Estimating critical bandwidths of temporal sensitivity to low-frequency amplitude modulation

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1 Estimating critical bandwidths of temporal sensitivity to low-frequency amplitude modulation Allison I. Shim a) and Bruce G. Berg Department of Cognitive Sciences, University of California, Irvine, Irvine, California (Received 17 February 2012; revised 27 February 2013; accepted 5 March 2013) Auditory filter bandwidths are measured for a temporal process using an amplitude-modulation detection task. The signal is a 200 Hz wide, sinusoidally amplitude-modulated band of noise centered within an unmodulated notched-noise masker. A modulation rate of 10 Hz is used to avoid possible information loss at more central processing levels for high modulation rates. Threshold functions are obtained for notch widths for each of four different center frequencies (0.6, 1, 2, and 4 khz) to determine the maximum notch width at which the masker has an effect. The ratio of center frequency to maximum notch width is 2 at all center frequencies. It is proposed that the bandwidths observed in temporal tasks, which are consistently greater than expected from the viewpoint of critical band theory, be characterized as temporal critical bands. This proposal does not oppose, but provides a complement to the traditional critical band obtained in tasks involving spectral discrimination. VC 2013 Acoustical Society of America. [ PACS number(s): Ba, Dc, Fe, Mk [EB] Pages: I. INTRODUCTION Psychophysical measurements of the detection of amplitude modulation (AM) with increasing modulation frequency demonstrate an upper limit to the temporal resolution of the auditory system. Seen in detection thresholds measured as a function of AM rate, the temporal modulation transfer function (TMTF; Viemeister, 1979) showed a cutoff point for higher modulation rates at which performance began to deteriorate, reflecting a characteristic low-pass shape. Recently, it has been proposed that the low-pass portion of the TMTF reflects a loss of information at levels more central than the initial peripheral filtering process (Strickland and Viemeister, 1997; Dau et al., 1997; Eddins, 1999). If peripheral filtering does limit temporal resolution in some way, it should be reflected most in low frequency regions (Strickland, 2000). In a task involving discrimination of AM/QFM (quasi-frequency modulated) noise, Strickland and Viemeister (1997) found identical cutoffs for TMTFs for frequency regions around 1 and 4 khz, implying that the cutoff is not consistent with loss of information at the peripheral level. If there are peripheral limitations to AM detection, then those limitations should be most apparent for stimuli with low carrier frequency and low stimulus level, since the latter are associated with narrow peripheral filtering (Strickland, 2000). A motivating factor behind the current study is the discovery that degrading single channel energy cues with roving level procedures have no effect on thresholds in tonein-noise detection tasks (Gilkey, 1987; Spiegel and Green, 1982), which violates a fundamental assumption of critical band theory. These findings decrease confidence in estimates of peripheral filtering based on tone-in-noise detection experiments, making it prudent to seek corroborating a) Author to whom correspondence should be addressed. Electronic mail: ashim@uci.edu evidence from other listening tasks. A review of the literature highlights a discrepancy between the observed bandwidths in discrimination tasks designed to primarily engage temporal domain processes (e.g., temporal envelope) and discrimination tasks designed to primarily engage spectral domain processing (e.g., power spectrum models). For the latter, a recent trend of studies (Shera et al., 2002; Heinz et al., 2001; Oxenham and Shera, 2003) report that bandwidths for spectral auditory filters may be narrower than traditional estimates of critical bands. On the other hand, a longer-term trend shows that discrimination tasks that ostensibly isolate information in the temporal domain yield bandwidth estimates for auditory filters that exceed a critical band (Mathes and Miller, 1947; Forrest and Green, 1987; Strickland and Viemeister, 1997; Berg, 2007; Turner, 2010; Nelson, 1994; Nelson and Schroder, 1995; Oxenham and Dau, 2001; Tabuchi et al., 2012; Buss et al., 2013). To avoid confusion here, the term critical bandwidth for a temporal process will be denoted by CB Temporal and will refer to bandwidth estimates obtained with discrimination tasks intended to engage temporal auditory processes. This term is to be considered distinct from the traditional critical band obtained with discrimination tasks that engage spectral discrimination processes, which will be denoted here as CB Spectral. The current study explores the idea that the traditional critical band, CB Spectral, is not an appropriate measure to be applied to models of temporal processing, and that a different characteristic critical band, CB Temporal, may provide a more reasonable estimate. A design similar to the traditional tone-in-notched-noise detection procedure (Patterson, 1976) is employed in which a pure tone signal is placed between two masking noise bands (the notch) and thresholds for signal detection are measured as a function of notch width, or the distance between the noise maskers. The pure tone signal is replaced with a sinusoidally amplitude modulated (SAM) narrow band of noise. Estimates of CB Temporal are obtained 2834 J. Acoust. Soc. 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2 here by measuring sensitivity to low frequency modulation of narrowband noise across different carrier frequency regions. By using a constant low frequency modulator, bandwidth estimates should not reflect a loss of information at more central processing levels. Additionally, even if CB Temporal estimates are broader than the typical CB Spectral, these estimates might still exhibit the same characteristics as CB Spectral, such as a roughly constant-q ratio of center frequency to filter bandwidth, consistent with the physical properties of the basilar membrane. Significant deviations from this could indicate that CB Temporal estimates do not strictly reflect peripheral filtering bandwidths. II. METHOD A. Observers Six naive subjects, three female and three male ranging in age from 20 to 49, participated as paid volunteers. All subjects were screened for normal hearing and displayed less than 20 db hearing loss for pure tones ranging from 0.5 to 8 khz (ANSI, 2004). All procedures were approved by the UCI Institutional Review Board. B. Stimuli The signal carrier is a 200-Hz wide band of noise generated in the frequency domain with the magnitude spectrum consisting of components with values sampled from a Rayleigh distribution. 1 The band is centered on one of four center frequencies (f C ): 0.6, 1, 2, or 4 khz. For all conditions, the signal modulator is a 10 Hz sinusoid with a dc component and amplitude defined as m. The parameter, m, determines the depth of modulation and is raised or lowered in 2 db steps from trial-to-trial using a two-interval, forced-choice, adaptive staircase procedure (Levitt, 1971). On the first trial of the first block of each condition, 20 log(m) ¼ 2dB, and the initial value is adjusted on subsequent blocks based on performance thresholds obtained on prior blocks. The notched-noise maskers have a bandwidth of 200 Hz. The bandwidth of each masker remains unchanged throughout the experiment to ensure constant level across conditions. Masking bands are centered equidistant logarithmically on either side of the signal, creating the notch. Notch width is defined by the distance between the high edge of the low frequency masker and the low edge of the high frequency masker. For example, a notch width of 1000 Hz could have the low masker centered at 500 Hz, with a lower edge at 400 Hz and an upper edge at 600 Hz, and a high masker centered at 1700 Hz, with a lower edge at 1600 Hz and an upper edge at 1800 Hz. The signal band and two masking bands are each presented at 70 db SPL (sound pressure level), resulting in an overall presentation level of approximately 74.8 db SPL. The level of the signal band is adjusted on each trial so that the modulated and unmodulated intervals have the same intensity. Each interval is 500-ms in duration with 20-ms linear onset and offset ramps. The inter-stimulus interval is 500-ms. Digitized waveforms are played through a two-channel, digital-to-analog converter (E-MU 0202 Audio/MIDI interface, Scotts Valley, CA) with a 44.1 khz sampling rate. The signal is then passed through a manual attenuator for level calibration, then to the TDT System II headphone buffer where the signal is split and sent to both headphone channels. Sounds are delivered over Sennheiser HD414SL (Old Lyme, CT) headphones to a listener seated in a singlewalled, sound-attenuating chamber. Subjects respond via keyboard and feedback is provided on a computer monitor after each trial. C. Procedure All subjects complete 5 blocks of 70 trials for each notch condition. For each center frequency, f C, there are conditions in which the width of the notch is systematically varied. Notch widths are determined by calculating equal logarithmic distances above and below the signal and measuring the distance between the inside edges of the high and low maskers, as outlined above. Notch width conditions are the same for each center frequency, with the exception of the 0.6 khz center frequency, which was limited in range on the low-frequency side. Condition 1 for each f C has no noise maskers and is run first to obtain baseline measurements and provide initial training. The order of conditions for each f c is otherwise random. Estimating the depth of modulation with a staircase procedure presents a special case because the signal becomes over-modulated when m > 1. There probably is no ideal solution to this problem. Strickland and Viemeister (1997) terminated blocks when the adaptive procedure required an m > 1, but this leads to a bias toward lower threshold estimates in difficult conditions. For the current procedure, if m reaches 1, it remains at 1 until two consecutive correct responses are entered, therefore allowing all blocks to be completed to their entirety. The schedule violates the assumptions underlying Levitt s (1971) derivation for calculating a threshold, so an alternative method of averaging all stimulus levels after the first four reversal points is used (Klein, 2001). A probability density function generated for thresholds obtained from 3000 random-response simulations with this schedule is used to determine the value of m corresponding to chance performance, calculated as 20 log(m) ¼ 2.47, a value that is less than 95% of the simulated thresholds (i.e., a ¼ 0.05). Any observed thresholds that are higher than 2.47 are excluded from the analysis. III. RESULTS A. Threshold functions Averaged thresholds across subjects as a function of notch width are presented in Figs. 1(a) 1(d) for each center frequency (open circles). For all f C, all subjects have similarly shaped threshold functions so only the averaged data are shown. In one condition, one subject s threshold falls above chance (subject AS10, f C ¼ 600 Hz, 4 Hz notch) and is not included in the analysis. The threshold functions for each f C are used to determine the approximate notch width at which the maskers first influence the detectability of the SAM signal. This point is referred to as the breakpoint and is considered to be an estimate of CB Temporal. J. Acoust. Soc. Am., Vol. 133, No. 5, May 2013 A. I. Shim and B. G. Berg: Sensitivity to low-frequency modulation 2835

3 FIG. 1. Results from linear regression analysis of breakpoint for center frequencies of 0.6, 1, 2, and 4 khz. Data are plotted as open circles with regression fits indicated by dashed lines. Error bars indicate the standard error between individual subjects thresholds. Closed stars show breakpoints. Estimated breakpoint values are listed in Table I. B. Breakpoint analysis Breakpoints are obtained with the following method. The subset of data with two or more points that yields the minimum standard error to a line with a constrained slope of zero is first found for the widest notch conditions. The zero slope constraint has the theoretical implication that the maskers at these notch widths have no effect on detection thresholds. The remaining data points are then fit using linear regression and the breakpoint is determined by calculating the intersection of the two lines. The advantage of using this method rather than a typical piecewise regression analysis is that with relatively few data points, the piecewise method limits breakpoint estimates to discrete values determined by the data. Figures 1(a) 1(d) show the fitted data with each estimated breakpoint indicated by a filled star. Estimated breakpoint values are provided in Table I. Q-values indicating broader tuning. Shown as closed triangles in Fig. 2, aq of 2 is obtained for all f C s. IV. DISCUSSION The estimates of CB Temporal follow a trend across a wide spectrum of recent investigations toward broad filter estimates for temporal processing in contrast with narrow estimates for spectral processing. Current results are consistent with evidence from several studies suggesting that the maximum effective bandwidth for a temporal process may be wider than the critical bandwidth of frequency resolution, even in high frequency regions where basilar membrane tuning is broadest with respect to frequency (Forrest and Green, 1987; Viemeister, 1979; Strickland and Viemeister, 1997; Oxenham and Dau, 2001; Berg, 2007; Turner, 2010). C. Q analysis Breakpoint estimates are converted into a dimensionless value, Q, which is calculated by dividing the center frequency by the estimated breakpoint (in Hz). Q-values provide information regarding the sharpness of tuning, with higher Q-values indicating sharper tuning and lower TABLE I. Breakpoint values (in Hz) from regression analysis for each center frequency tested. Frequency f C (Hz) Breakpoint (Hz) FIG. 2. Closed triangles show Q values for breakpoints estimated from the data (i.e., center frequency/breakpoint) J. Acoust. Soc. Am., Vol. 133, No. 5, May 2013 A. I. Shim and B. G. Berg: Sensitivity to low-frequency modulation

4 Evidence of wider filters for temporal processing has also been seen in the study of temporal phase responses of auditory filters using Schroeder-phase masking complexes (Oxenham and Dau, 2001). Schroeder-phase stimuli have the unique characteristic of producing masked threshold differences up to 20 db despite having identical power spectra and largely similar flat temporal envelopes, making them a useful tool in distinguishing spectral and temporal filtering properties. Simulations of a single-channel model using an initial filter with a bandwidth wider than a critical band were able to account for the threshold differences seen for negative and positive Schroeder-phase maskers, in addition to the frequency selectivity and the phase responses observed in the data. Oxenham and Dau (2001) proposed that the temporal phase responses observed do not necessarily require across-channel processing and that a single-channel mechanism with a broad initial filter may be appropriate. Using a novel paradigm, Berg (2007) and Turner (2010) also found evidence that CB Temporal is considerably greater than CB Spectral. Using a discrimination task that isolates information in the temporal domain, thresholds for detection of an increment in the central component of an n-component complex were measured. Varying both the number of components and the frequency separation between components allows thresholds to be estimated as a function of the overall bandwidth of the complex. Berg (2007) showed increasing thresholds in narrow bandwidth regions followed by a distinct change point at wider frequency regions in which thresholds show a decreasing trend. This change point was termed the estimated transition bandwidth, or ETB, which Berg (2007) suggests is indicative of the minimum upper limit of a singlechannel envelope detector and the point at which the listener presumably switches to a process of across-channel comparisons. For a stimulus centered at 1 khz, the median ETB for 44 listeners is 400 Hz, with 30% of all listeners displaying ETBs greater than 600 Hz. Turner (2010) found ETBs greater than 2 khz for a 2 khz center frequency using frequency separations ranging from 80 to 400 Hz between each component. ETB estimates from both studies are remarkably stable, even for frequency separations spanning multiple critical bands. Both studies support the idea that listeners use a single broadband channel for temporal processing. In contrast to evidence of broad filters for temporal processing, a number of studies show support for narrow estimates of CB Spectral. It has recently been suggested that spectral auditory filter estimates may in fact be narrower than previously thought (Shera et al., 2002; Oxenham and Shera, 2003; Heinz et al., 2001). Shera et al. (2002) provided one of the first studies linking behavioral and physiological estimates of cochlear tuning by comparing psychophysically derived cochlear filter estimates with stimulus-frequency otoacoustic emissions measured in humans and animals. Using a power-law conversion, comparisons were made between behavioral and physiological data across species. The results of their analyses suggest that previous behavioral estimates of peripheral cochlear filters were greatly overestimated; human cochlear tuning is at least two times sharper than previously believed. Oxenham and Shera (2003) further investigated the findings from Shera et al. (2002) by measuring auditory filter shapes for low level signals in notched-noise with forward- and simultaneous-masking conditions. They used a fixed, lowlevel signal where tuning is sharpest and forward-masking presentations to avoid suppression effects that are seen in simultaneous-masking data. Their results support the findings from Shera et al. (2002) that human cochlear tuning for low levels is substantially sharper than estimates previously obtained from notched-noise studies. In addition, they found that relative tuning becomes even sharper with increasing center frequency, bringing human cochlear tuning patterns closer to those observed in other mammals, such as the guinea pig and cat. Heinz et al. (2001) looked at the relationship between cochlear tuning and psychophysical estimates of frequency selectivity. A computational auditory-nerve (AN) model (Heinz et al., 2001) implementing many of the response properties of nonlinear cochlear tuning was used in combination with a signal detection theory analysis to generate spectral auditory filter estimates that are comparable with psychophysical estimates from tone-in-notched-noise experiments. The nonlinear AN model with suppression, however, produced simulated data that lead to overestimation of ERBs compared to the filters actually used by the model. Heinz et al. (2001) concluded that spectral auditory filters are actually narrower than most psychophysical estimates. The combined evidence for broadband tuning of peripheral auditory filters in temporal tasks contrasted with the evidence of sharply tuned peripheral auditory filters in spectral tasks suggests that the initial filtering properties for temporal and spectral information are different from one another. While spectral auditory filters have long been defined by their critical bandwidths, auditory filter bandwidths derived in temporal tasks have not been characteristically defined. It is proposed that the wider bandwidths observed in temporal tasks be recognized as a temporal critical band, a complement to the spectral critical band. This would lay the foundation for a dynamic system that can adjust its bandwidth to the stimulus context (Strickland and Viemeister, 1997). Alternatively, Berg (2004) proposed discrete filtering systems for spectral and temporal processes that reflect this distinction. Auditory spectral filters are commonly thought of as a bank of constant-q bandpass filters. Recent evidence suggests that this may not be the case (Shera et al., 2002; Oxenham and Shera, 2003). Results from these studies are in agreement, reporting an increasing Q above 1 khz. Oxenham and Shera s (2003) results indicate Q values of about 10 at 1 khz and 20 at 8 khz. This effectively suggests that spectral auditory filters (CB Spectral ) do not have a constant relative bandwidth across frequencies, but rather that the tuning of cochlear filters above 1 khz becomes increasingly sharpened with increases in center frequency. In contrast, current results indicate approximately constant-q for estimates of CB Temporal. While the implications of constantor non-constant-q on peripheral filtering are unclear, it remains that Q-values derived from spectral versus temporal tasks consistently highlight the differences in sharpness of tuning. J. Acoust. Soc. Am., Vol. 133, No. 5, May 2013 A. I. Shim and B. G. Berg: Sensitivity to low-frequency modulation 2837

5 V. CONCLUSIONS (i) (ii) (iii) (iv) Threshold functions obtained for a fixed 10 Hz sinusoidal modulation theoretically provide a way to measure peripheral sensitivity in temporal tasks. Breakpoint threshold estimates for detection of 10 Hz SAM narrowband noise in the presence of notchednoise are consistently wider across a carrierfrequency range of 0.6 to 4 khz than bandwidth estimates typically observed for tone-in-noise type tasks measuring spectral frequency selectivity. Wider bandwidths presented here agree with other behavioral studies investigating temporal processing in the auditory periphery. Breakpoint estimates across center frequency exhibit a constant-q value of 2. Q-values reported for filter bandwidth estimates derived from studies on spectral frequency resolution are typically around 8 to 10, suggesting much narrower tuning for spectral auditory filters compared to temporal auditory filters. Based on these and other results, it is suggested that broad auditory filter estimates obtained using temporal tasks be characterized as a temporal critical band. This term is not intended to replace or oppose the existence of the typical critical band obtained from spectral tasks, but rather provide a complementary term to be used where it is relevant. ACKNOWLEDGMENTS The authors would like to thank Ewa Borucki, Hisaaki Tabuchi, Curt Southworth, and Matt Turner for their assistance, and Virginia Richards, Yi Shen, and the rest of the GrandLab for their helpful comments. This study is part of a graduate dissertation in the Department of Cognitive Sciences at the University of California, Irvine (Shim, 2012). This work was supported by NSF Grant No. BCS The 10 Hz modulation is imposed after filtering the 200 Hz noise band, introducing the possibility that the discrimination is made on the basis of detecting a change in the stimulus bandwidth, per se, independent of any modulation cue. A follow-up experiment shows that some listeners are sensitive to very small changes in stimulus bandwidth, achieved by adding Rayleigh distributed components to both ends of the magnitude spectrum. All listeners report that the wider noise band has a lower pitch. In the presence of a notch-noise masker, however, performance falls to chance levels for all conditions and listeners, even when a single-sided noise masker is placed several thousand Hz above the carrier noise band. Since a notchednoise masker is used in the experiment, it is unlikely that a change in stimulus bandwidth affects the reported results. ANSI (2004). S3.6. American National Standard Specification for Audiometers (American National Standard Institute, New York). Berg, B. G. (2004). A temporal model of level-invariant tone-in-noise detection, Psychol. Rev. 111, Berg, B. G. (2007). Estimating the transition bandwidth between two auditory processes: Evidence for broadband auditory filters, J. Acoust. Soc. 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