Although the maximum length sequence (MLS) and iterative randomized stimulation and averaging (I-RSA) methods allow auditory brainstem response (ABR) measurements at high rates, it is not clear if high rates allow ABRs of a given quality to be measured in less time than conventional (CONV) averaging (i.e., fixed interstimulus intervals) at lower rates. In the present study, ABR signal-to-noise ratio (SNR) was examined in six bottlenose dolphins as a function of measurement time and click rate using CONV averaging at rates of 25 and 100 Hz and the MLS/I-RSA approaches at rates from 100 to 1250 Hz. Residual noise in the averaged ABR was estimated using (1) waveform amplitude following the ABR, (2) waveform amplitude after subtracting two subaverage ABRs (i.e., the “±average”), and (3) amplitude variance at a single time point. Results showed that high stimulus rates can be used to obtain dolphin ABRs with a desired SNR in less time than CONV averaging. Optimal SNRs occurred at rates of 500–750 Hz, but were only a few dB higher than that for CONV averaging at 100 Hz. Nonetheless, a 1-dB improvement in SNR could result in a 25% time savings in reaching criterion SNR.

## I. INTRODUCTION

For conventional (CONV) signal averaging during auditory brainstem response (ABR) measurements, where the interstimulus interval (ISI) is fixed, ABR overlap occurs when the ISI is less than the duration of the ABR. This can make identification of specific ABR peaks challenging or impossible. Several approaches have been described in the literature for circumventing this stimulus rate limitation. These approaches utilize stimuli with “jittered” ISIs (i.e., the ISI varies from one stimulus to the next) and specific temporal/spectral properties that allow recovery of the transient response (Valderrama *et al.*, 2014). The first such approach involves presenting stimuli with ISIs fitting a maximum length sequence (MLS), then cross-correlating the averaged ABR with a recovery sequence to disentangle overlapping responses (Eysholdt and Schreiner, 1981). The MLS approach has the disadvantages of relatively large and uneven jitter (e.g., Delgado and Özdamar, 2004) and ∼3 dB loss in signal-to-noise ratio (SNR) arising from cross-correlating the evoked response with a recovery sequence that contains nearly double the number of pulses as the stimulus sequence (Picton *et al.*, 1992; Bohórquez and Özdamar, 2006). Other techniques developed to allow high stimulation rates without the disadvantages of the MLS approach include continuous loop averaging deconvolution (CLAD; Delgado and Özdamar, 2004; Özdamar and Bohórquez, 2006), randomized stimulation and averaging (RSA; Valderrama *et al.*, 2012), and iterative randomized stimulation and averaging (I-RSA; Valderrama *et al.*, 2014). Unlike the MLS and CLAD methods, which require a deconvolution process to disentangle the overlapped responses and recover the transient ABR, the RSA and I-RSA methods present stimuli with randomized ISIs, and the ABR is obtained via synchronously averaging sweeps temporally aligned with each stimulus (Valderrama *et al.*, 2012; Valderrama *et al.*, 2014). Overlapping responses are eliminated via the jitter in stimulus onset created by the random ISI (provided the jitter is large enough). The I-RSA technique improves upon RSA by utilizing an iterative process where the interference associated with overlapping responses is estimated and subtracted during signal averaging (Valderrama *et al.*, 2014).

The MLS (Burkard *et al.*, 2017) and I-RSA (Finneran, 2017) techniques have recently been used to obtain ABRs in bottlenose dolphins (*Tursiops truncatus*) at click rates that extend above 1000 Hz. In a comparison of the two techniques, Burkard *et al.* (2018) showed that changes in ABR peak latency and amplitude with click rate were similar for the MLS and I-RSA methods, despite the temporal jitter in the MLS being much larger (up to seven times the minimum pulse interval, or MPI) than that of the I-RSA approach (temporal jitter fixed at 1 ms). It thus appears that the relatively large jitter inherent in the MLS approach does not substantially affect the averaged ABR compared to that obtained with I-RSA.

The Burkard *et al.* (2018) study did not, however, address whether there was an inherent temporal advantage in measuring ABRs at high stimulus rates—i.e., since adaptation causes ABR amplitude to decrease with increasing stimulus rate, does the use of MLS/I-RSA at high stimulus rates actually allow ABRs with a desired SNR to be measured in less time compared to CONV averaging? If so, the increased efficiency of MLS/I-RSA methods could provide an advantage in time-limited situations such as auditory health assessments for wild marine mammals (e.g., Ridgway and Carder, 2001; Nachtigall *et al.*, 2005; Cook *et al.*, 2006). The present study investigates several approaches to calculate ABR SNR as a function of measurement time and click rate for the CONV, MLS, and I-RSA approaches in bottlenose dolphins. The underlying ABR data were previously described by Burkard *et al.* (2018). The goal of the present study was to investigate how ABR SNR was affected by stimulus rate and determine if high stimulus rates could be used to obtain ABRs with a desired SNR in less time than CONV averaging.

## II. METHODS

The methods used to obtain ABRs in dolphins with CONV, MLS, and I-RSA were previously described by Burkard *et al.* (2018), and will only briefly be summarized here with emphasis on the methods used to calculate the ABR amplitude, residual background noise amplitude in the averaged ABR, and the SNR.

### A. Subjects

Subjects consisted of six bottlenose dolphins. Three dolphins (codes SAY, TRO, WHP) were defined as having “normal hearing” (NH) with their upper cutoff of hearing (interpolated frequency where behavioral threshold was 100 dB re: 1 μPa) above 140 kHz. The remaining three dolphins (codes BLU, COL, OLY) were considered to be “hearing impaired” (HI) with upper cutoff of hearing below 80 kHz (see Burkard *et al.*, 2018). Tests were conducted within a floating, netted enclosure located in San Diego Bay, CA, with the dolphins completely submerged during stimulus presentation/ABR recording.

### B. Stimulation and recording

Click stimuli were produced by delivering a ∼5-*μ*s pulse to an underwater sound projector (ITC 5446, International Transducer Corp, Santa Barbara, CA) at a peak-equivalent sound pressure level (peSPL) of 135 dB re 1 μPa (see Fig. 1 in Burkard *et al.*, 2018). Click rates for CONV averaging were 25 and 100 Hz. Average click rates for the MLS and I-RSA approaches were ∼100, 250, 500, 750, 1000, and 1250 Hz. For each ABR measurement, stimuli were presented for 31 s for all rates above 25 Hz and for 40 s at the 25-Hz rate. To help reduce stimulus artifacts, the click polarity was alternated on successive stimulus presentations (CONV, I-RSA) or sequences (MLS). Two replicates were obtained for each combination of method (CONV, MLS, I-RSA) and rate.

The MLS had a length *L* = 127 and consisted of 64 ones (a click was presented) and 63 zeros (no click presented). MPIs varied from 0.4 ms (∼1250 Hz average rate) to 5 ms (∼100-Hz rate), therefore, the total length of a single stimulus sequence varied from 50.8 ms to 635 ms. For each MLS the average interval equaled 127/64 × MPI or roughly 1.984 × MPI. Therefore, although this paper refers to average rates of 100, 250, 500, 750, 1000, and 1250 Hz, the actual rates differed slightly (101, 252, 504, 752, 1008, and 1260 Hz).

For the I-RSA method, ISIs were drawn from uniform random distributions with mean ISIs varying from ∼0.8 ms (1250 Hz) to ∼10 ms (100-Hz rate). Actual mean ISIs matched the specific values utilized by the MLS. Jitter within the ISI was fixed at 1 ms (±0.5 ms), regardless of average rate.

Evoked responses were recorded from gold-plated cup electrodes embedded in suction cups that were coupled to the skin using conductive gel. The electrodes were placed ∼5 cm posterior to the blowhole (non-inverting), immediately posterior to the right external auditory meatus (inverting), and in the seawater near the dolphin (common). Electrical activity between the non-inverting and inverting electrodes, representing the instantaneous electroencephalogram (EEG), was amplified (94 dB) and filtered (0.3–3 kHz) by a Grass ICP511 biopotential amplifier (Grass Technologies, West Warwick, RI), then digitized at 100 kHz with 16-bit resolution and saved for later analysis.

### C. ABR signal and noise estimation

ABR SNR estimates were performed for measurement times of ∼1, 2, 5, 10, 15, 20, 25, and 30 s. For each measurement time *T*, the stored instantaneous EEG data were divided into *N _{E}* epochs of data, each temporally aligned with the onset of a single stimulus (CONV, I-RSA) or sequence (MLS). For CONV and I-RSA, the epoch duration was 20-ms; for MLS, the epoch duration equaled the sequence duration (127 × MPI). Epochs with peak amplitude >40 μV were then excluded from analysis, and the remaining epochs divided into two groups, each containing

*N*/2 epochs and having an equal number of epochs associated with each stimulus/sequence polarity. Epochs for each group were obtained from interleaved pairs (i.e., group 1 = epochs 1,2,5,6,… and group 2 = epochs 3,4,7,8,…). The requirement to have an equal number of epochs of each polarity in the two groups constrained

_{E}*N*to an integral multiple of four. The exact measurement times therefore differed from the nominal values, depending on the duration of each epoch. In most cases, the actual measurement time was within 1% of the nominal value. When grouping data by nominal measurement time, data were excluded if the nominal and actual measurement times differed by more than 10%.

_{E}For the CONV approach, EEG epochs in each group were averaged to obtain two “subaverages” for each measurement. For the MLS approach, EEG epochs in each group were first averaged together, then “deconvolved” subaverages (i.e., with overlapping ABRs disentangled) were obtained by cross correlation with the recovery sequence (the original 127-element MLS comprised of 64 “1s” and 63 “-1s”). More details can be found in Eysholdt and Schreiner (1981) and Burkard *et al.* (1990). For I-RSA, subaverages were created from the EEG epochs in each group using an iterative process to minimize the effects of overlapping responses and any stimulus artifacts (for details, see Valderrama *et al.*, 2014; Finneran, 2017; Burkard *et al.*, 2018).

The two subaverages were then averaged together to yield a single averaged ABR. ABR signal amplitude (*S*) was defined as the root-mean-square (rms) amplitude of the averaged ABR calculated over a time period from 1 to 7 ms relative to stimulus onset (the time-of-arrival of the acoustic click at the dolphin). This time period was chosen to encompass the dominant components of the dolphin ABR.

The rms residual noise amplitude in the averaged ABR (*N*) was estimated using three approaches: (1) interval (INT) method; (2) ±averaging (±AVE) method; and (3) single-point (SP) amplitude method. Each method is described in detail below. To assess the relationship between the residual noise estimated with each method and the measurement time, nonlinear regression (OriginLab, 2018) was used to fit residual noise data with the power function

where *a* and *b* are fitting parameters. For our assumption of stationary Gaussian noise, *b* = −0.5.

For the INT method, *N* was defined as the rms amplitude of the averaged waveform over a time period from 13 to 19 ms relative to stimulus onset (i.e., a time period following the ABR with the same duration as that used to estimate *S*). Note that for the INT approach, it was not possible to calculate *N* for the CONV method at 100-Hz rate due to the overlap of the ABR from the subsequent stimulus with the noise interval. Thus, these results are not shown.

For the ±AVE approach, the ABRs resulting from each subaverage were first subtracted to create the ±average (see Schimmel, 1967; Wong and Bickford, 1980). Noise amplitude *N* was then defined as the rms amplitude of the ±average waveform, calculated over a time period from 1 to 7 ms relative to stimulus onset (the same time interval used to calculate *S*).

For the SP method, *N* was estimated from the sweep-to-sweep variance in the averaged ABR at a single time point relative to stimulus onset (Elberling and Don, 1984). For the CONV and I-RSA methods, SP amplitudes were extracted from each epoch at time = 3 ms relative to each stimulus onset (i.e., within the time interval containing the ABR). Provided the background noise is stationary, the specific time value for sampling the SP amplitudes is irrelevant. Although the assumption of stationary background noise is not always strictly fulfilled in evoked potential recordings, Elberling and Don (1984) and Finneran (2008) reported (in ten human and two dolphin subjects, respectively) no significant deviations from a Gaussian amplitude distribution. Changing the time location for the SP amplitudes also was found to have little effect on the resulting sweep-to-sweep variance (Elberling and Don, 1984; Finneran, 2008). Elberling and Don (1984) further note that violations of the underlying assumptions of their approach for residual noise estimation do not appear to be of significance in practice. For I-RSA, the final estimated ABR was subtracted from each epoch at all times corresponding to stimulus onsets before the SP amplitudes were extracted. This was necessary to prevent the existence of overlapping, but temporally jittered, ABRs from inflating the variance of the SP amplitudes. For MLS, 64 SP amplitudes were extracted from each epoch, 3 ms after each stimulus onset (i.e., one SP amplitude associated with each stimulus onset in the MLS at the same time value used with the CONV and I-RSA methods). For the CONV and I-RSA methods,

where VAR(SP) is the variance in the collection of SP amplitude values. For MLS,

where *L* is the MLS length (i.e., 127) and *N _{S}* is the number of stimuli in the MLS (i.e., 64). The second term under the radical in Eq. (3) is equivalent to Eq. (2) because

*N*equals the number of stimuli presented across all stimulus sequences and matches the number of SP amplitude values. Therefore, the value of

_{E}N_{S}*N*for MLS is $L/NS$ higher than that for CONV or I-RSA with the same number of individual stimuli; for an MLS,

*L*= 2

*N*− 1, meaning that

_{S}*N*is ∼$2$ (3 dB) larger for MLS compared to CONV or I-RSA with the same number of individual stimuli.

For measurement times less than half the overall recording duration, *S* and *N* were computed using multiple, mutually exclusive collections of *N _{E}* epochs. Mean values for

*S*or

*N*were obtained by averaging the signal or noise power, respectively, and taking the square root. The mean SNR ($SNR\xaf$) was then estimated using

where $S2\xaf$ is the mean signal power and $N2\xaf$ is the mean noise power. The −1 term arises because the measured value for *S* consists of signal + noise, not signal alone.

The calculations described above were performed after grouping dolphins by NH or HI status. The methodology was verified by computing mean SNR as a function of time for simulated data consisting of a 1-kHz sinusoid with known rms amplitude embedded in Gaussian noise with known standard deviation.

## III. RESULTS

### A. ABR amplitude

Figure 1 shows averaged ABRs from two dolphins, one NH (dolphin SAY) and one HI (dolphin OLY), for the three averaging approaches (CONV, MLS, I-RSA) with *T* ≃ 30 s. As expected (and previously reported), ABR peak amplitudes decrease and peak latencies increase with increasing click rate, and ABRs from the HI dolphins are smaller than those from the NH dolphins.

Figure 2 shows mean ABR rms amplitudes as functions of mean stimulus rate for NH and HI dolphins for each averaging approach. Note that the HI dolphins show substantially smaller rms ABR amplitudes across all rates. All three averaging approaches (for both NH and HI dolphins) show nearly identical mean rms ABR amplitudes at 100 Hz. Mean amplitudes for the MLS and I-RSA approaches are similar for rates up to 500 Hz, but at higher rates ABR amplitude for MLS is (on average) larger than that observed for I-RSA.

### B. Residual noise

Figure 3 shows the effects of averaging time on the mean estimated residual noise amplitude for CONV averaging (25 Hz and 100 Hz) for the three noise estimation approaches. The left panels show residual noise estimates for NH dolphins and the right panels show values for HI dolphins. As noted in Sec. II, it is not possible to obtain a noise estimate for CONV averaging at 100 Hz using the interval approach due to overlap of the ABR and noise epochs at this rate (see Fig. 1). Noise amplitude decreased with increasing time (as expected). Although patterns were similar for all three noise estimation methods, the ±AVE method consistently resulted in lower noise amplitudes.

Figure 4 shows mean residual noise as a function of averaging time for MLS and I-RSA for each stimulus rate. The two leftmost columns show mean residual noise for the three NH dolphins with the two rightmost panels showing mean residual noise for the HI dolphins. Overall, the residual noise estimates shown in Fig. 4 demonstrate the expected decrease in residual noise with increasing averaging time (i.e., increasing number of sweeps). For a given averaging time, residual noise estimates for MLS are somewhat larger than those for I-RSA, regardless of click rate or noise-estimation approach, which is expected due to the cross-correlation approach used for MLS.

For all noise estimation approaches and averaging methods, fits of Eq. (1) to the noise data were good, with the mean adjusted *R*^{2} (±SD) = 0.991 ± 0.0158, 0.997 ± 0.00270, and 1.00 ± 0.000762 for the INT, ±AVE, and SP methods, respectively. The means (±SD) for the best-fit values of the exponent *b* across test conditions (CONV, MLS, I-RSA) were INT, *b* = −0.462 ± 0.0685; ±AVE, *b* = −0.509 ± 0.0363; SP, *b* = −0.499 ± 0.00642.

Figure 5 shows SNR across averaging time for the three averaging methods (CONV, MLS, I-RSA) for each stimulus rate. Regardless of the method used to estimate residual noise, or whether evaluating NH or HI dolphins, SNR tends to increase with increasing averaging time. For click rates of 500 Hz and below for a given averaging time at a fixed rate, the SNR is typically larger for I-RSA than MLS. In addition, for a fixed click rate and averaging time, the SNR for NH dolphins is larger than that for HI dolphins (largely the result of the larger ABR amplitudes in the NH dolphins).

Figure 6 shows the SNR for NH and HI dolphins as a function of stimulus rate for measurement times of ∼5, 15, and 25 s (left to right columns). From top to bottom, the rows show SNRs based on noise estimates obtained via the INT, ±AVE, and SP methods. Regardless of averaging time, noise estimation approach, or whether evaluating responses from NH or HI dolphins, the SNR for a fixed averaging time tends to increase with increasing click rate up to 500–750 Hz, and decreases thereafter. For rates of 500 Hz and below, I-RSA shows a better SNR than does MLS. Generally speaking, the largest SNR for a fixed averaging time is for I-RSA at a click rate of 500 Hz; however, at this optimal rate (for I-RSA), SNR is typically only a few dB higher than the SNR obtained using CONV averaging at 100 Hz.

## IV. DISCUSSION

### A. Response amplitude

In agreement with previous studies of the effects of stimulus rate on dolphin ABRs (Ridgway *et al.*, 1981; Popov and Supin, 1990; Burkard *et al.*, 2017; Finneran, 2017; Burkard *et al.*, 2018), ABR amplitude decreased with increasing click rate. ABR peak amplitude decrease with rate has also been observed in humans (Jewett and Williston, 1971; Burkard and Hecox, 1987; Burkard and Sims, 2001; Valderrama *et al.*, 2012), gerbils (Burkard and Voigt, 1989), mice (Burkard *et al.*, 2001), chickens (Burkard *et al.*, 1994), cats (Burkard *et al.*, 1996a,b), and seals (Reichmuth *et al.*, 2007). In the present study, dolphins with high-frequency hearing loss (HI dolphins) showed smaller ABR peak amplitudes than NH dolphins. This effect of high-frequency hearing loss has been reported in previous work with bottlenose dolphins (Finneran *et al.*, 2016; Mulsow *et al.*, 2016). What is new herein regarding ABR amplitude is that the effects of rate and hearing status on specific ABR peaks can be seen in the rms amplitude of the ABR over a 6-ms time window (from 1 to 7 ms post-stimulus onset), indicating that it is not necessary to identify a given ABR peak to quantify ABR presence or to quantify differences in ABR amplitude across, for example, NH versus HI dolphins.

### B. Residual noise estimates

The three noise estimation approaches showed the expected decrease in residual background noise with increasing averaging time, and similar residual noise estimates were obtained regardless of the specific mathematical approach; however, for some test conditions there were systematic differences. The INT method tended to result in higher, more variable residual noise estimates compared to ±AVE and SP methods. This is particularly noticeable for CONV at 25 Hz, and may reflect the existence of a small-amplitude middle-latency response within the noise calculation interval (13–19 ms after stimulus onset). Fits of Eq. (1) to the noise data were slightly better (smaller *R*^{2}) for the ±AVE and SP methods. The resulting best-fit exponents were also closer to the expected value of −0.5 and showed less variability across test conditions for the ±AVE and SP methods compared to the INT method. These considerations make the INT approach the least attractive method for estimating residual background noise. In comparing the ±AVE and SP methods, Elberling and Don (1984) recommended the SP method because the ±AVE method has higher uncertainty in the residual noise estimation (due to relatively low degrees of freedom in the ±AVE noise estimate). In the present study, noise estimates from the ±AVE and SP methods were generally similar; however, the ±AVE method consistently resulted in lower noise values for the CONV method (but not for MLS and I-RSA). The exact reasons for low residual noise estimates for CONV with the ±AVE method are not clear, but may be related to the increased uncertainty in the ±AVE method compared to the SP approach mentioned by Elberling and Don (1984). The SP method yielded more consistent noise estimates with respect to Eq. (1); however, this is to be expected since the SP method residual noise estimates feature $NE$ in the denominator, so noise decreasing with $T$ simply means that the VAR(SP) remains constant with increasing *T*.

Both the SP and ±AVE methods assume the underlying background noise is Gaussian and stationary. These assumptions are not likely to be strictly fulfilled during ABR testing; however, this appears to have limited practical consequences (Elberling and Don, 1984), at least when brief periods of large amplitude myogenic activity are addressed by artifact rejection or related approaches. In the present study, a single amplitude value following each stimulus was used to estimate the residual noise. Stürzebecher *et al.* (2001) reported improved performance when residual noise was estimated using multiple time points for the variance ratio calculation, rather than a single time point from each epoch. In the present study, stimulus rates with the MLS and I-RSA approaches were relatively high, thus, the number of stimulus presentations (i.e., the number of SP amplitude values) was large: for a measurement time of ∼1 s, the number of SP amplitude values ranged from 100 to ∼1300 for rates of 100 to 1250 Hz. For a 30-s measurement time, the number of SP amplitude values ranged from 3000 to 38 000. The SP amplitude variance tends to converge to the true variance of the background noise after a few hundred epochs (Don *et al.*, 1984; Elberling and Don, 1984; Finneran, 2008); therefore, the use of multiple amplitude values would not have significantly affected results for the majority of MLS/I-RSA conditions. For the CONV method, the number of stimulus presentations was lower (from 24 to 760 for CONV at 25 Hz, depending on measurement time), so the use of multiple time values may have led to more accurate noise estimates at shorter measurement times.

For a given stimulus condition, the residual noise is higher for MLS than I-RSA. As discussed by Bohórquez and Özdamar (2006), residual noise is higher in the averaged MLS ABR (as compared to CONV averaging or I-RSA averaging) because the original MLS train has length 127 but only 64 stimuli, resulting in residual noise ∼3 dB higher compared to that obtained with the CONV or I-RSA methods and the same number of stimuli [see Eq. (3)]. As noise in theory decreases in proportion to the square root of the number of stimuli, this 3-dB increase in residual noise would require twice as many stimuli (or doubling the averaging time) compared to CONV or I-RSA to obtain the same residual noise estimate.

### C. SNR

ABR quality can be quantified using the SNR, defined in the present study as the ratio of the rms amplitude of the ABR from 1 to 7 ms after stimulus onset to the rms value of the residual background noise. Residual noise decreases with the number of stimulus presentations or measurement time (and thus for a given time, stimulus rate). Therefore, in theory, increases in measurement time should always improve SNR (Fig. 5), although other factors (such as deviations from stationary background noise) can lead to violations of this expectation. Since ABR amplitude decreases with increasing rate (Fig. 2), increases in stimulus rate will only increase SNR if the drop in ABR amplitude with increasing rate is less than the drop in residual noise for a given *T*. Since noise decreases with $T$ (Figs. 3 and 4), if the decrease in ABR amplitude with increasing rate is <$2$ (or 3 dB) with each doubling of rate (i.e., 3 dB/oct), then SNR increases with rate. If the decrease in ABR amplitude with rate is >3 dB/oct, then SNR decreases. The rate at which the amplitude change exactly matches −3 dB/oct represents the optimal rate for SNR. Therefore, the slope of the ABR amplitude versus rate function can be used to estimate the optimal rate for SNR. From Fig. 2, it can be seen that optimal rates for SNR (compare dotted line with the ABR amplitude data in each panel) are ∼500 Hz for I-RSA and ∼750 Hz for MLS. Therefore, regardless of noise estimation approach, rates of 500 - to 750-Hz appear to be the most efficient (in terms of obtaining the largest SNR for a given averaging time) for I-RSA and MLS, respectively. Plots of SNR as a function of stimulus rate (Fig. 6) show peaks at 500 Hz for I-RSA and 750 Hz for MLS, confirming these estimates.

The existence of an optimal rate for SNR means that the MLS or I-RSA techniques can be used with high stimulus rates to obtain ABRs of a given quality (as defined by SNR) in less time than CONV averaging at lower rates. The actual improvement in SNR at high rates is small: the I-RSA SNR at 500 Hz is typically only a few dB higher than that observed for CONV averaging at 100 Hz. However, even small increases in SNR could account for considerable time savings in terms of averaging until a criterion SNR is achieved, as even a 1-dB increase in SNR could (in theory) require 25% less time.

As the recovery process adds 3 dB residual noise for MLS, and MLS and I-RSA ABR amplitudes are similar for click rates of 500 Hz and below, for the click level used in this study (135 dB re 1 μPa) the MLS SNR is several dB less than that for I-RSA. Clearly, the use of I-RSA is superior to MLS, at least for click rates of 500 Hz or less. I-RSA also allows more flexibility in experimental design and relatively small temporal jitter in the ISI, which may be important if the primary interest is in studying auditory adaptation or other effects of stimulus rate. At rates above 500 Hz, dolphin ABR rms amplitudes are smaller for I-RSA than for MLS, and the SNR for a specified averaging time is typically higher for MLS than I-RSA at these higher rates. In Burkard *et al.* (2018), it was reported that several ABR peak amplitudes were larger at these higher rates for MLS compared to I-RSA, and several possible reasons for this were discussed, including the greater range of ISI jitter for MLS versus I-RSA.

### D. Normal hearing versus hearing impaired dolphin ABRs

The high-frequency emphasis of the click used herein (its spectrum level drops off at 12 dB/octave below resonance of ∼160 kHz) combined with the elevated thresholds in the HI dolphins at frequencies above ∼40–70 kHz resulted in a substantial decrease in ABR amplitude for the HI dolphins compared to the NH dolphins. A decrease in ABR peak amplitudes in HI compared to NH dolphins has been previously reported (Finneran *et al.*, 2016; Mulsow *et al.*, 2016). As the proportional change in ABR peak amplitude with rate is similar for NH and HI animals (see Fig. 2), it is perhaps not surprising that the effects of click rate on SNR are similar for NH and HI dolphins. For high-level click stimuli, it also appears that optimal click rates for obtaining a fixed SNR in the least amount of time are not strongly dependent on high-frequency hearing cutoff. Note that we cannot readily generalize the present results to lower-level clicks or tone burst stimuli of various carrier frequencies (or even to clicks with different changes in level across frequencies), and such generalization must await empirical confirmation.

## V. CONCLUSIONS

The SNR of dolphin click-evoked ABRs increases with increasing stimulus rate up to ∼500–750 Hz, above which SNR decreases with increasing rate. The MLS or I-RSA techniques, which allow ABRs to be measured at rates above those possible with CONV averaging, can therefore be used to obtain ABRs of a given quality (as defined by SNR) in less time than CONV averaging at lower rates. Assuming Gaussian, stationary background noise, the optimal stimulus rate for SNR can be estimated by determining the rate at which the slope of the ABR amplitude versus rate function equals −3 dB/oct. The three computational methods used to estimate residual noise provided similar estimates of residual noise magnitude. The INT approach cannot be used for CONV averaging when the ABR duration approaches the ISI, and the ±AVE and SP approaches produced smaller variability in residual noise estimation than did the INT approach.

## ACKNOWLEDGMENTS

The authors acknowledge the assistance of D. Houser, J. Powell, R. Dear, M. Wilson, G. Goya, R. Echon, H. Bateman, T. Wu, R. Simmons, and the animal care and training staff of the Navy Marine Mammal Program. The authors also thank one anonymous reviewer for suggesting that a small middle latency response may have influenced the results for one of the noise-estimation approaches. Experimental procedures were approved by the Institutional Animal Care and Use Committee (IACUC) at the Biosciences Division, Space and Naval Warfare Systems Center (SSC) Pacific and the Navy Bureau of Medicine and Surgery. This work was supported by the U.S. Navy Living Marine Resources (LMR) Program and the SSC Pacific Naval Innovative Science and Engineering (NISE) program. Portions of these data were presented at the 2018 meeting of the American Auditory Society.