Behavioral Measures of Frequency Selectivity in the Chinchilla · Five chinchillas (three males and...

Behavioral measures of frequency selectivity in the chinchilla AndrewJ. Niemiec a) and William A. Yost Parrnly Hearing Institute, Department of Psychology, Loyola University Chicago, 6525 •V. Sheridan Road, Chicago, Illinois 60626

William P. Shofner

Parrely Hearing Institute, Loyola University Chicago, 6525 N. Sheridan Road, Chicago, Illinois 60626

( Received 16 September 1991; revised 29 January 1992; accepted 13 July 1992)

A simultaneous masking procedure was used to derive four measures of frequency selectivity in the chinchilla. The first experiment measured critical masking ratios (CRs} at various signal frequencies. Estimates of the chinchillas' critical bandwidths derived from the CRs were much broader than comparable human estimates, indicating that the chinchilla may have inferior frequency selectivity. The second experiment measured critical bandwidths at 1, 2, and 4 kHz in a band-narrowing experiment. This technique yielded narrower estimates of critical bandwidth; however, chinchillas continued to exhibit poor frequency selectivity compared to man. The third experiment measured auditory-filter shape at 0.5, 1, and 2 kHz via rippled noise masking. Results of the rippled noise masking experiment indicate that auditory filters of humans and chinchillas are similar in terms of shape and bandwidth with chinchillas showing only slightly poorer frequency selectivity. The final experiment measured auditory filter shape at 0.5, 1, 2, and 4 kHz using notched noise masking. This experiment yielded auditory filter shapes and bandwidths similar to those derived from man. The discrepancy between the indirect estimates of frequency selectivity derived from CR and band-narrowing techniques and the direct estimates derived from rippled noise and notched noise masking are explained by taking into account the processing efficiency of the subjects.

PACS numbers: 43.66.Gf, 43.66.Dc, 43.66.Ba [LDB]

INTRODUCTION

One general conclusion of masking experiments is that a signal will be masked most effectively by a sound with spectral components close to or at the same frequency as the signal (Wegel and Lane, 1924; Fletcher, 1940; Hamilton, 1957; and Greenwood, 1961 ). This result indicates that the ability to analyze and discriminate the various spectral components in complex sounds is at least partially determined by the frequency resolving ability of the auditory system.

Fletcher (1940) proposed the "critical band" to account for data obtained in masking experiments. The width of the critical band can be estimated from the critical ratio

(CR) and band-narrowing experiments. However, the CR and band-narrowing experiments measure only the "effec- five" bandwidth of the auditory filter. Furthermore, recent experiments (Patterson et al., 1982) have shown that th• CR estimate of critical bandwidth is more closely related to the efficiency with which subjects process complex sound than it is to auditory-filter width. Efficiency, as used here, refers to the ratio of signal power to noise power required at the output of the auditory filter to achieve threshold. Experi- ments which focus on the shape of the auditory filter (Egan and Hake, 1950; Houtgast, 1974, 1977; Patterson, 1976; Moore, 1978) help to separate processing efficiency from frequency selectivity.

Present address: Comparative Perception Laboratory, Kresge Hearing Research Institute, University of Michigan Medical School, Ann Arbor, M148109-0506.

Two methods for behaviorally measuring auditory-filter shape include rippled noise and notched noise masking. Houtgast ( 1974,1977) measured auditory-filter shape by using rippled noise to mask a tonal signal. Rippled noise, a complex, nonperiodic stimulus with a cosinusoidal energy spectrum, is generated by delaying a source of white noise (which has a continuous, flat spectrum ) by some amount (r s) and adding the output of the delay to the original noise source. This results in a continuous masking noise with a cosinusoidal energy spectrum in which the spacing or density of the spectral peaks and valleys are functions of the delay (r). Houtgast used this attribute of rippled noise to measure frequency selectivity by measuring masked thresholds for a pure tone signal masked by rippled noise as a function of the spectral density of the rippled noise. Houtgast assumed that the power in the signal at masked threshold is proportional to the power in the noise passed by the filter. If masked threshold corresponds to a constant signal-to-masker ratio at the output of the filter, then the change in masked threshold as a function of ripple density can be used to define an intensity weighting function which is the shape of the auditory filter. By an application of Fourier analysis to the rippled noise masking function and under the assumption of linearity, Houtgast was able to estimate auditory-filter shape. Houtgast demonstrated that the auditory filter had a somewhat Gaussian shape with a rounded top and fairly steep skirts. Although rippled noise had originally been used to derive estimates of frequency selectivity in humans (Houtgast, 1974, 1977; Pick, 1980; and Yost, 1982), similar

2636 J. Acoust. Sec. Am. 92 (5), November 1992 0001-4966/92/112636-14500.80 ̧ 1992 Acoustical Society of America 2636

procedures have also been used by Pickles (1979) in the cat and by Fay et al. (1983) in goldfish.

Patterson (1976) measured thresholds for tonal signals masked by noise with a bandstop or notch centered at the signal frequency. Patterson varied the width of the notch and measured the signal threshold as a function of notch width. For a signal placed symmetrically in a notched noise, the best signal-to-masker ratio is obtained with a filter centered at the signal frequency. As notch width increases, the power of the noise passing through the filter decreases. Con- sequently, the threshold for the signal decreases. Patterson assumed that the power in the signal at masked threshold is proportional to the power in the noise passed by the filter. If masked threshold corresponds to a constant signal-to-masker ratio at the output of the filter, then the change in masked threshold as a function of notch width shows how the area

under the filter varies with notch width. By differentiating the function relating masked threshold to notch width and by assuming a symmetrical filter shape, Patterson was able to estimate the shape of the auditory filter. Patterson's experiment also demonstrated that the shape of the auditory filter could be reasonably approximated with a Gaussian curve.

Animal psychephysical studies are important in their own right as descriptions of auditory function in nonhuman animals. Due to similarities between human and chinchilla

audiograms, the chinchilla often serves as a model of the human auditory system (Miller, 1970). By measuring the psychephysical tuning of the chinchilla, it becomes possible to obtain information about the animal's perception of rippled noise and notched noise and to place its response into a comparative and physiological context.

Estimating the psychephysical tuning of the chinchilla using direct measures of auditory-filter shape has gained ad- ditional importance following the work of Halpern and Dal- los (1986). Halpern and Dallos used a forward masking paradigm to study auditory-filter shape in the chinchilla and showed that while their notched-noise masking technique yielded estimates of tuning similar to those obtained using other techniques, the auditory-filter shapes showed an unexpected dip in the region of the center frequency. By using a different technique {simultaneous masking) as well as addi- tional masking stimuli (rippled noise and notched noise maskers), other types of frequency selectivity that may clar- ify the differences and similarities in filter shapes of humans and chinchillas can be studied.

This study determines the chinchilla's frequency selectivity via four different techniques: CRs, band-narrowing experiments, rippled noise masking, and notched noise masking. The characteristics of the chinchilla auditory filters derived with these techniques will be compared with measures of frequency selectivity obtained from man as well as with other measures of frequency selectivity obtained from chinchillas.

I. EXPERIMENT 1--4•RITICAL MASKING RATIOS

A. General psychophysical procedure

The animal psychephysical procedure used in these studies was a computer-controlled, behavioral adaptive

tracking paradigm based on the procedure used by Clark and Bohne (1978). Animals were maintained at 80% of their normal ad libiturn body weight and were trained to detect the presence of a tonal signal by reinforcing correct detections with food pellets. To perform this task, the chinchilla was put into a testing cage housed inside a sound attenuating chamber. The cage, modeled after one used by Clark et al. (1974), contained a response lever and a reward chute which dispensed food pellets. The signal tone and the masking noise were presented via a loudspeaker housed inside the chamber, but outside the testing cage.

In the procedure, a trial was initiated when the chinchilla pressed the response lever. Once a trial was initiated, the animal was trained to hold the lever down for a variable

hold time which lasted from 1-8 s. If the animal released the

response lever during the variable hold time, the entire process stopped and the computer waited for the animal to initiate a new trial. This procedure maintained the animal in a relatively fixed position so that the sound field at the animal's head did not differ greatly from trial to trial.

Once the animal held the response lever through the variable hold time, the animal was presented with either a tone trial or a catch trial. During tone trials, which comprised 75% of the trials, a tonal signal was presented after the variable hold time elapsed. The chinchilla was trained to signal that it detected a tone by releasing the response lever. During catch trials, which comprised 25% of the trials, a tone was not presented after the variable hold time elapsed. The chinchilla signaled that no tone was detected by contin- uing to hold down the response lever for 2 s. Each correct response, either a correct detection or a correct rejection, was rewarded with a food pellet. Incorrect responses were not rewarded.

The paradigm used a two-down/one-up tracking rule in which the level of the tone was reduced after two correct

responses in a row and increased after each incorrect response. The two-down/one-up rule tracks the level that gives 70.7% correct detection for the tonal signal (Levitt, 1971 ). After the chinchilla's response to a trial was classi- fied, stimulus parameters were altered according to the animal's performance and the computer waited for the animal to initiate a new trial.

Animals were tested in this paradigm in fixed blocks of 30 trials. The initial step size for increasing or decreasing the level of the tone was 4 dB. After the first two reversals of the

attenuator, the step size for incrementing or decrementing the level of the tone was reduced to 2 dB to allow finer track-

ing of the animal's performance within the vicinity of the threshold. At the end of a 30-trial block, the first two reversals of the attenuator, which took place at the larger step size, were discarded. The remaining reversals were averaged to estimate the animal's threshold. Between 4 and 12 rever-

sals were averaged to obtain a threshold estimate. Across all five animals and all four experiments, the average number of reversals used to compute a given threshold estimate was 8.3. Unless otherwise noted, threshold estimates were measured on at least 3 different days and final thresholds were the average of the three threshold estimates. Typically, final thresholds are the average of five threshold estimates mea-

2637 d. Acoust. Sec. Am., Vol. 92, No. 5, November 1992 Niemiec oral.: Frequency selectivity in chinchilla 2637

sured on 5 different days. If the animal responded to more than 20% of the catch

trials in a daily testing session, the data from that session were discarded. Typical false alarm rates for all testing ses- sions in all experiments were below 15%.

B. Method

Five chinchillas (three males and two females) were trained to serve as subjects for this experiment. The animals were trained in quiet using the previously described technique. Once the animals were responding correctly to signal tones in a quiet environment, the level of the masking noise was gradually increased. The total duration of training was approximately 3 months. Threshold testing was begun after thresholds had stabilized (i.e., standard deviations for averaged threshold estimates were less than 5 dB for 2 consecu- tive weeks).

The masker in this experiment was a continuous white noise generated by a Wavetek model 132 noise generator and filtered by a Krohn-Hite 3550 filter with 24-dB/oct rolloff such that it was 2 oct wide. The overall level of the noise was

adjusted so that its pressure spectrum level (No) was 40 dB/Hz. The signal, a 1-s pure tone at the center frequency of the noise masker, was generated by a Hewlett-Packard 3312 A function generator. The signal was gated on and off with a 20-ms linear ramp by a Coulbourn S84-04 shaped rise-fall gate. A Coulbourn S85-08 programmable attenuator under computer control increased and decreased the level of the signal according to the animal's performance. The signal and masker were mixed using a Coulbourn S82-24 mixer/ amplifier. The mixed stimuli were amplified by a Bryston 2BLP power amplifier and presented in the sound attenuating chamber via a Realistic Minimus 3.5 speaker.

The acoustics of the chamber were measured by placing a condenser microphone at the position the animal's head normally occupied when it was in the testing cage. Wide- band noise was presented to the microphone over the speaker and a fast Fourier transform (FFT) of the wideband noise was computed. The frequency response of the sound attenuating chamber was determined by averaging 100 FFTs of the wideband noise. The chamber had an overall

frequency response of + 7 dB over the frequency range of 250-10 000 Hz. The frequency response of the chamber was + 5 dB from 250-750 Hz, + 2.5 dB from 500-1500 Hz, + 5 dB from 1000-3000 Hz, and + 7 dB from 2000-6000 Hz. ] In quiet, the overall ambient noise level in the chamber was 43 dB SPL.

Masked thresholds for each of the five chinchillas were

measured using the behavioral adaptive tracking paradigm described above at signal frequencies of 500, 1000, 2000, 4000, and 8000 Hz. The signal frequencies were presented in a random order. Each chinchilla was tested at each signal frequency for at least 5 days. A typical day's data collection for a chinchilla involved five sets of 30 trials, one set at each signal frequency. CRs were computed for each chinchilla by subtracting the spectrum level of the masker (No) from the level of the chinchilla's threshold signal.

C. Results and discussion

The CRs for each of the five chinchillas are shown in

Fig. 1. CRs are plotted as a function of signal frequency at 500, 1000, 2000, 4000, and 8000 Hz. The five chinchillas in this study show little variability in their CRs. The individual masked thresholds used to compute the CRs also showed little variability. The standard deviations of the individual masked thresholds ranged from 1.1-5.7 dB with the typical standard deviation for each animal being about 3 dB. The average individual masked thresholds and standard deviations are shown in the Appendix (Table AI).

Also plotted in Fig. 1 are CRs measured by Miller (1964) and Seaton and Trahiotis (1975) using shock-avoidance paradigms. The data from the chinchillas in this study are comparable to those measured using shock-avoidance techniques in that CRs increase as a function of signal frequency; however, on the average, the data measured using the positive-reinforcement behavioral tracking technique were between 2.8 and 8.3 dB higher than those measured using negative-reinforcement techniques. The discrepancy between our data and Miller (1964) and Seaton and Trahio- tis (1975) probably results from overestimation of the animal's sensitivity due to the inability of negative-reinforcement techniques to fix the position of the animal's head in the sound field. Clark et al. (1974) and Hefther and Heffner ( 1991 ) point out that behavioral procedures that do not fix an animal within the sound field, such as the procedures used by Miller (1964) and Seaton and Trahiotis (1975), may lead to different estimates of the animals' sensitivity.

The critical bandwidth can be computed by taking the antilog of the CR. In man, this estimate of the critical bandwidth tums out to be 2.5 times smaller than measures ob-

tained from more direct methods of estimating the critical bandwidth. Scharf (1970) showed CR data for man which, when corrected by multiplying by 2.5, yielded estimates of critical bandwidth that typically ranged from 15 %-22% of the center frequency over the frequency range from 500-

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FIG. 1. The critical masking ratios (CRs) for the five chinchillas in this experiment are plotted along with CRs measured using shock-avoidance paradigms (Miller, 1964, and Seaton and Trahiotis, 1975)'. The data from the chinchillas in this experiment are comparable to those measured using shock avoidance techniques.

2638 d. Acoust. Sec. Am., Vol. 92, No. 5, November 1992 Niemiec eta/.: Frequency selectivity in chinchilla 2638

10 000 Hz. Average critical bandwidths computed from the chinchillas' averaged CRs range from 102%-317% of the center frequency. This would indicate that the chinchilla is either very broadly tuned in comparison to man or has a high detection criterion, or there may be a combination of broad tuning and a high detection criterion.

II. EXPERIMENT 2--BAND NARROWING EXPERIMENT

A. Method

Four male chinchillas served as subjects in this experiment. Two of the four subjects in this experiment were also subjects in experiment 1.

The masker in this experiment was a continuous white noise generated by a Wavetek model 132 noise generator. The noise was bandpass filtered by a Rockland 751A brick- wall filter with a 100-dB/oct rolloff. The 6-dB bandwidths of

the noise bands were measured at the position the chinchilla's head would normally occupy while it was working in the testing cage and the overall level of the noise bands was adjusted such that the pressure spectrum level (No) was 43 dB/Hz for all bandwidths.

Thresholds were measured for each of three signal frequencies ( 1000, 2000, and 4000 Hz) in five to seven bands of noise centered at the appropriate test frequency. Thresholds were measured for 3 days at the 1000-Hz signal frequency, 2 days at the 2000-Hz signal frequency, and I day at the 4000- Hz signal frequency. The noise bands were presented in the same order (from widest to narrowest) for each signal frequency. A typical day's data collection for a chinchilla involved five to seven sets of 30 trials, one set at each noise band.

B. Results and discussion

Table I presents the 6-dB bandwidths (BW), the average masked thresholds (in dB SPL) across all the subjects (average), and the standard deviations (s.d.) for each of the narrow-band maskers at each test frequency. Also presented for each test frequency are the number of subjects run at that frequency (N) and the approximate critical bandwidth (CBW) at that frequency. (The individual data from this experiment are shown in the Appendix, Table AII.)

The approximate critical bandwidth was defined by drawing a horizontal line at the average value of the "unchanging" thresholds and drawing another line through the thresholds for the two narrowest bandwidths. The intersec- tion of these two lines was defined as the critical bandwidth.

For the purposes of this analysis, the "unchanging" thresholds were defined as those thresholds within 4 dB of the

largest threshold for any noise band. Table I shows that critical bandwidth increases as a

function of signal frequency. The average estimates of the chinchilla critical bandwidths range from 45%-51% of the center frequency when measured using this technique. These measurements are similar to those obtained by Seaton and Trahiotis (1975) for the chinchilla. In comparison, human critical bandwidths measured using similar techniques range from 15%-17% of the center frequency over the same fre-

TABLE I. Results of the band-narrowing experiment at 1, 2, and 4 kHz. For each signal frequency, the table gives the masker bandwidth (Hz }, the average threshold (dB SPL), the standard deviation, the number of animals in each condition (N), and the approximate critical bandwidth (Hz) for the averaged data.

BW (Hz) Average s.d.

1000-Hz tone 125 60.9 2.3

363 65.1 2.3

CBW•510 Hz 575 67.4 l.l 975 68.2 0.4

N= 4 1345 68.2 1.1

! 580 68.4 0.7

1813 68.3 1.7

2000-Hz tone 248 64.3 2.9

687 68.0 3.7

CBW .• 920 Hz 1140 69.4 2.8 1550 71.4 2.0

N=4 1882 71.1 0.6

4000-Hz tone 490 68.5 2. ! 1365 71.0 1.4

CBW •. 1800 Hz 1993 71.0 1.4 2945 72.5 0.7

N = 2 3755 72.0 0.0 4345 74.5 0.7

quency range (Scharf, 1970). These results show that according to the band-narrowing technique chinchillas are still more broadly tuned than man, however, this technique provides a narrower estimate of tuning than the CR for the animals in this study.

IlL EXPERIMENT 3--AUDITORY FILTERS DERIVED USING RIPPLED NOISE

A. Method

Six chinchillas (two females and four males) served as subjects in this experiment. Five of the six subjects were subjects in experiment I and three of the six were also subjects in experiment 2.

In this experiment, the masker was a continuous rippled noise generated by delaying a wideband noise by r s and either adding the output of the delay to the original noise source to generate cosine positive rippled noise or subtracting the output of the delay from the original noise source to generate cosine negative rippled noise. The wideband noise source was a Wavetek model 132 noise generator. The delay line was a Reticon analog delay with a built-in attenuator and mixer. The rippled noise masker was filtered by a Krohn-Hite 3550 filter with 24 dB/oct rolloff such that it

was 2 oct wide, centered on the signal frequency. The overall level of the rippled noise was adjusted so that a flat noise at the same overall level would have a pressure spectrum level (N o) of 43 dB/Hz.

The chinchillas' auditory-filter shapes were estimated from two masking functions derived from four sets of masking conditions measured in this experiment: cosine positive

2639 J. Acoust. Sec. Am., VoL 92, No. 5, November 1992 Niemioc otal.: Frequency selectivity in chinchilla 2639

( cos + ) masking, cosine negative ( cos -- ) masking, sine positive ( sin + ) masking, and sine negative ( sin -- ) masking. The masking functions were measured for signal frequencies ( f, ) of 500, 1000, and 2000 Hz.

Cosine masking functions, which determine the general shape and width of the auditory filter, were derived by measuring each animal's threshold for a pure-tone signal masked by both cos + and cos -- rippled noise as alppie density (n) was varied between 1 and 6. Ripple density, which is a function of the delay (n----r'f,), is defined as the number of ripples between f= 0 and f,, the signal frequency. Each animal's cosine masking function was obtained by subtracting its cos -- masked thresholds from its cos + masked thresh-

olds as a function of ripple density. For many animals, data on the cosine limit condition,

n ---- 0, were also collected. The cosine, n = 0 condition is a flat noise masker for which the peak-to-trough difference is equal to the peak-to-trough difference of the cosine rippled noise at the signal frequency. In this experiment the peak-to- trough difference between cos + and cos -- rippled noise maskers at the signal frequency was 23 dB; therefore, the cos +, n = 0 data point corresponds to the threshold for the signal masked by a fiat noise at the same level as the cos + rippled noise masker. The cos--, n = 0 data point corresponds to the threshold for the signal masked by the flat noise after the noise had been attenuated by 23 dB. This n = 0 threshold difference is not used to estimate auditory- filter shape, except in the case of the 2000-Hz signal frequency for which the delay line could not generate the 500-/rs delay needed to collect data for the cos + and cos --, n = 1 conditions. For this signal frequency, the cosine, n = 1 threshold difference was estimated by a second-order polynomial regression on the remaining threshold differences in the cosine masking function (n = 0, 2, 3, 4, 5, and 6). A second-order polynomial regression was used to estimate the 2000-Hz cosine, n = 1 threshold difference because the cosine masking functions for 500, 1000, and 2000 Hz tended to be shaped like second-order polynomials.

The sine masking functions, which determine the symmetry of the auditory filter, were derived by measuring each animal's thresholds for pure-tone signals masked by both sine positive ( sin + ) and sine negative ( sin -- ) rippled noise as ripple density was varied between 1 and 6. In prac- tice, sine rippled noise is difficult to generate; however, sine rippled noise can be approximated by generating cosine rippled noise at the appropriate phase ( + / -- ) and ripple density and adjusting the delay such that it is 1.25 times the delay used for the cosine rippled noise. In this experiment, the sine masking functions were generated using the approximated sin + and sin -- rippled noise. The sine masking functions were obtained by subtracting the animals' sin - masked thresholds from their sin + masked thresh-

olds as a function of ripple density. The sine, n = 0 condition is a flat noise masking condition for which the peak-to- trough difference is equal to the peak-to-trough difference of the sine rippled noise at the signal frequency. In this experiment the peak-to-trough difference between sin + and sin -- rippled noise maskers at the signal frequency was 0 dB; therefore, the sin +, n = 0 data point corresponds to the

threshold for the signal masked by a fiat noise at the same level as the sin + rippled noise masker. The sin --, n = 0 data point corresponds to the threshold for the signal masked by the flat noise after an attenuation of 0 dB. There- fore, in theory, the sine, n = 0 threshold difference should always be 0 dB. These sine, n = 0 threshold differences are not used to estimate auditory-filter shape; however, in the case of the 2000-Hz signal frequency, the delay line could not generate the 625-/•s delay needed to collect data for the sin + and sin --, n = I condition. For this signal frequency, the n = 1 threshold difference was estimated by a linear regression on the remaining threshold differences in the sine masking function (n ---- 0, 2, 3, 4, 5, and 6). A linear regression was used to estimate the 2000-Hz sine, n = 1 threshold difference because the sine masking functions for 500, 1000, and 2000 Hz tended to be linear.

A typical day's data collection for a chinchilla involved six to seven sets of 30 trials, one set at each ripple density for either the cos +, cos --, sin +, or sin -- conditions. This type of session generally lasted about 1 h.

Auditory-filter shapes were computed for each chinchilla by using the cosine and sine masking functions to solve the equation for the weighting function derived by Houtgast ( 1974, 1977). 2


The chinchilla rippled noise data will be discussed in terms of the average data since, with the exception of very few individual differences, the average data represent the individual data quite well. The top panel of Fig. 2 shows average relative weighting or auditory-filter functions at a signal frequency of 500 Hz. The masking functions from which these filter shapes are derived are the average of the cosine and sine masking functions across all subjects at each signal frequency. The important part of the auditory-filter functions is the peak which rises up out of the "noise." The "noise" reflects the fact that the masking functions are not perfectly smooth and may not reach an asymptote exactly at 0. The function labeled ave cos I•( f,f, ) (open symbols) is an auditory-filter function based only on the average cosine masking function. This computation of the filter function assumes that the sine masking function is a flat line at zero and, therefore, that the filter function is symmetrical. The filter function labeled ave sin Ig( f,f, ) (closed symbols) is an auditory-filter function based on both the average cosine and the average sine masking functions. This computation does not assume a symmetrical filter function. A comparison of these two filter functions shows that the chinchilla's 500-

Hz auditory filter is reasonably symmetrical about the center frequency. The chinchillas' auditory-filter shape does not change appreciably with the inclusion of the sine masking function.

The middle and bottom panels of Fig. 2 show average relative weighting functions at 1000 and 2000 Hz. The shapes of the auditory-filter functions at these frequencies are qualitatively similar to the shape of the 500-Hz auditory filter. Although there are some differences in the auditory- filter "noise," there are few, if any, differences in the shapes

2640 J. Acoust. Sec. Am., Vol. 92, No. 5, November 1992 Niemiec oral.: Frequency selectivity in chinchilla 2640

Average 500 Hz

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FIG. 2. This figure compares the auditory-filter functions derived using only the average cosine masking functions [ labeled ave cos W (F,F,) ] with the auditory-filter functions derived using both the average sine and cosine masking functions [labeled ave sin W (F,F,) ] for all three signal frequencies. All three filters show a simple bandpass characteristic which is roughly symmetrical about the center frequency. In addition to this, the bandwidths of the filters increase with center frequency.

of the auditory-filter peaks. In the upper left-hand corner of each panel is the equiva-

lent rectangular bandwidth or ERB of the filter. 3 The ERBs of the chinchillas' average auditory filters are 86 Hz at the 500-Hz center frequency, 265 Hz at the 1000-Hz center fre-

quency, and 440 Hz at the 2000-Hz center frequency. The ERBs of the individual filter functions ranged from 77-100 Hz at the 500-Hz signal frequency, 209-356 Hz at the 1000- Hz signal frequency, and 322-527 at the 2000-Hz signal frequency. (Individual sine and cosine masking functions as well as individual filter ERBs are presented in Appendix Table AIII.)

In addition to being reasonably symmetrical, the shapes of the chinchillas' derived auditory filters are very similar to the shapes of the auditory-filter functions derived for human subjects tested in similar paradigms (Houtgast, 1974 and 1977). Moreover, the data from this experiment show that the chinchilla auditory filters are not much broader than the human auditory filters measured by Houtgast. Houtgast's data showed that human ERBs were approximately 15%- 20% of the center frequency over the frequency range from 500-2000 Hz. The data from this experiment show that the average chinchilla ERBs were approximately 17%-27% of the center frequency over the same frequency range.

Thus there are two strong trends in these data and both of these trends can be seen in Fig. 2. First, the filters at all three signal frequencies (and across all animals) are similar in shape, showing a simple bandpass characteristic roughly symmetrical about the center frequency and, second, the ERBs of the filters increase with center frequency. With respect to these two results, it can be concluded that chinchillas respond to rippled noise in a manner that is similar to man, especially in terms of their frequency selectivity.

To provide a simpler mathematical expression for the average auditory-filter shapes, the filters were modeled by assuming a single-parameter rounded-exponential [Roex(p) ] filter shape and the parameter of the assumed function was varied to find the best least squares fit between the actual average cosine masking function and the predicted cosine masking function. 4 Figure 3 shows the results of modeling the average auditory filters as Roex(p) filters. This figure plots the average cosine weighting function at each of the three center frequencies with the appropriate Roex(p) filter function superimposed on it. The figure also shows the ERBs for both the average cosine weighting functions and the Roex(p) weighting functions. The Roex(p) filters provide a reasonably accurate approximation to the average cosine weighting functions.

IV. EXPERIMENT 4--AUDITORY FILTERS DERIVED USING NOTCHED NOISE

A. Method

Three male chinchillas served as subjects in this experiment. Two of the three served as subjects in experiment 1 and all three served as subjects in experiments 2 and 3.

The continuous notched noise masker was generated by passing a wideband noise from a Wavetek model 132 noise generator through four cascaded Krohn-Hite 3550 band-reject filters. Each of the band-reject filters had a 24-dB/oct rolloff. The notched noise masker was filtered by a Krohn- Hite 3550 filter with 24-dB/oct rolloff such that is was 2 oct

wide with the notch centered on the signal frequency. The 3- dB notch widths of the masking noise were measured at the

2641 J. Acoust. Sec. Am_. Vol_ g2. No. 5. November 1992 Niemiec otal.: Frequency selectivity in chinchilla 2641

Average 500 Hz Roex(p) Weighting Function

1.4 COS ERR- 86 HZ

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• 0.4

• 0.2

13: 0.0

-0.2

COS ERB = 440 HZ

ROLEX ERa = 364 HZ I AVG COS W(F. Ft) [ ß OEX W(•, Ft)

-0.4 ..... , ..... , ..... , ..... 800 1400 2000 2600 32•0

Frequency (Hz)

FIG. 3. This figure shows the results of modeling the average chinchilla auditory filters as single-parameter rounded-exponential [ Roex(p) ] filters. The figure plots the average cosine filter function at each of the three signal frequencies along with the best least-squares fit of the Roex(p) filter function superimposed on it. The figure also shows the ERBs for both the average cosine filter functions and the Roex (p) weighting functions.

position the chinchilla's head would normally occupy while it was working in the testing cage, and the overall level of the notched noise masker was adjusted so that a flat noise at the same overall level would have a pressure spectrum level (No) of 43 dB/Hz.

Chinchillas' auditory-filter shapes were estimated from masking functions derived by measuring masked threshold as a function of rdative notch width. Masking functions were measured for signal frequencies of 500, I000, 2000, and 4000 Hz and the auditory-filter shapes were derived using the same mathematical analysis as Patterson (1976). 5 This method of measuring auditory-filter shape assumes that the filters are symmetrical and that the auditory system is linear over some limited dynamic range. The assumption of symmetry appears to be reasonable in light of the results of the rippled noise masking experiment described previously. The linearity assumption was tested at 1000 Hz by measuring masking functions at three different levels of the masking noise. For this signal frequency, the masker levels were adjusted such that flat noise maskers at the same overall levels would have pressure spectrum levels (No) of 37, 43, and 49 dB/Hz. In this way, the 1000-Hz auditory filters could be evaluated at three different levels of the masker.


The chinchilla notched noise data will also be discussed

in terms of the average data since the average data represent the individual data quite well. Figure 4 shows the average auditory-filter shape at each of the four center frequencies. The masking functions from which these filter shapes are derived are the average of all the individual masking functions at each signal frequency. Due to the assumption of symmetry, the low-frequency portion of the auditory filter is presented as the mirror image of the high-frequency portion of the filter. In the upper left-hand comer of each panel is the ERB of the filter. The ERB was derived by simply integrat- ing the area under the normalized filter. The ERBs of the chinchillas' average auditory filters are 59 Hz for the 500-Hz filter, 185 Hz for the 1000-Hz filter (at No = 43 dB/Hz), 304 Hz for the 2000-Hz filter, and 335 Hz for the 4000-Hz filter. The ERBs of the individual filter functions ranged from 52-80 Hz for the 500-Hz filter, 148-228 Hz for the 1000-Hz filter (at No = 43 dB/Hz), 255-346 Hz for the 2000-Hz filter, and 304-378 Hz for the 4000-Hz filter. (The individual masking functions as well as the individual filter ERBs are presented in the Appendix in Table AIV.) The individual data at 1000 Hz show that the masking functions tended to remain parallel as a function ofmasker level, indicating that the chinchilla auditory system is linear over this limited dynamic range. The result of this is that the ERBs of the 1000-Hz filter functions tend to remain stable as a func-

tion of masker level. This result is representative of all three subjects in this experiment.

As was the case with the rippled noise filter functions, the shapes and bandwidths of the notched noise filter functions resemble those of human subjects tested under similar conditions. Patterson's (1976) data showed that human ERBs were approximately 11%-14% of the center frequency over the frequency range from 500-2000 Hz. The data from this experiment show that the average chinchilla ERBs were approximately 8%-19% of the center frequency over the frequency range from 500-4000 Hz. Therefore, it appears that chinchillas respond to the notched noise masker in

2642 J. Acoust. Sec. Am., VoL 92. No. 5, November 1992 Niemioc etaL: Frequency selectivity in chinchilla 2642

Average 500 Hz Auditory Filter (No = 43 dB)

ERB - 59 Hz 1.0

0.8

0.2

200 300 400 500 600 700 800

Frequency (Hz)

1.2

1.0

0.8

.E 0.6

0.4

0.8

Average lkHz Audltow Filters

NO ERB(Hz) - I'-• NO=37 {

6oo 80o •ooo •2oo •4oo •60o

Frequency (Hz)

Average 2kHz Auditory Filter (No = 43 dB)

ERB - 304 Hz

0.2

800 1200 1600 2000 2400 2800 3200

Frequency (Hz)

Average 4kHz Auditory Filter (No = 43 dB) 1.2 i I • I ß

ERB = 335 Hz 1.0

0.8

g• ß - 0.6

0.4

0.2 ,• 0.0 ß I[--•:::-:: ß

1000 2000

0.0 ß , ......... ß ß

400 3000 4000 5000 6000 7000

Frequency (Hz)

FIG. 4. This figure shows the auditory-filter functions derived using the average notched noise masking functions for all four signal frequencies. All four filters show a simple bandpass characteristic and the bandwidths of the filters increase with center frequency. In addition, the average 1000-Hz filters show that filter shape does not change appreciably as a function of masker level over the range of levels used in this experiment.

a manner similar to man.

Thus the trends seen in the rippled noise data in experiment 3 are also seen in the data from this experiment. The filters at all four signal frequencies (across all animals and across all masker levels) are similar in shape. Filter shapes derived with the notched noise masking technique have a simple bandpass characteristic similar to those derived using rippled noise and, like the bandwidths of the rippled noise filters, the bandwidths of the notched noise filters also increase with center frequency.

To provide a simpler mathematical expression for the average notched noise auditory-filter shapes, the filters were modeled by assuming a Roex (p) filter shape and varying the parameter of the assumed filter shape to find the best least- squares fit between the actual masking functions and the predicted masking functions. a Figure 5 shows the results of modeling the average notched noise auditory filters as Roex(p) filters. This figure plots the average filter function at each of the four center frequencies with the appropriate Roex(p) filter function superimposed on it. The figure also shows the ERBs for both the average notched noise filter functions and the Roex(p) filter functions. The Roex(,p) filters provide an acceptable approximation to the average notched noise filter functions.

V. GENERAL DISCUSSION

This study examined psychophysical tuning in the chinchilla at several frequencies with four different measures of frequency selectivity. The first measure, the critical masking ratio (CR}, is an indirect measure of frequency selectivity, whereas the second measure, the band-narrowing technique, is more direct. However, both of these measures must be considered indirect in that they only measure the "effective" bandwidth of the auditory filter and not the shape of the filter per se. The remaining two measures of frequency selectivity, rippled noise masking and notched noise masking, can be considered direct measures of tuning in that both of these measures provide information concerning the shape of the auditory filter as well as the bandwidth of the filter.

Scharf (1970) showed CR data for human subjects which, when corrected by multiplying by 2.5, yielded estimates of critical bandwidth that typically ranged from 15%- 22% of the center frequency over the frequency range from 500-10 000 Hz. In experiment !, which used test tones over approximately the same frequency range, the chinchilla CRs yielded average corrected estimates of critical bandwidth which ranged from 102%-317% of the center frequency. This result indicates that the chinchilla either has broad tun-

2643 J. Acoust. Soc. Am., VoL 92, No. 5, November 1992 N,emiec etal.: Frequency selectivity in chinchilla 2643

AVERAGE 500 HZ ROEX NOTCHED NOISE FILTER 1.2

AVG ERE) = 59 Hz

FIOEX(P) ERE) = 87 Hz 1.0

0.8

0.6

0,4

0.2

0.0

20O 300 400 500

500 Hz Flter ß ROEX Filter

600 700 800

Frequency (Hz)

AVERAGE I kHZ ROEX NOTCHED NOISE FILTER

1.2 AVG ERE) - 185 Hz ROEX(P) ERB - 154 Hz

1.0

lkHz Filter I 0.8 ß ROEX Filter

0.6,

0.4

O2

O.O :=- , .... , - -•= , 400 700 1000 1300 1 SO0

Frequency (Hz)

AVERAGE 2 kHZ ROEX NOTCHED NOISE FILTER

1.2 AVG ERB = 304 Hz ROEX(P) ERB = 333 Hz

2kHz Filter

0.8 ß ROEX Filter

0.6

02

o t ooo 2000 3000 4000

Frequency (Hz)

AVERAGE 4 kHZ ROEX NOTCHED NOISE FILTER

1.2 AVG ERB - 335 Hz ROEX(P) ERB = 533 Hz

I 4kHz Filter 0-8 ß ROEX Filter

• ooo 4000 7000

Frequency (Hz)

0.6 0.4

0.2

0.0

FIG. 5. This figurc shows the results of modeling the average chinchilla notched noise auditory filters as singlc-paramcler rounded-exponential [ Rocx(p) ] filters. The figure plots the average notched noise filter function at each of the four signal frequencies along with the best least-squares fit of the Roex(p} filter function superimposed on it. The figure also shows the ERBs for both the average notched noise filter functions and the Roex (p} filter functions.

ing or a high detection criterion, or a combination of broad tuning and a high detection criterion. 7 Although the chinchilla exhibits better frequency selectivity when tuning is measured with the band-narrowing technique, it is still much poorer than human subjects tested under similar conditions, with average chinchilla critical bandwidths about three times wider than the human critical bandwidths.

The weighting functions derived from the rippled noise masking functions showed that the chinchillas' auditory-filter shapes are similar to human auditory-filter shapes. Both the human and the chinchilla auditory filters have a simple bandpass characteristic and are roughly symmetrical. In terms of bandwidth, the chinchilla weighting function is only slightly wider than the human weighting function. Houtgast's (1974, 1977) data showed that human ERBs were approximately 15%-20% of the center frequency over the frequency range from 500 to 200(YHz. The data from this study showed that the average chinchilla ERBs were approximately 17%-27% of the center frequency over the same frequency range. This comparison between the average human rippled noise ERBs and the average chinchilla rippled noise ERBs shows that the chinchilla compares quite favorably with man in terms of frequency selectivity. With respect to these results, it can be concluded that chinchillas respond to rippled noise in a manner similar to man.

Filter shapes measured with the notched noise masking technique yield similar results. Both the human and chinchilla auditory filters show a simple bandpass characteristic, as well as showing similar ERBs. Patterson's (1976) data showed that human ERBs were approximately 11%-14% of the center frequency over the frequency range from 500 to 2000 Hz. The data from this study showed that the average chinchilla ERBs were approximately 8%-19% of the center frequency over the frequency range from 500-44300 Hz. This comparison also demonstrates that, when frequency selectivity is measured by a more direct technique, the chinchilla compares quite favorably with man. Moore and Glasberg (1983) compared human ERBs estimated using rippled and notched noise masking techniques and found that ERBs estimated from rippled noise masking were approximately 35% greater than those estimated from notched noise masking. The chinchilla ERBs presented in this study show a similar difference, with average rippled noise ERBs being approximately 30% greater than average notched noise ERBs.

There is a large discrepancy between the results of the CR and band-narrowing experiments and the results of the rippled noise and notched noise masking experiments. This discrepancy can be seen in Table II which lists the average ERBs from both the rippled noise and notched experiments as well as the average corrected bandwidths derived from the

2644 J. Acoust. Sec. Am., VoL 92. No. 5, November 1992 Niemiec et al.: Frequency selectivity in chinChilla 2644

TABLE II. Average bandwidths from the "direct" [rippled noise (RN) and notched noise (NN) ] and "indirect" [critical masking ratio (CR) and band- narrowing (CB) ] measures of frequency selectivity. The direct estimates of tuning yield results which show that chinchillas and man have similar frequency selectivity, whereas the indirect estimates of tuning yield results which show that chinchillas have much poorer frequency selectivity than man. The most plausible explanation for this discrepancy between the various measures of frequency selectivity is that the rippled noise and notched noise masking experiments estimate frequency selectivity independent of the processing efficiency of the subject whereas the CR experiment assumes that processing efficiency is fixed. The band-narrowing experiment also estimates frequency selectivity independent of the processing efficiency of the subject; however, processing efficiency is more likely to vary as a function of masker bandwidth in this experiment than in the notched noise and rippled noise masking experiments.

Average Average Average Average f• (Hz) CR BW (Hz) CB BW (Hz) RN ERB (Hz) NN ERB (Hz)

500 1506 -.- 86 59

1000 1023 510 265 185

2000 3681 920 440 304 4000 4425 1800 -.. 335

8000 25348 .........

CR experiment and the average critical bandwidths derived from the band-narrowing experiment. The more direct estimates of tuning (rippled noise and notched noise masking) yield results which show that chinchillas and man have similar frequency selectivity, whereas the indirect estimates of tuning (CR and band-narrowing experiments) yield results which show that chinchillas have much poorer frequency selectivity than man.

The most plausible explanation for this discrepancy between the various measures of frequency selectivity is that the rippled noise and notched noise masking experiments estimate frequency selectivity independent of processing efficiency or absolute signal-to-noise ratio of the subject, whereas the CR experiment assumes that processing efficiency or signal-to-noise ratio is fixed. Processing efficiency, as used here, refers to the ratio of signal power to noise power required at the output of the auditory filter to achieve threshold. With a broadband noise masker, it is impossible to dis- tinguish between changes in frequency selectivity and changes in processing that are independent of frequency selectivity (Patterson et al., 1982 ). For example, if one subject has a CR which is 3 dB higher than another subject, the bandwidth derived from the first subject's CR will be twice as wide as the bandwidth derived from the more sensitive

subject. This is the ease when we compare chinchillas to man in these types of experiments. In masking experiments, human subjects typically have signal-to-noise ratios ( E/No ) of 5 to 15 dB over the frequency range from 200-10 000 Hz (Reed and Bilger, 1973 ). The signal tone must be 5 to 15 dB higher than the noise spectrum level in order for the tone to be detected. The chinchillas in this study have signal-to- noise ratios (E/No) of 25 to 40 dB over the same frequency range. This difference in signal-to-noise ratio between man and chinchilla explains the chinchilla's inferior frequency selectivity based on the CR experiment. Rippled noise and notched noise masking experiments are not affected by differences in signal-to-noise ratio because the estimates of frequency selectivity derived from these experiments are based on either threshold differences or on the general shape of the masking function, not on the raw threshold data themselves.

Like the rippled noise and notched noise masking ex-

periments, the band narrowing experiment also measures frequency selectivity independent of processing elfieiency; however, processing efficiency is more likely to vary as a function of masker bandwidth in the band-narrowing experiment than in the notched noise and rippled noise masking experiments (Bos and de Boer, 1966).

Although this study shows that human and chinchilla auditory-filter shapes are similar when derived under rip- pied noise and notched noise conditions, it fails to show a similarity to the chinchilla auditory-filter shapes derived by Halpern and Dallos (1986). Halpern and Dallos used notched noise in a forward masking paradigm to study auditory-filter shape in the chinchilla and showed that, while their notched noise masking technique yielded estimates of tuning that were similar to those obtained using other techniques, there was a major difference in the auditory-filter shapes of humans and chinchillas. Auditory-filter shapes derived by Halpern and Dallos showed an unexpected dip in the region of the center frequency, whereas auditory-filter shapes in this study show a simple bandpass characteristic. The dips in the derived filter functions in the Halpern and DaBos paper were partially due to the fact that signal thresholds did not change as the spectral notch was increased until the notch was approximately 33% of the center frequency. The insensitivity of their chinchillas in the forward masking condition for these narrow spectral notches may relate to the "perceptual cuing" hypothesis of Terry and Moore (1977). This hypothesis was proposed to explain the form of forward masking psychephysical tuning curves. The hypothesis sug- gests that there are two cues used to detect a tonal signal in a forward masking procedure. When the differences between the signal frequency and the masker frequencies are small (as might occur for a narrow spectral gap), the subject uses the perception era temporal change in the signal-plus-masker to discriminate it from the masker-alone condition. When

the frequency differences are larger, the subject uses the perception of a pitch difference between the signal and masker as the cue for discrimination. The form of the masking functions in the Halpern and Dallos study might reflect the inability of their chinchillas to use the temporal cue for narrow spectral gaps, resulting in the dips at center frequency in the

2645 J. Acoust. Sec. Am., Vol. 92, Mo. 5. Iqovember 1992 Niomioc oraL: Frequency selectivity in chinchilla 2645

derived filter functions. Even if this is not the explanation for the differences in the derived filter functions between our

data and those of Halpern and Dallos (1986), the differences are most likely due to differences in psyehophysical procedure (i.e., forward versus simultaneous masking).

VI. CONCLUSIONS

The major conclusions of this study arc the following. ( 1 ) Chinchilla critical masking ratios measured with a

positive-reinforcement behavioral tracking technique were found to be comparable to those measured using shock- avoidance techniques (Miller, 1964, and Seaton and Trahio- tis, 1975). Estimates of frequency selectivity based on critical masking ratios indicate that the chinchilla's auditory system may be very poorly tuned in comparison to the human auditory system.

(2) Results of band-narrowing experiments show better frequency selectivity than the critical ratio experiments would indicate; however, chinchillas still show inferior frequency selectivity when compared to man.

(3) Estimates of auditory-filter shape derived from rip- pied noise and notched noise masking indicate that the auditory-filter shapes of man and chinchilla are similar. The filters are roughly symmetrical and have a simple bandpass characteristic with both human and chinchilla auditoryrill- ter bandwidths increasing with center frequency. Estimates of filter bandwidth based on these techniques indicate that the chinchilla auditory filters compare favorably with human auditory filters, reflecting only a slight difference in frequency selectivity.

(4) The discrepancy between the estimates of frequency selectivity derived from the critical masking ratio experiment and those derived from the rippled noise and notched noise masking experiments can be explained by taking into account the subjects' processing efficiency. The discrepancy between the estimates of frequency selectivity derived from the band-narrowing experiment and rippled noise and notched noise masking experiments can be explained by taking into account the effects of the band narrowing experiment on processing efficiency.

(5) Differences in psychophysieal procedure (simultaneous versus forward masking) presumably account for the differences between our data and those of Halpern and Dal- los (1986).

TABLE AI. Average masked thresholds in dB SPL and (standard deviations) for individual subjects in the critical masking ratio experiment.

500 Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz

CI 66.2 (2.0) 66.4 (I.I) 71.2 (3.7) 70.2 (I.3) 77.3 (5.7) C2 64.0 (1.6) 65.0 (4.0) 69.6 (3.7) 72.4 (1.8) 77.0 (5.4) C3 66.2(3.4) 63.2(2.3) 70.6(3.2) 71.6(3.1) 77.4(1.1) C4 69.4 (3.0) 66.6 (3.6) 73.6 (4.9) 72.8 (2.0) 85.2 (3.3) C5 73.2 (2.4) 69.4 (3.2) 73.4 (!.7) 75.4 (2.7) 83.4 (4.3)

average data were representative of the individual data. However, in an attempt to fully disclose as much of the individual data as possible while limiting the number of figures needed to communicate the results of the experiments, the individual data are presented in this Appendix in tabular

TABLE AII. Average masked thresholds in dB $PL and (standard deviations) for individual subjects in the critical band (band-narrowing) experiment.

Masker bandwidth (Hz) 125 363 575 975 1345 1580 1813

1000-Hz signal frequency (average based on three threshold estimates/animal)

C3 58.0 63.3 65.7 67.7 68.3 69.3 68.7

(!.0} (2.5) (1.5) (2.3) (0.6) (1.2) (1.2)

C4 62.7 68.0 68.0 68.0 66.7 68.3 66.3

(1.5) (1.7) (1.7) (I.7) (0.6) (1.5) (0.6)

C6 60.3 63.3 68.0 68.7 68.3 67.7 67.7

(0.6) (2.1) (1.0) (1.2) (1.2) (1.5) (2.3)

C7 62.7 65.7 67.7 68.3 69.3 68.3 70.3

(1.5) (I.5) (1.2) (2.1) (1.2) (1.5) (0.6)

2000-Hz signal frequency (average based on two threshold estimates/animal)

248 687 1140 1550 1882

C3 61.5 67.5 68.5 69.0 71.0

(0.7) (0.7) (0.7) (2.8) (2.8)

C4 68.0 73.0 73.5 73.0 71.0

(1.4) (1.4) (3.5) (1.4) (1.4)

ACKNOWLEDGMENTS

We are grateful to Toby Dye and Dick Fay for many helpful discussions and to Charles Wheeles and Bill Madi- gan for technical support. This work was supported by NIDCD/NIH Center Grant P50 DC 00293 and by a Loyola University Dissertation Fellowship to Andrew J. Niemiec.

C6 65.0 67.5 68.5 70.5 72.0

(1.4) (0.7) (0.7) (0.7) (1.4)

C7 62.5 64.0 67.0 73.0 70.5

(2.1) (0.0) (0.0) (0.0) (2.1)

4000-Hz signal frequency (based on one threshold estimate/animal)

APPENDIX: INDIVIDUAL DATA

The results of these experiments were discussed in terms of the average data because with very few exceptions, the

490 1365 1993 2945 3755 4345

C3 67.0 70.0 70.0 72.0 72.0 75.0 C4 70.0 72.0 72.0 73.0 72.0 74.0

2646 d. Acoust. Sec. Am., Vol. 92, No. 5, November 1992 Niemiec et al.: Frequency selectivity in chinchilla 2646

TABLE Alii. Individual cosine and sine masking functions derived from the rippled noise masking experiment. For each animal at each ripple density, the table provides the threshold difference (in dB} between the cos + and cos -- masking conditions as well as the threshold difference between the sin + and sin -- masking conditions. The table also provides the individual equivalent rectangular bandwidths (ERB) of the filters derived from these masking functions. Averaged cosine and sine masking functions are provided for each signal frequency. The average ERBs are based on the averaged masking functions. Note: The 2000-Hz n = I data points for both the sine and cosine masking functions are estimated from the remaining data since the delay line could not generate the short delays needed to generate rippled noise for these two conditions.

Masking Ripple density ERB function 0 I 2 3 4 5 6 (Hz)

CI

C2

C3

C4

C5

Ave

Cl

c2

c3

c4

c5

c6

Ave

cosine

sine

cosine

sine

cosine

sine

cosine

sine

cosine

sine

cosine

cosine

sine

Cosine

sine

cosine

sine

COSlOe

sine

cosine

sine

cosine

sine

cosine

sine

CI cosine sine

C3 cosine sine

C4 cosine

sine

C5 cosine sine

C6 cosine

sine

500-Hzma•ing•nctions

28.0 12.0 5.2 2.6 4.8 2.1 2.6 77 --- 2.8 --1.4 --1.4 --0.2 --1.0 1.6

--- 6.7 6.4 2.4 3.0 --1.0 2.6 98

20.5 8.6 3.6 5.8 3.2 3.2 0.8 83 --- 1.4 1.6 --3.4 --0.6 --0.2 --0.2

15.5 8.8 4.3 2.2 4.0 1.0 4.1 85 ß " 0.8 --i.6 --0.4 --1.4 --1.8 --0.4

25.5 7.2 4.6 0.5 1.4 4.2 i.4 .... •2 0.2 --2.4 --i.0 0.4 --4.0

22.4 8.7 4.8 2.7 3.3 1.9 2.3 86

"- 1.2 --0.3 --1.9 --0.8 --0.7 --0.8

1000-Hzmasking•nctions

29.7 10.4 2.3 3.0 1.4 --0.4 0.6 237

--' 0.4 0.0 0.0 --0.4 --I.0 --2.0

9.3 4.6 0.• 2.0 1.2 2.3 2•

29.7 10.0 4.7 2.0 0.0 --03 --0.7 2•

ß " 1.3 0.7 --0.3 --1.7 --04 --1.0

24.7 7.0 3.0 0.3 --1.0 --0.3 0.6 3•

.... 1.6 --0.6 0.7 --0.7 --1.4 --0.7

24.7 3.7 1.4 1.3 0.0 •7 1.0 356

"- 2.0 1.3 0.7 --0.4 --2.0 1.0

18.0 4.3 1.7 0.7 1.7 --0.3 2.6 297

25.4 7.5 3.0 1.2 0.7 0.1 l.l 265 -'- 0.5 0.4 0.3 --0.8 --1.2 --0.7

2000-Hz masking functions •

27.0 14.8 3.5 1.0 1.5 0.2 --0.7 489

0.0 --1.8 --2.0 --i.3 --2.0 --2.3 --1.6

28.5 15.7 4.5 --0.3 1.5 0.0 0.2 480

0.0 i.4 1.7 0.7 --1_0 --1.4 0.7

27.8 15.1 4.5 0.0 --0.5 1.5 0.8 471

0.0 0.7 0.3 1.0 3.0 --2.4 2.3

23.7 13.1 3.3 3.0 1.7 2.2 5.5 322 0.0 0.1 --0.7 0.7 1.7 --1.0 0.3

26.3 13.8 1.6 0.3 2.0 --0.7 1.0 527 0.0 1.3 0.0 0.6 2.0 --0.6 --I.3

2647 d. Acoust. Sec. Am., Vol. 92, No. 5, November 1992 Niemiec otal.: Frequency selectivity in chinchilla 2647

TABLE Alii. (Continued.)

Masking Ripple density ERB function 0 I 2 3 4 5 6 (Hz)

2000-Hz masking functions

Ave cosine 26.7 14.5 3.5 0.8 1.2 0.6 1.4 440 sine 0.0 0.3 -- 0.1 0.3 0.7 -- 1.5 0.1

The threshold differences for the 2000~Hz, n = ! cosine masking function are estimated by a second-order polynomial regression on the remaining cosine threshold differences (n = 0,2,3,4,5,6). The threshold differences for the 2000 Hz, n = I sine masking function were estimated by assuming that there are no threshold differences at n = 0 and using this point along with the remaining threshold differences (n = 0,2,3,4,5,6) to compute a linear regission estimate for the missing data point.

form (see Tables AI-AIV). Where possible, the means and standard deviations of the individual threshold measure-

ments are included; however, for the rippled noise and notched noise experiment only the mean thresholds are pre-

sented. Individual standard deviations in these experiments, like those of the critical ratio and band-narrowing experiments, ranged from 0 to 6 dB, with a typical standard deviation being 2-3 dB.

TABLE AIV. Individual masking functions derived from the notched noise masking experiment. For each animal, the table provides the masked threshold (in dB SPL) as a function of relative notch width (Af/fa). The table also provides the individual equivalent rectangular bandwidths (ERB) of the filters derived from these masking functions. Averaged masking functions are provided for each signal frequency. The average ERBs are based on the averaged masking functions. Note: The 1000-Hz data are listed at all three masker levels.

Relative notch width (Af/f,) 0 0.15 0.28 0.41 0.44 0.46 0.47 ERB

500-Hz signal frequency (masker at N o = 43 dB/Hz) C3 75.7 62.7 57.3 55.0 52.0 52.3 51.0 52

C4 75.3 59.7 56.7 54.0 49.7 49.0 47.3 52

C6 78.3 67.7 65.7 59.7 59.0 58.0 56.0 80

Ave 76.4 63.4 59.9 56.2 53.6 53.1 51.4 59

1000-Hz signal frequency (masker at N o = 37 dB/Hz) 0 0.17 0.23 0.30 0.35 0.40 0.42 0.44 0.47 ERB

C3 66.0 60.3 55.3 50.3 43.7 40.0 41.3 36.0 33.7 197

C4 67.7 61.7 54.0 49.7 44.7 40.7 36.7 36.7 34.0 165

C6 63.7 59.3 56.0 53.7 52.7 50.0 50.0 47.0 45.0 280

Ave 65.8 60.4 55.1 51.2 47.0 43.6 42.7 39.9 37.6 202

1000-Hz signal frequency (masker at N o -• 43 dB/Hz) 0 0.17 0.23 0.30 0.35 0.40 0.42 0.44 0.47 ERB

C3 71.3 66_0 58.0 54.7 51.0 45.3 47.3 42.0 36.0 202

C4 73.7 66.0 60.7 53.0 51.7 44.7 45.7 42.0 41.0 148

C6 69.7 67.0 59.3 56.7 55.7 55.3 55.3 51.3 48.0 228

Ave 71.6 66.3 59.3 54.8 52.8 48.4 49.4 45.1 41.7 185

Relative notch width (Af/fo) 0 0.17 0.23 0.30 0.35 0.40 0.42 0.44 0.47 ERB

1000-Hz signal frequency (masker at No = 49 dB/Hz) C3 75.8 73.0 67.3 59.0 57.0 53.0 50.5 46.6 46.3 229

CA 78.3 76.7 68.3 61.7 56.3 54.7 51.3 53.7 54.3 163

C6 72.0 69.7 66.0 60.3 58.3 57.3 57.0 56.3 57.0 230

Ave 75.4 73.1 67.2 60.3 57.2 55.0 52.9 52.2 52.5 201

2000-Hz signal frequency (masker at N o = 43 dB/Hz) 0 0.14 0.19 0.22 0.25 0.31 0.45 0.50 ERB

C3 73.3 70.3 69.0 67.7 60.7 56.7 57.0 56.3 346

CA 76.7 72.7 69.0 66.3 61.7 57.7 58.7 57.7 255

C6 75.3 74.7 70.7 68.7 61.3 58.3 57.6 56.3 324

Ave 75.1 72.6 69.6 67.6 61.2 57.6 57.8 56.8 304

4000-Hz signal frequency (masker at No = 43 dBDtz) 0 0.17 0.23 0.33 0.42 0.52 ERB

C3 78.7 68.0 60.0 51.0 49.0 49.0 330

CA 80.7 69.7 62.3 46.7 47.7 45.3 304

C6 80.0 70.7 62.3 52.3 47.3 44.3 378

Ave 79.8 69.5 61.5 50.0 48.0 46.2 335

2648 J. Acoust. Sec. Am., Vol. 92, No. 5, November 1902 Niomiec eta/.: Frequency selectivity in chinchilla 2646

• Given the variability in the sound field, the ability to discern small changes in filter bandwidth would be difficult since small changes in threshold could lead to large changes in bandwidth. However, the final results of these e,periments are unlikely to reflect the full variation of the sound field since we are interested only in the variation in the total power integrated over the critical band function.

2 According to Houtgast, the weighting function or auditory-filter shape can be written as

w(f,f,)= l + ,y•a. k L

+ • b, sin('2*rn('--f--f')'• k f, ]' (1) where n is the ripple density, f, is the signal frequency, and the coefficients a, and b, are

a•=K[(cn--I)/(cn+l)]; cn=!O (c; •.)/m (2)

b, =K[(sn-- l)/(sn+ I)]; sn= 10 ('•' -'" )/•o (3)

where K is a constant depending on the attenuation of the delayed noise used in the generation of the rippled noise masker. The value ofc• - c•- is the masked threshold difference (in dB) between the cos + and cos -- masking conditions for each value ofn used. The value ors,* -- s• is the masked threshold difference (in dB) between the sin + and sin -- masking conditions for each value of n used. It is further assumed that the weighting function is located in the range 0.5 -l.Sf• in that W ( .f, f• ) -- 0 for 0.5.f, • l.Sf, (see Houtgast, 1977 or Pick, 1980 for a complete deriva- tion ot the weighting function).

• The ERB is equal to the area under the function I,V ( .f,f, ) divided by the value of W( f,f, ) at f, (see Houtgast, 1977). This can be written as

œ f, ERB (Hz) --- (4)

wfff)

4 The single-parameter rounded-exponential [ Roex(p) ] filter has the form •V(g) = (1 +pg) cxp(--pg), (5)

where p is the fitting parameter that determines the steepness of the filter and g is relative frequency (g = [ ( f--f• )/f• ] ). Giasberg et al. (1984) showed that for this type of filter the ratio of threshold at the valley to threshold at the peak in the rippled noise spectrum is

1_• • I + m[p'/(p 2 + 4n2n 2) ]• (6) I• I -- m[p2/(p 2 + 4•r2n; ) ]2 '

where m is the modulation depth (m = 2A/( 1 + A •), A is the attenuation of the delayed noise), and n is the ripple density. The predicted intensity ratios were converted to decibels by fitting ten times the logarithm of Eq. (6) to the actual average cosine masking functions. (Since it has been shown that the auditory filters are roughly symmetrical, only the average cosine masking functions were fit with the mathematical functions.) For the 500, 1000, and 2000 Hz average cosine masking functions, the best fitting values ofp were 20, 14, and 22, respectively.

•ln this technique the masking function is fit with a regression curve. A second-order regression curve was used for the masking functions measured in this study because the masking functions tended to be shaped like second-order polynomials. The regression curve is then converted from dB to linear units and the derivative of the linear masking function is taken as one-half of the filter shape. Finally, the filter is normalized.

•The Rocx(p) filter has the form shown previously in Eq. (5). Patterson and Moore (1986) showed that for this type of filter, the masking function [P• (Af/fo) ] can be expressed as

P•(Af /fo} = 2KfdVo[p -•(2 +pg)e •'], (7)

where Kis the proportionality constant (the power of the signal at threshold divided by the total noise power passing through the critical band ),re is the center frequency of the filter, and p and g are defined as before. The value ofp was obtained by fitting ten times the logarithm of Eq. (7) to the actual masking functions. For the 500-, 1000-, 2000-, and 4000-Hz average masking functions, the best fitting values ofp were 23, 26, 24, and 30, respectively.

?To check the reliability of the original CR estimates from experiment I, CR estimates were also extracted from the band-narrowing, rippled noise, and notched noise experiments. For all chinchillas tested in more than one

experiment, the original estimates of the CR were reliable. The variability of a chinchilla's CR estimates between the four experiments was about the same as the chinchilla's variability within the CR experiment.

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2649 J. Acoust. Sec. Am., Vol. 92, No. 5, November 1992 Niemiec otal.: Frequency selectivity in chinchilla 2649

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