Cuing mechanim in auditory ignal detection RONALD HÜBNER and ERVIN R. HAFTER Univerity of California, Berkeley, California Detection of auditory ignal under frequency uncertainty can be improved by preenting cue to the litener. Since variou cue have been found to differ in effectivene, three conceivable mechanim were conidered which might account for thee difference. Cuing might reduce the number and/or width of the employed auditory filter or litening band. Alo, cue could modulate the preciion of frequency tuning of the filter. Pychometric function were collected in a detection experiment with frequency uncertainty employing three kind of cue: pure tone whoe frequency wa identical to that of the ignal (iconic cue), complex tone with a miing fundamental equal to the ignal (complex cue), and pure tone with a certain frequency relation to the ignal (relative cue). Compared with a no-cue condition, all cue type improved detection performance. Fitting model to the data ugget that in the no-cue condition a well a the complex-cue condition, multiple band were utilized, and that the iconic and relative cue induced ingle-band litening. There i no indication that accuracy of frequency tuning wa reponible for cue-efficiency difference. For the detection of inuoidal auditory ignal in noie, trial-by-trial variation of ignal frequency reult in lower performance than when it i fixed (e.g., Creelman, 196; Green, 1961; Swet & Sewall, 1961). However, thi uncertainty effect can be compenated for by providing clearly audible cue at the beginning of each trial. Variou kind of cue have been hown to be effective. Thee include what Schlauch and Hafter (1991) called iconic cue, which match the ignal in frequency, and cue that provide le direct information about the ignal frequency. The latter include multitonal cue for which only one component matche the ignal (Gilliom & Mill, 1976; Schlauch & Hafter, 1991), viual cue in which one of two frequencie i cued with light (Swet & Sewall, 1961), and tonal complexe whoe fundamental i related to the ignal (Hafter, Schlauch, & Tang, 1993). Cue baed on muical relation (Hafter et al., 1993) and on tonal pattern (Howard, O Toole, Parauraman, & Bennett, 1984) or viual pattern (Howard, O Toole, & Rice, 1986) related to the ignal have alo been applied uccefully, and, for litener with abolute pitch, o have viually preented muical note (Hafter & Schlauch, 1992). Although all thee cue type may erve to reduce frequency uncertainty, there are neverthele appreciable difference in their efficiency (e.g., Hafter et al., 1993; Schlauch & Hafter, 1991). Generally, it can be aid that Thi reearch wa conducted while the firt author wa a viiting cholar at the Pychology Department of the Univerity of California at Berkeley a holder of a NATO cience fellowhip. The author would like to thank the unknown reviewer for valuable comment which helped u to improve on the former verion of thi paper. Correpondence hould be addreed to the firt author, who i now at the Intitut für Pychologie, Techniche Univerität Braunchweig, Spielmanntr. 19, D-3816 Braunchweig, Germany (e-mail: t.huebner@ tu-b.de). iconic cue are the mot effective, uually eliminating the frequency-uncertainty effect completely. How can the oberved efficiency difference between different cue type be explained? Poible anwer depend on the pecific ignal detection model under conideration. Uually it i aumed that under optimal condition, detection of tonal ignal in wideband noie i baed on the output of auditory filter centered near the ignal frequencie. For intance, in a two-interval forcedchoice (2IFC) experiment, where a deciion ha to be made about which one of two temporal interval contain the ignal, it i aumed that litener chooe the interval containing the larget filter output. Although le agreement exit with repect to what the filter output repreent (ee, e.g., Jeffre, 1964), the energy detection model, which aume that the filter output correpond to timulu energy, i widely ued to decribe auditory detection (cf. Green & Swet, 1966). When the ignal i a pure tone with a ingle fixed frequency, it i reaonable to aume the ue of a ingle bandpa filter whoe center frequency matche that of the ignal. However, when there i frequency uncertainty, mot theorit have propoed that the litener imultaneouly monitor the output of multiple filter (Green, 1961; cf. Swet, 1984). To obtain a ingle deciion variable for thi cae, one mut devie a combination rule for the multiple output. One rule (Creelman, 196) that i widely ued ay that the ubject chooe the interval that ha the maximum output of any of the monitored filter. The more filter, the more likely it will be that the maximum output will be due to noie alone, thu lowering performance. Another rule i to contruct a weighted um of the output, thereby increaing the effective noie, which alo predict a decreae in performance. Within thee multiple-band conceptualization, cuing-efficiency difference can be modeled according to their capacity to reduce the number of monitored band. 197
198 However, it ha alo been argued that there are litening band whoe width are labile and that an effect of frequency uncertainty i to widen thee litening band (Hafter & Kaplan, 1976). Since band widening increae the amount of effective noie, detection performance drop. In thi cae, it i reaonable to uppoe that cuing reduce uncertainty by reducing the effective bandwidth. Thi hypothei received upport from recent reult of Hafter et al. (1993). They employed a modified verion of the o-called probe-ignal method (Dai, Scharf, & Buu, 1991; Greenberg & Larkin, 1968; Schlauch & Hafter, 1991) to meaure the width of litening band during detection with iconic and relative cue. The latter were tone with two third of the ignal frequency. It turned out that the relative cue were le effective than the iconic cue and that thi difference wa attributable to bandwidth difference. The model conidered o far uually ignore poible effect of filter hape. However, auditory filter are modeled a having loping kirt (Patteron & Moore, 1986), which implie that performance i maximal for a choen filter only when it i centered on the ignal frequency, or, to put it another way, when it frequency tuning i optimal. Any hift would produce an attenuation of the ignal and, conequently, a decreae in detection performance. Thi fact offer a third mechanim poibly related to cuing. The efficiency difference of variou cue type could reflect the accuracy of frequency tuning that they permit. Thu, at leat three different mechanim might account for cue effect and their difference. Fortunately, a ha been hown by one of the preent author (Hübner, 1993), there i a method to dicriminate empirically between the conidered cuing mechanim. Idealoberver analyi reveal that each mechanim affect pychometric function in a pecific way. Common to all mechanim i that decreaing efficiency i reflected by a hift of the pychometric function toward higher level. However, there are difference concerning the lope. Wherea inaccurate frequency tuning lead to flattened pychometric function, increaing the width or number of the auditory filter caue jut the oppoite the function teepen. Unfortunately, the predicted lope difference are rather mall for uual experimental ituation and o might not be detected. For intance, even in condition with frequency uncertainty without cue, Green (1961) found lope that were imilar to thoe obtained with fixed frequencie. He drew thi concluion, however, by viually inpecting collection of function from different ituation, and ince he oberved only mall frequencyuncertainty effect for mot of hi condition, the quetion of whether a mall lope difference could have been hown at leat for the condition that produced the larget effect remained open. In contrat, Schlauch and Hafter (1991) howed appreciable change in the lope of pychometric function a the amount of uncertainty increaed. In another related tudy, Buu, Schorer, Florentine, and Zwicker (1986) randomized one complex and three pure tone and compared the reulting pychometric function with thoe obtained with fixed ignal. Although they did not employ a conitent within-ubject deign, they found a ignificant lope difference at leat for one frequency. The aim of the experiment reported here wa to provide further evidence for the idea that the lope are affected in a ytematic manner by frequency uncertainty and to utilize that information for ditinguihing between mechanim poibly involved in cuing. Therefore, pychometric function were collected in a ignal detection experiment with frequency uncertainty for different cue type: iconic, complex, and relative cue. The complex cue were harmonic tone that had a miing fundamental equal to the ignal. On the bai of pat reult (Hafter & Schlauch, 1992), we expected the iconic cue to be the mot, and the relative cue the leat effective. The variation in the lope of the pychometric function with decreaing efficiency hould provide information about the conidered cuing mechanim. METHOD The ignal were pure tone of one of eight frequencie: 535, 625, 755, 835, 975, 125, 1145, and 1285 Hz. In a random-frequency condition, all ignal were randomly preented with equal probability. Three different kind of cue were employed: iconic, complex, and relative. A control condition with no cue wa alo included. The complex cue conited of the 2nd, 3rd, 4th, 5th, and 6th harmonic of the repective ignal frequencie. The relative cue were pure tone with two third the frequency of the repective ignal. An accelerated adaptive 2IFC procedure (Falmagne, 1985) wa ued to meaure the fixed-frequency threhold of the individual tone. The obtained threhold correpond to 7.7% correct repone. The iconic and relative cue were preented at a level of 1 db above thi threhold. The complex cue were preented at a level uch that their component were 1 db above the threhold of the correponding ignal. The timuli were generated by a D/A-converter connected to an IBM-AT computer, which alo controlled the preentation of the timuli and regitered the repone of the ubject. The timuli, which had abrupt onet and offet, were mixed with continuouly preent white noie with a noie power denity of 35 db (SPL) and preented monaurally through a Stax SR5 headphone. The ubject were eated in a oundproof booth. The cue had the ame duration, T, of.2 ec a the ignal and were preented.5 ec before the firt interval. The two interval, which were indicated by light, were eparated by.3 ec. Viual feedback wa given after each repone. Three normally hearing ubject participated in the experiment, which wa divided into thirteen 1-h eion. Each eion conited of eight block of 8 or 96 trial. To obtain etimate of the pychometric function, level of the individual tone were choen to cover the range around 75% correct repone in a 2IFC random-frequency condition. To average the performance over the different frequencie, enation level (SL) were ued (i.e., the level of the individual tone in decibel, relative to their fixedfrequency threhold). With a tepize of 2 db, thi reulted in 5 to 6 point of the pychometric function. Each point for each ubject i the reult of 4 trial.
199 RESULTS The pychometric function of the 3 ubject and of their pooled data for the different condition are depicted in Figure 1. Obviouly, the iconic cue were mot effective. However, the other cue type alo improved detection performance in comparion with the no-cue condition. Were the complex cue more effective than the relative cue? Their pychometric function are rather cloe. However, for mot level, the data point of the complex cue are above the correponding point of the relative cue. A Wilcoxon matched-pair igned-rank tet with all 15 data pair (ubject level) revealed a ignificant difference in the predicted direction (T 3, N 15, p <.5). To get etimate of lope and threhold, logitic function were fitted to the data by minimizing 2 with a minimizing algorithm (Gegenfurtner, 1992). The reult are diplayed in the firt three row of Table 1. Parameter were alo etimated for the pooled data. They are given in the fourth row of the table. Generally, a good fit wa obtained [e.g., for the pooled data, iconic: 2 (3) =.227; complex, 2 (2) =.31; relative, 2 (2) =.148; no-cue, 2 (2) =.184; p >.9 for all condition]. Inpection of Table 1 how that the efficiency order expected for the cue type i reflected by the order of each ubject etimated threhold, except that there i one tie for Subject R.H. A different order, but alo identical for all ubject, with the exception again of one tie for Subject R.H., hold for the lope. To examine whether the lope and threhold pattern hold acro frequencie, the ubject data were pooled, and logitic function were fitted to the pychometric function correponding to the individual frequencie. No indication of a ytematic relationhip between lope and frequency could be found within each condition. However, a a repeated meaure analyi of variance (ANOVA) revealed, there were ignificant lope [F(3,21) 1.8, p <.1] and threhold [F(3,21) 69.1, p <.1] difference between the experimental condition. The Student-Newman-Keul tet wa ued for multiple pairwie comparion. It turned out that the iconiccue condition produced ignificantly flatter pychometric function (lope: M.473) than did the other condition [comparion with the complex-cue condition, M.633, q(3,21) 6.1, p <.1; with the relativecue condition, M.569, q(2,21) 3.67, p <.5; with the no-cue condition, M.672, q(4,21) 7.54, p <.1]. While the lope of the complex-cue condition were not ignificantly different from thoe of the relative-cue condition or from thoe of the no-cue condition, the relativecue condition produced ignificantly maller lope than did the no-cue condition [q(3,21) 3.89, p <.5]. The iconic-cue condition alo produced ignificantly lower threhold (M.61) than did all other condition [comparion with the complex-cue condition, M 1.55, q(2,12) 5.5, p <.1; with the relative-cue con- Figure 1. Empirical pychometric function of Subject R.H., J.N., and K.O., and of their pooled data. The error bar indicate the tandard error with repect to the experimental eion.
2 Table 1 Etimated Slope and Threhold of the Empirical Pychometric Function for the 3 Subject Slope Threhold Subject Iconic Complex Relative No Cue Iconic Complex Relative No Cue R.H..534.63.534.696.45 1.51 1.51 3.62 J.N..52.644.621.73 1.8 2.36 2.61 5.54 K.O..419.638.521.674.77.65 1.28 2.65 M.484.637.559.691.66 1.51 1.8 3.94 Model.468.618.557.635.62 1.56 1.87 3.98 Note All parameter were etimated by fitting logitic function. The unit of the lope and threhold are P(C)/SL and SL, repectively. In the fourth row, the average parameter are given, and the correponding value predicted by the model are in the lat row. dition, M 1.84, q(3,12) 7.2, p <.1; with the nocue condition, M 3.92, q(4,21) 19.7, p <.1]. Threhold of the complex-cue condition were not ignificantly lower than thoe of the relative-cue condition but were lower than thoe of the no-cue condition [q(3,21) 14.16, p >.1]. The relative-cue condition alo produced ignificantly lower threhold than the no-cue condition [q(2,21) 12.5, p <.1]. DISCUSSION All cue type employed in the experiment improved detection behavior appreciably in comparion with the no-cue condition. Moreover, the pychometric function correponding to the different cue condition howed ignificant lope difference. The iconic cue, which were mot efficient, produced the flattet pychometric function. Since all other condition led to higher threhold and to teeper pychometric function, there i no indication that the decreae in cue efficiency can be attributed to poorer frequency tuning; thi would have caued the function to flatten (Hübner, 1993). Therefore, we conclude that the oberved performance difference were due to variation in the number and/or width of the utilized auditory filter. To examine the mechanim in greater detail, different quantitative model were fitted to the pychometric function for the individual frequencie (pooled acro ubject) in each condition. For the ake of implicity, only the value correponding to the data point were predicted. If we let P(C) denote the probability of a correct repone in a 2IFC tak, then the energy-detection model tate that P(C) = Φ(z), (1) where Φ denote the cumulative normal ditribution and z i given by In the cae of a ingle band, the expected value of the deciion variable X n in the noie interval i 2WT and it variance 4WT, where W denote the bandwidth of the auz = EX ( ) EX ( n) var( X ) + var( X ). (2) n ditory filter in hertz, and T, the interval duration in econd. In the interval containing ignal plu noie, the expected value of X i 2WT + 2E /N and the variance 4WT + 8E /N, with N denoting noie power denity (cf. Green & Swet, 1966). Iconic-Cue Condition: A Single-Band Model To obtain a tarting point, a ingle-band energydetection model wa fitted to each frequency pychometric function of the iconic-cue data, employing time and noie parameter a in our experiment. Since the energy-detection model i an ideal-oberver model, it i more enitive than our ubject. Although increaing the filter width, W, decreae enitivity, thi wa not ufficient to fit the data well, becaue the reulting lope alo varied with W. Therefore, the threhold wa taken a a econd free parameter for each pychometric function. The threhold are needed for tranforming the employed SL value to ignal energy. Changing the threhold imply hift the function without affecting it lope. Varying both the threhold and the filter width, W, for each function by mean of the algorithm mentioned above lead to good fit, although not all of the obtained value were reaonable (threhold in decibel [SPL] = 5.6, 46.8, 51.9, 44.6, 46.3, 5.9, 51.7, 53.8, and W: 39, 78, 922, 13, 38, 472, 975, 1573, correponding to frequency in acending order). However, we were not intereted in the abolute value within the cue condition but in the relationhip between the condition. Logitic function were fitted to the obtained theoretical data to compare the reulting lope and threhold with the correponding value etimated from the empirical data. A t tet for paired obervation indicated no difference [lope, M theo =.468, t(7) =.74, p >.48; threhold, M theo =.61, t(7) =.65, p >.53]. Relative-Cue Condition: A Single-Band Model In the next tep, a ingle-band model for the relativecue data wa contructed by uing the threhold parameter of the iconic-cue condition directly and by increaing the bandwidth parameter obtained in that condition linearly that i, by employing two free parameter a and b:
21 W i (relative) = aw i (iconic) + b, (3) for all frequencie i = 1,..., 8. Thi model wa fitted imultaneouly to all eight pychometric function. The obtained parameter are a = 1.4 and b 37.2 [ 2 (37) 14.4, p >.99]. There were no ignificant difference to the empirical data [lope, M theo =.58, t(7) = 2.34, p >.5; threhold, M theo = 1.92, t(7) = 1.42, p >.19]. Thi reult i in line with that of Hafter et al. (1993), who found that the bandwidth obtained with relative cue wa 1.6 time greater than that obtained with iconic cue. Here, the width i 1.4 time larger plu a contant, which i urpriingly cloe. No-Cue Condition: A Multiple-Band Model Since the relative cue provide no energy at the ignal frequency, it i reaonable to aume that imilar threhold and width parameter hold for the no-cue condition, but that under thi condition multiple filter are utilized. If multiple filter are utilized, a combination rule for the multiple output mut be choen (cf. Hübner, 1993). Here, we choe the weighted um of the filter output a a deciion variable: X* = Σ 8 g i X i. (4) It wa aumed that in the ignal interval, the filter that do not correpond to the ignal frequency behave a they do in the noie interval. Therefore, the expected value for the noie interval i E(X* n )= 2T Σ 8 g i W i, (5) and the expected value for the ignal-plu-noie interval i E(X* n )= 2T Σ 8 g i W i + 2g E /N, (6) where g denote the repective weight of the ignal channel. It wa further aumed that the auditory filter do not overlap and, conequently, do not produce correlated output. In thi cae, the output can be treated a independent random variable with the variance for noie, and var (X* n )= 4T Σ 8 var (X* n )= 4T Σ 8 g 2 i W i (7) g 2 i W i + 8g 2 E /N (8) for ignal plu noie. The reulting z value for thi model i z = 8 i = 1 ge / N 2 2 i i 2T g W + 2g E / N. (9) While uing the threhold and width parameter baed on fit to the relative-cue data, the weight g i for each filter were conidered a free parameter. However, the data fit with thi model wa diappointing [ 2 (31) = 74.3, p <.1]. The increae in lope for the pychometric function wa underetimated (lope, M theo =.426), and the decreae in performance, overetimated (threhold, M theo = 6.22). The latter could reflect overlapping auditory filter that led to overetimated variance. To keep the model relatively imple, merely two additional free parameter a* and b* were introduced for linearly modifying the variance part produced by the filter width. But how to increae the lope? An ideal oberver would chooe weight h i, i=1,..., 8, which may vary with ignal level (Green & Swet, 1966): E(Xi ) E(X i n ) h i =. (1) var(x n i ) Fortunately, the modified model with deciion variable and z value z = X* = Σ 8 hge/ N g i h i X i (11) 8 2 2 2 2 i = 1 i i i a* 2T h g W + b* + 2hgE/ N (12) turned out to fit the data quite well [ 2 (29) = 3.38, p >.995] and produced no ignificant difference [lope, M theo =.633, t(7) 1.41, p >.2; threhold, M theo = 3.96, t(7) 1.42, p >.19]. The parameter value for modifying the variance are a* =.694, and b* = 2.42. The obtained parameter for the weight are.73,.132,.142,.18,.124,.11,.14,.97. With one exception, the weight increae toward the central frequencie, which might repreent the ditribution of attentional reource acro the different output. Complex-Cue Condition: A Multiple-Band Model Finally, we tried fitting a model to the complex-cue data. Although their lope and threhold were not ignificantly different from thoe for the relative-cue condition, the data could not be fitted in the ame way that i, by linearly increaing the filter width parameter of the model of the iconic-cue condition. The lope were ignificantly underetimated [lope, M theo =.48, t(7) 5.2, p <.1]. (Remember that there are difference between the two cue condition, a ha been hown above with the raw data acro ubject.) Therefore, a multiple-band model wa applied. That complex cue induce multiple-band litening ha already been uggeted by Schlauch and Hafter (1991). Since the complex cue conited of five component and did not include the ignal frequency, we aumed a
22 model with ix band, each poeing the width and threhold parameter of the repective ignal band, which were taken from the model of the relative-cue condition. Ideal weight h i (ee Equation 1) were aumed for the ignal band and a linearly related weight h i comp for all cue-component band with free parameter a and b: h i comp = ah i b. (13) A for the no-cue data, two additional parameter a* and b* were ued to modify the variance attributable to the filter width. The z value for each,..., 8 in thi cae i z = he i / N a*[ 1( h ) WT + 2h WT] + b* + 2h E / N (14) With thee four free parameter, the eight pychometric function fitted well [ 2 (35) = 1.9, p >.995] and produced no ignificant difference [lope, M theo =.563, t(7) 2.29, p >.5; threhold, M theo = 1.54, t(7).5, p >.96]. The obtained parameter are a.471, b.48, and a*.377, b*.784. Concluion In Figure 2, the pooled data and the theoretic pychometric function averaged acro frequencie are hown. A can be een, the fit are quite good. Etimating the lope and threhold parameter in the ame way a for the empirical data produce the value given in the lat row of Table 1, which are rather cloe to their empirical counterpart. To um up, our analyi how that frequency uncertainty (with no cue) lead to multiple-band litening. Our reult are compatible with the idea that a weighted comp 2 2 2 i i i i i. um of the output of the individual band, which correpond to the poible frequencie, i utilized a deciion variable. Alo, complex cue lead to multiple-band litening. Preentation of iconic or relative cue induce utilization of ingle auditory filter with iconic cue cauing maller bandwidth. REFERENCES Buu, S., Schorer, E., Florentine, M., & Zwicker, E. (1986). Deciion rule in detection of imple and complex tone. Journal of the Acoutical Society of America, 8, 1646-1657. Creelman, C. D. (196). Detection of ignal of uncertain frequency. Journal of the Acoutical Society of America, 32, 85-81. Dai, H., Scharf, B., & Buu, S. (1991). Effective attenuation of ignal in noie under focued attention. Journal of the Acoutical Society of America, 89, 2837-2842. Falmagne, J.-C. (1985). Element of pychophyical theory. New York: Oxford Univerity Pre. Gegenfurtner, K. R. (1992). PRAXIS: Brent algorithm for function minimization. Behavior Reearch Method, Intrument, & Computer, 24, 56-564. Gilliom, J. D., & Mill, W. M. (1976). Information extraction from contralateral cue in the detection of ignal of uncertain frequency. Journal of the Acoutical Society of America, 59, 1428-1433. Green, D. M. (1961). Detection of auditory inooid of uncertain frequency. Journal of the Acoutical Society of America, 33, 897-93. Green, D. M., & Swet, J. A. (1966). Signal detection theory and pychophyic. New York: Wiley. Greenberg, G. Z., & Larkin, W. D. (1968). Frequency-repone characteritic of auditory oberver detecting ignal of a ingle frequency in noie: The probe-ignal method. Journal of the Acoutical Society of America, 44, 1513-1523. Hafter, E. R., & Kaplan, R. (1976). Report on attention and f lying. Unpublihed manucript prepared for NASA Ame Reearch Center. Hafter, E. R., & Schlauch, R. S. (1992). Cognitive factor and election of auditory litening band. In A. L. Dancer, D. Henderon, R. J. Salvi, & R. P. Hamernik (Ed.), Noie-induced hearing lo (pp. 33-31). St. Loui: Moby. Hafter, E. R., Schlauch, R. S., & Tang, J. (1993). Attending to auditory filter that were not timulated directly. Journal of the Acoutical Society of America, 94, 743-747. Howard, J. H., O Toole, A. J., Parauraman, R., & Bennett, K. B. (1984). Pattern-directed attention in uncertain-frequency detection. Perception & Pychophyic, 35, 256-264. Howard, J. H., O Toole, A. J., & Rice, S. E. (1986). The role of frequency veru informational cue in uncertain frequency detection. Journal of the Acoutical Society of America, 79, 788-791. Hübner, R. (1993). On poible model of attention in ignal detection. Journal of Mathematical Pychology, 37, 266-281. Jeffre, L. A. (1964). Stimulu-oriented approach to detection. Journal of the Acoutical Society of America, 63, 766-774. Patteron, R. D., & Moore, B. C. J. (1986). Auditory filter and exitation pattern a repreentation of frequency reolution. In B. Moore (Ed.), Frequency electivity in hearing (pp. 123-177). London: Academic Pre. Schlauch, R. S., & Hafter, E. R. (1991). Litening bandwidth and frequency uncertainty in pure-tone ignal detection. Journal of the Acoutical Society of America, 9, 1332-1339. Swet, J. A. (1984). Mathematical model of attention. In R. Parauraman & D. Davi (Ed.), Varietie of attention (pp. 183-242). New York: Academic Pre. Swet, J. A., & Sewall, S. T. (1961). Stimulu veru repone uncertainty in recognition. Journal of the Acoutical Society of America, 33, 1586-1592. Figure 2. The pooled data with curve predicted by the model.