptual dimensions associated with physical parameters.
`This technique has also been applied to the study of haptic
`texture perception [24] and perfumers’ odor perception
`space [25]. One of the main difficulties in conducting an
`MDS experiment is the amount of time required to collect
`scaling data for all pairs of stimuli. A cluster-sorting method
`was proposed in [16] to speed up data collection, although
`
`there remain some unresolved issues and concerns with this
`approach [26]. In Brown et al.’s work [15], performance was
`reported in terms of percent-correct scores and information
`transfer. The former can be misleading in the sense that a
`decrease in percent-correct score with a larger stimulus set
`does not necessarily imply that
`the total number of
`identifiable signals have decreased. Although these authors
`also report information transfer, it was used mainly as a
`performance metric rather than an integral part of the
`stimulus design process.
`The present study uses an information theoretical frame-
`work to study the design and evaluation of identifiable key-
`click signals for mobile devices. One-dimensional and
`multidimensional absolute identification experiments are
`conducted to measure the channel capacity associated with
`a single physical parameter and multiple parameters,
`respectively.
`In one-dimensional absolute identification
`experiments,
`the values of the background parameters
`(i.e.,
`the nontarget physical parameters making up a
`stimulus) are either kept fixed or varied randomly. While
`the fixed-background experiments allow us to estimate the
`“ideal” channel capacity achievable with a single physical
`parameter, the roving-background experiments produce a
`more “realistic” channel capacity when multiple parameters
`must be attended to in order to identify a signal [27]. We
`show how these experiments can guide the design of a
`multivariable stimulus set, and under what conditions
`results from one-dimensional absolute identification experi-
`ments can be used to predict the outcome of a multi-
`dimensional absolute identification experiment, the latter of
`which is usually too time-consuming to conduct
`for
`practical purposes.
`The present study makes two important contributions.
`From a methodology perspective, we demonstrate how to
`assess the overall information transmission capacity of a
`stimulus set with multiple parameters that interact percep-
`tually. From an application perspective, we provide the
`specifications for a set of identifiable key-click simulation
`signals that can be incorporated into mobile devices
`equipped with piezoelectric actuators. In what follows, we
`summarize the general methods in Section 2. Details
`specific to the four experiments conducted during the
`present study are presented in Sections 3 to 5. The paper
`concludes in Section 6.
`
`2 GENERAL METHODS
`2.1 Apparatus
`The test apparatus resembled a typical mobile phone in its
`size and appearance (see Fig. 1). A single layer piezoelectric
`actuator (CTS standard 3,203, 4 cm L  3:5 cm W  0:2 mm
`H, 147 nF capacitance, occupying the lower half of the
`apparatus) was affixed to a stainless steel plate that served as
`the cover of the apparatus. A piece of polycarbonate frame at
`the same size as the stainless steel plate was attached to the
`back of the apparatus. Four force sensing resistors (FSRs
`from Interlink) were mounted at the corners of the intended
`keypad area and sandwiched between the polycarbonate
`frame and a polycarbonate back plate. They were used to
`trigger a high-voltage input pulse to the piezo whenever the
`total force exceeded 200 g (or equivalently, a resistance of
`
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`CHEN ET AL.: DESIGN AND EVALUATION OF IDENTIFIABLE KEY-CLICK SIGNALS FOR MOBILE DEVICES
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`231
`
`Fig. 1. (a) Back view as seen through a clear Plexiglas cover and (b) front
`view of test apparatus. (From [1], Fig. 1, ß 2010 IEEE).
`
`20 k
` for the four FSRs connected in parallel).1 The 200 g
`force value was selected empirically. To emulate the weight
`of a typical mobile phone, a piece of metal weighing 40 g was
`glued to the upper half of the apparatus (the yellow block in
`Fig. 1a). The total weight of the apparatus was about 78 g. A
`red dot marked the center of the piezoelectric actuator where
`the participants were told to press down with the thumb and
`feel a virtual key click (see Fig. 1b). Upon detection of a key
`press through the FSRs, a waveform was sent through a
`computer sound card (Creative Sound Blaster SB0100,
`Creative Resource, Singapore) to a voltage amplifier with a
`gain of 100 (Dual Channel High Voltage Precision Power
`Amplifier, Model 2,350, TEGAM, Inc., Geneva, OH). The
`output of the amplifier was subsequently sent
`to the
`piezoelectric actuator to create the sensation of a virtual
`key click.2
`
`2.2 Participants
`Twelve participants (P1-P12; 3 females; all right-handed
`except P12; age range 23-43 years old) took part in the
`present study. Participants P1-P3 were research staff and
`experienced with haptic devices. They participated in all the
`experiments in the present study. Participants P4-P12 were
`compensated for their time. They completed the first three
`of the four experiments conducted in the present study. All
`participants signed a written consent form approved by the
`Institute Review Board at Purdue University.
`
`1. The latency between the detection of a >200 g force by the FSR and the
`onset of a key-click signal was less than 1 ms using a PC. In real applications
`where the latency is limited by firmware, the latency can be significantly
`longer (e.g., 40 ms in Motorola’s ROKR E8 music phone).
`2. The haptic stimuli could be sensed by all the fingers holding the test
`apparatus. However, the signal was the strongest near the center of the
`piezoelectric actuator, and all participants (including the authors) located
`the key-click feedback signal at where the thumb was. It only became
`apparent that the signal could be felt by the four fingers holding the test
`apparatus if the thumb was lifted away and someone else pressed on the
`red dot to trigger the haptic stimuli.
`
`Fig. 2. (a) Recorded acceleration profile of a key press; and (b) a typical
`input waveform for driving the piezoelectric actuator.
`
`2.3 Stimuli
`To determine the shape of waveforms for driving the
`piezoelectric actuator, acceleration profiles of pop-dome
`keys on a telephone, a computer keyboard, and a cell
`phone were measured. Fig. 2a shows a typical recording
`from the keypad of an office phone during the key-down
`phase. There is a clear initial pulse, followed by several
`“ringing” pulses with diminishing amplitudes. Based on
`the measurements, raised sinusoidal waveforms were used
`to drive the piezoelectric actuator (see Fig. 2b).
`A series of preliminary experiments were conducted to
`determine the relevant parameters for generating key-click
`signals on the piezoelectric actuator. Among the variables
`considered were peak amplitude, frequency, number of
`cycles, initial/peak velocity, and initial/peak acceleration.
`Measurements were also taken to examine the transfer
`function of the piezoelectric actuator. In the interest of
`space, readers are referred to the [Appendices, 28] for
`details.
`In the end,
`three parameters were found to
`influence the perceived quality of simulated key clicks:
`amplitude,
`frequency, and number of cycles of
`the
`sinusoidal waveform. Amplitude of the waveform con-
`tributed to the overall perceived intensity of a key-click
`signal. The maximum amplitude was 200 V using the
`setup described in Section 2.1. Frequency of the waveform
`determined the perceived “crispness” of a key-click signal.
`The frequency range was selected to be 125-500 Hz that
`corresponded to perceptually “dull” to “crisp” key clicks.
`Finally,
`the number of cycles also contributed to the
`perceived intensity of the signal, but more than three
`cycles resulted in an eerie sensation of something alive.
`Therefore, the number of cycles ranged from 1 to 3 in the
`present study. Other waveforms such as sinusoidal pulses
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`TABLE 1
`The Full Stimulus Set Used in Experiments I and II
`
`with exponentially decaying envelopes were also investi-
`gated, but were found not to result in perceptually distinct
`key-click sensations when compared to the signal shown
`in Fig. 2b.
`The full stimulus set used in Experiments I and II of the
`present study consisted of 60 alternatives (5 amplitude 
`4 frequency  3 number of cycles). Table 1 lists the values for
`the three parameters and their associated labels. The high-
`lighted values indicate the parameter values when the
`corresponding parameter was fixed as a background para-
`meter (see Section 2.4.2). This full stimulus set was pared
`down in Experiments III and IV for reasons that will become
`clear later. The proximal stimuli were characterized by an
`accelerometer placed near the center of the piezo actuator.
`Fig. 3 compares the PC output waveform to the measured
`piezo acceleration profile for two representative signals.
`
`Fig. 4. Calibration curve for the piezoelectric actuator.
`
`To characterize the proximal stimuli in response to the
`stimuli listed in Table 1, the pizeoactuator responses were
`calibrated in terms of the peak acceleration at the red dot
`(Fig. 1b) as a function of the peak voltage of one cycle of a
`raised cosine input waveform. The results are shown in
`Fig. 4.
`
`2.4 Procedures
`In this section, we first describe the procedures for running
`an absolute identification experiment, which are used in all
`four experiments conducted in the present study. We then
`discuss the distinction between a one-dimensional (1D) and
`a multidimensional
`(multi-D)
`identification experiment.
`This is followed by a presentation of the procedures for
`running 1D identification experiments with fixed or roving
`background. We then discuss how the results from 1D and
`multi-D identification experiments may be related, in the
`form of a general additivity law for information transfer.
`
`2.4.1 Absolute Identification Experiment
`A typical identification experiment consists of the following
`steps: A set of K stimuli (Si;1  i  K) is constructed for the
`experiment; a set of K responses (Rj; 1  j  K) is con-
`structed with a one-to-one association with each of the K
`stimuli; the participant is presented with stimuli selected at
`random from the stimulus set; on each presentation, the
`participant chooses a response from the response set; and the
`experimental results are tabulated in the form of a stimulus-
`response confusion matrix from which measurements of
`information transfer are computed. The quantity IT measures
`the increase in information about the signal transmitted
`resulting from knowledge of the received signal. For a
`particular stimulus-response pair (Si; Rj), the quantity IT is
`½PðSijRjÞjPðSiފ, where PðSijRjÞ is the condi-
`given by log2
`tional probability of Si given Rj, and PðSiÞ is the a priori
`probability of Si. The average information transfer is given by
`
`
`XK
`XK
`PðSijRjÞ
`PðSi; RjÞ log2
`PðSiÞ
`j¼1
`i¼1
`
`;
`
`ð1Þ
`
`IT ¼
`
`Fig. 3. Comparison of input waveform to piezo and measured piezo
`acceleration profile for two stimuli. (a) A5 ¼ 200 V, F1 ¼ 125 Hz,
`C3 ¼ 3 cycles. (b) A5 ¼ 200 V, F4 ¼ 500 Hz, C1 ¼ 1 cycle. (Modified
`from [1], Figs. 2 and 3, ß 2010 IEEE)
`
`IT ¼
`
`or, equivalently
`
`XK
`j¼1
`
`PðSi; RjÞ log2
`
`
`
`PðSi; RjÞ
`PðSiÞPðRjÞ
`
`;
`
`XK
`i¼1
`
`ð2Þ
`
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`233
`
`where PðSi;; RjÞ is the joint probability of stimulus Si and
`response Rj, and PðRjÞ is the probability of Rj.
`The maximum likelihood estimate of IT derived from a
`stimulus-response matrix, denoted ITest, is computed by
`approximating the underlying probabilities with frequen-
`cies of occurrence
`
`ITest ¼
`
`XK
`j¼1
`
`XK
`i¼1
`
`nij
`n log2
`
`
`
`
`
`nij n
`ni nj
`
`;
`
`ð3Þ
`
`where n is the total number of trials collected, nij is the
`nij and nj ¼ PK
`PK
`number of times the joint event (Si; Rj) occurs, and ni ¼
`nij are the row and column sums. A
`j¼1
`i¼1
`related measure, computed as 2ITest, is interpreted as the
`number of stimulus levels that can be correctly identified
`without error.
`It has been shown that ITest
`is a statistically biased
`estimated of IT and the bias generally decreases as total
`number of trials increases [29]. In the present study, we use
`Miller’s recommendation that the total number of trials
`should be at least 5K2, where K is the number of stimulus
`alternatives.
`More details on information theory as it relates to
`psychophysical studies can be found in [23]. A summary
`of issues related to the design of an identification experi-
`ment can be found in [30].
`
`2.4.2 Identification Experiment with Fixed or Roving
`Background
`The stimulus set shown in Table 1 is called a multi-
`dimensional stimulus set in the sense that more than one
`parameter can vary in order to make up the stimulus
`alternatives. When running a 1D identification experiment,
`the parameter being identified is called the target, and the
`other parameters the background. For example,
`in a
`1D amplitude identification experiment, amplitude is the
`target and frequency and number of cycles are the
`background. A multi-D identification experiment has more
`than one target parameters that need to be identified. For
`example,
`in a 3D identification experiment using the
`stimulus set shown in Table 1, all the three parameters
`are targets.
`In the present study, we conducted 1D identification
`experiments with fixed or roving background. With fixed
`background, the background parameters are assigned fixed
`values throughout an experiment while the value of the
`target parameter is randomized from trial to trial. The IT
`results so obtained represent the best identification perfor-
`mance that can be achieved with the target parameter. In a
`1D identification experiment with roving background,
`however, the values of all parameters are randomly selected
`from trial to trial. The participant is asked to identify the
`value of the target parameter while ignoring the random
`variations in the background parameters. The roving
`background procedure is more demanding than the fixed
`background procedure, and the resulting IT is usually
`lower. The lower IT values from identification experiments
`with roving background reflect the interactions among the
`parameters that make up the stimulus alternatives.
`The participants wore earmuffs (Peltor, with a nominal
`sound reduction of 29 dB for noise levels up to 105 dB) to
`
`block possible audio cues and noises. Each experimental run
`started with a short training session that lasted 5 to 15 min.
`Participants could choose the level of the target parameter
`they would like to feel by pressing a number on the
`keyboard. The training session ended when the participants
`decided to start the experiment. Participants were instructed
`to press down on the red dot attached to the test apparatus
`(see Fig. 1b) to trigger the presentation of a key-click signal.
`Participants were asked to indicate the perceived level of the
`target parameter by typing the corresponding number on
`the computer keyboard. Trial-by-trial correct-answer feed-
`back was provided. The total number of trials was divided
`into multiple runs. Between runs, participants were given
`the option to take a break if needed.
`In Experiment I where fixed background was used, the
`values of the background parameters were fixed at A3 (120 V)
`for amplitude, F2 (250 Hz) for frequency, and C2 (2 cycles) for
`number of cycles (see the highlighted parameter values in
`Table 1). For example, in a 1D amplitude identification
`experiment with fixed background, the frequency was fixed
`at 250 Hz and the number of cycles was fixed at 2. The
`participant’s task was to identify the level of the amplitude
`parameter when stimulus amplitude varied from trial to trial.
`In Experiment II where roving background was used, the
`values of the three parameters were chosen independently
`and randomly from trial
`to trial. For example,
`in a
`1D amplitude identification experiment with roving back-
`ground, any of the 60 stimulus alternatives shown in Table 1
`may be presented on a given trial. The participant’s task was
`to identify the level of the amplitude parameter despite
`random variations in the frequency and number of cycles of
`the stimulus.
`Experiments III and IV used a 3D identification para-
`digm. The main difference in the 3D experiment was that
`the participants had to identify all three parameters on each
`trial. In Experiment III, they were asked to identify the level
`of each parameter by sequentially entering three numbers
`that corresponded to amplitude, frequency, and number of
`cycles, respectively. In Experiment IV, the participants were
`asked to use a graphic code to identify the stimulus
`presented on each trial.
`
`2.4.3 A General Additivity Law
`With any multi-D stimulus set such as the one in the present
`study, it is generally of interest to measure the multi-D IT
`achievable with such a stimulus set. To run a full-scale
`3D identification experiment with the 60 stimuli shown in
`Table 1, however, would require a minimum of 5  602 ¼
`18;000 trials!
`Alternatively, one can ask the question of whether a
`multi-D IT can be predicted from the sum of 1D ITs
`estimated with each of the parameters making up the
`stimulus set. In general, ITðmulti-DÞ <  ITð1-DÞ, due to
`perceptual interferences among the stimulus parameters
`which is generally not accounted for by 1D identification
`experiments with fixed background (e.g., [31]). However, it
`appeared that when 1D identification experiments were
`conducted with roving background, then the sum of 1-D ITs
`will approximate the multi-D IT closely [32]. Durlach et al.
`[27] proposed a general additivity law that predicted, in the
`case of the present study
`
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`ITðA; F; CÞ  ITðAjrovF; CÞ þ ITðFjrovA; CÞ
`þ ITðCjrovA; FÞ;
`
`ð4Þ
`
`where IT(A, F, C) denotes the IT from a 3D identification
`experiment where all
`three parameters, the amplitude,
`frequency, and number of cycles of a key-click signal, have
`to be identified; IT(A|rov F, C) is the 1D IT from an
`amplitude identification experiment with frequency and
`number of cycles as the roving background; IT(F|rov A, C)
`is the 1D IT from a frequency identification experiment with
`roving amplitude and number of cycles; and IT(C|rov A, F)
`is the 1D IT from an identification experiment with number
`of cycles as the target and amplitude and frequency as the
`roving background. The general additivity law therefore
`states that a multi-D IT can be predicted from the sum of
`1D ITs, if the perceptual dependence of the parameters is
`properly accounted for by the roving background paradigm.
`Since it takes many more trials to collect enough number
`of trials for a 3D identification experiment than those
`required of several 1D identification experiments, it gen-
`erally takes less number of total trials to estimate all three
`terms on the right of (4) than to estimate the one term on the
`left of the equation. For example, in the case of the present
`study, a minimum of 18,000 trials are needed in order to
`obtain an unbiased IT estimate from a 3D identification
`experiment, as compared to a total of only 250 trials needed
`from three 1D identification experiments with roving
`background (i.e., 5  52 trials for amplitude identification,
`5  42 trials for frequency identification, and 5  32 trials for
`the identification of number of cycles). Therefore,
`the
`general additivity law can significantly save the experi-
`mental time required to obtained unbiased estimates of
`multi-D ITs.
`In the present study, we measured 1D ITs with fixed and
`roving background, and compared their, respectively, sums
`to the 3D IT obtained from a 3D identification experiment.
`To make it tractable to collect sufficient number of trials in
`the 3D identification experiment in order to obtain an
`unbiased estimate of
`IT, we used the results of
`the
`1D identification experiments to pare down the number of
`alternatives in the full stimulus set shown in Table 1.
`Therefore, our experiments were designed to guide the
`development of a final set of perceptually identifiable key-
`click signals, and at the same time to verify the general
`additivity law proposed by Durlach et al. [27].
`
`2.5 Data Analysis
`Results from each experiment were summarized in a K-by-K
`stimulus-response confusion matrix. The ITest values were
`also calculated using (3). Although we present one confu-
`sion matrix per experimental condition by pooling multiple
`participants’ data, the ITest values were always calculated
`for individual participants first and then averaged.
`In addition to the 1D IT results for each stimulus
`parameter, denoted IT(A), IT(F), or IT(C), the sum of the
`three IT values were also reported. The sums, denoted
`IT(SUM), were calculated separately for fixed and roving
`background experiments. They were used to check the
`validity of the general additivity law proposed in [27].
`
`TABLE 2
`Pooled Data from Experiment I
`
`3 EXPERIMENTS I & II: 1D IDENTIFICATION
`EXPERIMENTS WITH FIXED AND ROVING
`BACKGROUND
`
`In the first two experiments, the 1D IT achievable with the
`parameters amplitude, frequency, and number of cycles were
`estimated, using both a fixed background (Experiment I) and
`a roving background (Experiment II) paradigm.
`
`3.1 Methods
`As explained in Section 2.3, the amplitude parameter in the
`stimulus set used in the present study had five levels, the
`frequency parameter four levels, and the number of cycles
`parameter three levels. Accordingly, the total number of
`trials collected during the 1D identification experiments
`was different for each of the parameters. In order to obtain
`unbiased IT estimates, a minimum of 125 trials was needed
`for a 1D amplitude identification experiment, 80 trials for
`frequency identification, and 45 trials for the identification
`of number of cycles. Since we divided all experiments into
`50-trial runs, a total of 3 runs (150 trials) were collected for
`1D amplitude identification experiments, 2 runs (100 trials)
`for frequency identification, and 1 run (50 trials)
`for
`identification of number of cycles. In all, a total of 12 50-
`trial runs were conducted per participant (6 for the fixed
`background condition, and another 6 for the roving
`background condition). It took each participant between 1
`to 2 hours to complete the experiments, including the time
`for breaks.
`
`3.2 Results
`Table 2 shows the stimulus-response confusion matrices
`pooled from all participants for the fixed-background
`
`6
`
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`CHEN ET AL.: DESIGN AND EVALUATION OF IDENTIFIABLE KEY-CLICK SIGNALS FOR MOBILE DEVICES
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`235
`
`TABLE 3
`Pooled Data from Experiment II
`
`TABLE 4
`Information Transfer (in Bits) from Experiments I & II
`
`experiments (Experiment I). Each cell entry shows the
`number of trials that a particular stimulus was called a
`particular response. The shaded cells along the main
`diagonals of the confusion matrices correspond to the
`number of trials with correct answers. Overall, the percent-
`correct score for each stimulus ranged from 43 (A4) to
`90 percent (A1) for amplitude (Table 2a), 39 (F3) to 91 percent
`(F1) for frequency (Table 2b), and 63 (C2) to 88 percent (C1)
`for number of cycles (Table 2c). It appears that the lowest
`stimulus level always resulted in the highest identification
`accuracy. Looking at the error patterns in Tables 2a and 2c,
`the majority of confusions occurred between adjacent
`parameter levels (i.e., most of the error trials occurred
`among the cells adjacent to the main diagonal cells).
`Table 3 shows the stimulus-response confusion matrices
`pooled from all participan