Bias Tone Research Articles

Tunable pattern recognition of optical QPSK data using optical correlation and direct detection.

Performing pattern recognition via correlation in the optical domain has potential advantages, including: (i) high-speed operation at the line rate and (ii) tunability and scalability by operating on the optical wave properties. Such pattern recognition might be performed on quadrature-phase-shift-keying (QPSK) data transmitted over an optical network, which generally requires using coherent detection to distinguish the phase levels of the correlator output. To enable simpler detection, we combine optical correlation with optical biasing to experimentally demonstrate tunable and scalable QPSK pattern recognition using direct detection. The pattern is applied by adjusting the relative phases of the local pumps. Delayed QPSK signals, a coherent bias tone, and local pumps undergo nonlinear wave-mixing in a periodically poled lithium niobate (PPLN) waveguide to perform optical correlation and biasing. The biased correlator output is captured using direct detection, where the highest power level corresponds only to the pattern. Multiple QPSK pattern recognitions are achieved error-free over 3072 symbols using power thresholding values of (i) 0.78 at a 5-Gbaud rate and 0.73 at a 10-Gbaud rate for 2-symbol pattern recognition and (ii) 0.81 at a 5-Gbaud rate and 0.79 at a 10-Gbaud rate for 3-symbol pattern recognition.

Breathy voice and low-register: A case of trading relation in Shanghai Chinese tone perception?

In Shanghai Chinese as well as many other Wu dialects, breathy voice is a well-documented accompaniment of the low-register tone syllables with obstruent as well as sonorant onsets. But Shanghai Chinese is rapidly changing and the breathy voice associated with low-register tones tends to disappear in young speakers' productions. In this study, we asked whether breathy voice is nevertheless still perceived and whether it pushes tone identification toward low-register tones. We conducted forced-choice tone identification tests on young native listeners of Shanghai Chinese, using low-high register tone continua-from tone T3 (23) to tone T2 (34)-imposed on base syllables with either modal or breathy voice quality, and beginning with various onset consonants. We used continua constructed from either naturally produced or synthesized syllables. Our results show that breathy voice does bias tone identification responses toward the low-register tone T3. This result held for both synthesized and natural stimuli, except for the /m/-onset stimuli derived from naturally produced syllables. We propose that the phonetic change at issue-loss of breathiness in production-is not due to misperception but reflects the ever-stronger influence of Standard Mandarin Chinese. In other words, this particular case of sound change seems to be led by production rather than perception. It remains an open question whether this kind of sound change is only determined by sociolinguistic factors (here, the dominance of Mandarin Chinese) or is independently motivated by phonetic and/or phonological factors.

Non-tip auditory-nerve responses that are suppressed by low-frequency bias tones originate from reticular lamina motion

Recent cochlear mechanical measurements show that active processes increase the motion response of the reticular lamina (RL) at frequencies more than an octave below the local characteristic frequency (CF) for CFs above 5 kHz. A possible correlate is that in high-CF (>5 kHz) auditory-nerve (AN) fibers, responses to frequencies 1-3 octaves below CF (“tail” frequencies) can be inhibited by medial olivocochlear (MOC) efferents. These results indicate that active processes enhance the sensitivity of tail-frequency RL and AN responses. Perhaps related is that some apical low-CF AN fibers have tuning-curve (TC) “side-lobe” response areas at frequencies above and below the TC-tip that are MOC inhibited. We hypothesized that the tail and side-lobe responses are enhanced by the same active mechanisms as CF cochlear amplification. If responses to CF, tail-frequency, and TC-side-lobe tones are all enhanced by prestin motility controlled by outer-hair-cell (OHC) transmembrane voltage, then they should depend on OHC stereocilia position in the same way. To test this, we cyclically changed the OHC-stereocilia mechano-electric-transduction (MET) operating point with low-frequency “bias” tones (BTs) and increased the BT level until the BT caused quasi-static OHC MET saturation that reduced or “suppressed” the gain of OHC active processes. While measuring cat AN-fiber responses, 50 Hz BT level series, 70–120 dB SPL, were run alone and with CF tones, or 2.5 kHz tail-frequency tones, or side-lobe tones. BT-tone-alone responses were used to exclude BT sound levels that produced AN responses that might obscure BT suppression. Data were analyzed to show the BT phase that suppressed the tone responses at the lowest sound level. We found that AN responses to CF, tail-frequency, and side-lobe tones were suppressed at the same BT phase in almost all cases. The data are consistent with the enhancement of responses to CF, tail-frequency, and side-lobe tones all being due to the same OHC-stereocilia MET-dependent active process. Thus, OHC active processes enhance AN responses at frequencies outside of the cochlear-amplified TC-tip region in both high- and low-frequency cochlear regions. The data are consistent with the AN response enhancements being due to enhanced RL motion that drives IHC-stereocilia deflection by traditional RL-TM shear and/or by changing the RL-TM gap. Since tail-frequency basilar membrane (BM) motion is not actively enhanced, the tail-frequency IHC drive is from a vibrational mode little present on the BM, not a “second filter” of BM motion.

Widely Tunable On-Chip Microwave Circulator for Superconducting Quantum Circuits

We report on the design and performance of an on-chip microwave circulator with a widely (GHz) tunable operation frequency. Non-reciprocity is created with a combination of frequency conversion and delay, and requires neither permanent magnets nor microwave bias tones, allowing on-chip integration with other superconducting circuits without the need for high-bandwidth control lines. Isolation in the device exceeds 20 dB over a bandwidth of tens of MHz, and its insertion loss is small, reaching as low as 0.9 dB at select operation frequencies. Furthermore, the device is linear with respect to input power for signal powers up to hundreds of fW ($\approx 10^3$ circulating photons), and the direction of circulation can be dynamically reconfigured. We demonstrate its operation at a selection of frequencies between 4 and 6 GHz.

Low-frequency bias tone suppression of auditory-nerve responses to low-level clicks and tones

We used low-frequency “bias” tones (BT's) to explore whether click and tone responses are affected in the same way by cochlear active processes. In nonlinear systems the responses to clicks are not always simply related to the responses to tones. Cochlear amplifier gain depends on the incremental slope of the outer-hair-cell (OHC) stereocilia mechano-electric transduction (MET) function. BTs transiently change the operating-point of OHC MET channels and can suppress cochlear-amplifier gain by pushing OHC METs into low-slope saturation regions. BT effects on single auditory-nerve (AN) fibers have been studied on tone responses but not on click responses. We recorded from AN fibers in anesthetized cats and compared tone and click responses using 50 Hz BTs at 70–120 dB SPL to manipulate OHC stereocilia position. BTs can also excite and thereby obscure the BT suppression. We measured AN-fiber response synchrony to BTs alone so that we could exclude suppression measurements when the BT synchrony might obscure the suppression. BT suppression of low-level tone and click responses followed the traditional pattern of twice-a-BT-cycle suppression with more suppression at one phase than the other. The major suppression phases of most fibers were tightly grouped with little difference between click and tone suppressions, which is consistent with low-level click and tone responses being amplified in the same way. The data are also consistent with the operating point of the OHC MET function varying smoothly from symmetric in the base to offset in the apex, and, in contrast, with the IHC MET function being offset throughout the cochlea. As previously reported, bias-tones presented alone excited AN fibers at one or more phases, a phenomena termed “peak splitting” with most BT excitation phases ∼¼ cycle before or after the major suppression phase. We explain peak splitting as being due to distortion in multiple fluid drives to inner-hair-cell stereocilia.

Modeling dynamic properties of spontaneous otoacoustic emissions: Low-frequency biasing and entrainment

Spontaneous otoacoustic emissions (SOAE) are sounds generated inside the living cochlea and are regarded as by-products of the active mechanism present in the peripheral auditory system. There is still debate whether these emissions are the product of local oscillators located at various positions along the cochlea (local oscillator model) or if they result from standing waves due to a global collective phenomenon that involves different aspects of the cochlea (global standing wave model). This paper uses a global standing wave cochlear model to predict various features of SOAEs. This involves a state-space formulation with a spatially distributed set of nonlinear active micromechanical elements coupled via cochlear fluid coupling. Simulation results have been compared with available experimental data and demonstrate two interesting nonlinear features of the cochlea: first, nonlinear properties of SOAEs modulated by external low-frequency bias tones are easily predicted and can be used to investigate the plausibility of different nonlinear functions incorporated in the micromechanical elements. Second, entrainment patterns can be obtained when the model is stimulated by a swept-tone: results show distinct areas of beating and others of entrainment between the external stimulus and the SOAE, which depend on the level and instantaneous frequency of the sweep.

Large endolymphatic potentials from low-frequency and infrasonic tones in the guinea pig

Responses of the ear to low-frequency and infrasonic sounds have not been extensively studied. Understanding how the ear responds to low frequencies is increasingly important as environmental infrasounds are becoming more pervasive from sources such as wind turbines. This study shows endolymphatic potentials in the third cochlear turn from acoustic infrasound (5 Hz) are larger than from tones in the audible range (e.g., 50 and 500 Hz), in some cases with peak-to-peak amplitude greater than 20 mV. These large potentials were suppressed by higher-frequency tones and were rapidly abolished by perilymphatic injection of KCl at the cochlear apex, demonstrating their third-turn origins. Endolymphatic iso-potentials from 5 to 500 Hz were enhanced relative to perilymphatic potentials as frequency was lowered. Probe and infrasonic bias tones were used to study the origin of the enhanced potentials. Potentials were best explained as a saturating response summed with a sinusoidal voltage (Vo), that was phase delayed by an average of 60° relative to the biasing effects of the infrasound. Vo is thought to arise indirectly from hair cell activity, such as from strial potential changes caused by sustained current changes through the hair cells in each half cycle of the infrasound.

Low-frequency modulated quadratic and cubic distortion product otoacoustic emissions in humans

Previous studies have used low-frequency tones to modulate distortion product otoacoustic emissions (DPOAEs). The cubic DPOAE (CDPOAE) is mostly chosen because amplitudes sufficient for modulation can be evoked with moderate sound pressure levels. Quadratic DPOAEs (QDPOAEs) however, are more sensitive to minute changes of the cochlear operating point (OP) and are better suited to assess changes of the cochlear OP.Here, we compare the properties of low-frequency (30 Hz, 80–120 dB SPL) modulated CDPOAE and QDPOAEs evoked with f2 = 2 and 5 kHz in human subjects with normal hearing. The modulation depth was quantified with the modulation index (MI), a measure which considers both amplitude and phase.Modulated CDPOAEs evoked with f2 = 2 kHz have amplitude maxima at the zero crossings and amplitude minima at the extremes of the biasing tone (BT) which correlate positively with the BT level. CDPOAEs evoked with f2 = 5 kHz were recorded during biasing in exactly the same way as described before. At the highest BT levels used (120 dB SPL), very little modulation could be detected. Not only the depth, but also the shape of the QDPOAE modulation pattern is correlated with the BT level. At moderate BT levels (about 90–100 dB SPL) QDPOAEs evoked with f2 = 5 kHz show one amplitude notch around the zero crossing of the positive going flank of the BT (a single modulation pattern). At and above a BT level of about 105 dB SPL, the pattern reverses and shows a double modulation pattern. At the highest BT level used (120 dB SPL), quadratic MIs exceed cubic MIs (2.0 ± 0.5 and 0.97 ± 0.06, respectively).Patterns of low-frequency modulated QDPOAEs in humans are similar to the modulation seen in animal studies and as predicted by mathematical models. Human low-frequency modulated QDPOAEs are ideally suited to estimate cochlear OP shifts because of their high sensitivity to the OP shift.

Effects of Low-Frequency Biasing on Otoacoustic and Neural Measures Suggest that Stimulus-Frequency Otoacoustic Emissions Originate Near the Peak Region of the Traveling Wave

Stimulus-frequency otoacoustic emissions (SFOAEs) have been used to study a variety of topics in cochlear mechanics, although a current topic of debate is where in the cochlea these emissions are generated. One hypothesis is that SFOAE generation is predominately near the peak region of the traveling wave. An opposing hypothesis is that SFOAE generation near the peak region is deemphasized compared to generation in the tail region of the traveling wave. A comparison was made between the effect of low-frequency biasing on both SFOAEs and a physiologic measure that arises from the peak region of the traveling wave--the compound action potential (CAP). SFOAE biasing was measured as the amplitude of spectral sidebands from varying bias tone levels. CAP biasing was measured as the suppression of CAP amplitude from varying bias tone levels. Measures of biasing effects were made throughout the cochlea. Results from cats show that the level of bias tone needed for maximum SFOAE sidebands and for 50% CAP reduction increased as probe frequency increased. Results from guinea pigs show an irregular bias effect as a function of probe frequency. In both species, there was a strong and positive relationship between the bias level needed for maximum SFOAE sidebands and for 50% CAP suppression. This relationship is consistent with the hypothesis that the majority of SFOAE is generated near the peak region of the traveling wave.

Harmonic and intermodulation performance of carbon nanotube field-effect transistor-based and single-electron tunnelling transistor-based inverting amplifiers

This article presents a simple mathematical model for the output-voltage/input-voltage characteristics of the carbon nanotube field-effect transistor (CNTFET)-based and the single-electron tunnelling transistor (SET)-based inverting amplifiers. The model, basically a Fourier-series, yields closed-form expressions for the amplitudes of the harmonic and intermodulation components of the output voltage resulting from a multisinusoidal input voltage. The special case of a two-tone equal-amplitude input signal is considered in detail. The results show that the harmonic and intermodulation performance of the CNTFET-based and SET-based inverting amplifiers is strongly dependent on the values of the bias voltage and the amplitudes of the input tones. Moreover, the results show that for the CNTFET-based inverting amplifier, either the relative second-order or the relative third-order intermodulation component is dominant, while for the SET-based inverting amplifier, the relative third-order intermodulation is always dominant. The results also show that all the harmonics and intermodulation products may exhibit minima at different values of the input bias voltages and tone amplitudes.

Estimating the operating point of the cochlear transducer using low-frequency biased distortion products

Distortion products in the cochlear microphonic (CM) and in the ear canal in the form of distortion product otoacoustic emissions (DPOAEs) are generated by nonlinear transduction in the cochlea and are related to the resting position of the organ of Corti (OC). A 4.8 Hz acoustic bias tone was used to displace the OC, while the relative amplitude and phase of distortion products evoked by a single tone [most often 500 Hz, 90 dB SPL (sound pressure level)] or two simultaneously presented tones (most often 4 kHz and 4.8 kHz, 80 dB SPL) were monitored. Electrical responses recorded from the round window, scala tympani and scala media of the basal turn, and acoustic emissions in the ear canal were simultaneously measured and compared during the bias. Bias-induced changes in the distortion products were similar to those predicted from computer models of a saturating transducer with a first-order Boltzmann distribution. Our results suggest that biased DPOAEs can be used to non-invasively estimate the OC displacement, producing a measurement equivalent to the transducer operating point obtained via Boltzmann analysis of the basal turn CM. Low-frequency biased DPOAEs might provide a diagnostic tool to objectively diagnose abnormal displacements of the OC, as might occur with endolymphatic hydrops.

Displacements of the organ of Corti by gel injections into the cochlear apex

In order to transduce sounds efficiently, the stereocilia of hair cells in the organ of Corti must be positioned optimally. Mechanical displacements, such as pressure differentials across the organ caused by endolymphatic hydrops, may impair sensitivity. Studying this phenomenon has been limited by the technical difficulty of inducing sustained displacements of stereocilia in vivo. We have found that small injections (0.5–2 μL) of Healon gel into the cochlear apex of guinea pigs produced sustained changes of endocochlear potential (EP), summating potential (SP) and transducer operating point (OP) in a manner consistent with a mechanically-induced position change of the organ of Corti in the basal turn. Induced changes immediately recovered when injection ceased. In addition, effects of low-frequency bias tones on EP, SP and OP were enhanced during the injection of gel and remained hypersensitive after injection ceased. This is thought to result from the viscous gel mechanically limiting pressure shunting through the helicotrema. Cochlear microphonics measured as frequency was varied showed enhancement below 100 Hz but most notably in the sub-auditory range. Sensitivity to low-frequency biasing was also enhanced in animals with surgically-induced endolymphatic hydrops, suggesting that obstruction of the perilymphatic space by hydrops could contribute to the pathophysiology of this condition.

Effects of low-frequency biasing on spontaneous otoacoustic emissions: Frequency modulation

It was previously reported that low-frequency biasing of cochlear structures can suppress and modulate the amplitudes of spontaneous otoacoustic emissions (SOAEs) in humans [Bian, L. and Watts, K. L. (2008). "Effects of low-frequency biasing on spontaneous otoacoustic emissions: Amplitude modulation," J. Acoust. Soc. Am. 123, 887-898]. In addition to amplitude modulation, the bias tone produced an upward shift of the SOAE frequency and a frequency modulation. These frequency effects usually occurred prior to significant modifications of SOAE amplitudes and were dependent on the relative strength of the bias tone and a particular SOAE. The overall SOAE frequency shifts were usually less than 2%. A quasistatic modulation pattern showed that biasing in either positive or negative pressure direction increased SOAE frequency. The instantaneous SOAE frequency revealed a "W-shaped" modulation pattern within one biasing cycle. The SOAE frequency was maximal at the biasing extremes and minimized at the zero crossings of the bias tone. The temporal modulation of SOAE frequency occurred with a short delay. These static and dynamic effects indicate that modifications of the mechanical properties of the cochlear transducer could underlie the frequency shift and modulation. These biasing effects are consistent with the suppression and modulation of SOAE amplitude due to shifting of the cochlear transducer operating point.

Effects of low-frequency biasing on spontaneous otoacoustic emissions: amplitude modulation.

The dynamic effects of low-frequency biasing on spontaneous otoacoustic emissions (SOAEs) were studied in human subjects under various signal conditions. Results showed a combined suppression and modulation of the SOAE amplitudes at high bias tone levels. Ear-canal acoustic spectra demonstrated a reduction in SOAE amplitude and growths of sidebands while increasing the bias tone level. These effects varied depending on the relative strength of the bias tone to a particular SOAE. The SOAE magnitudes were suppressed when the cochlear partition was biased in both directions. This quasi-static modulation pattern showed a shape consistent with the first derivative of a sigmoid-shaped nonlinear function. In the time domain, the SOAE amplitudes were modulated with the instantaneous phase of the bias tone. For each biasing cycle, the SOAE envelope showed two peaks each corresponded to a zero crossing of the bias tone. The temporal modulation patterns varied systematically with the level and frequency of the bias tone. These dynamic behaviors of the SOAEs are consistent with the shifting of the operating point along the nonlinear transducer function of the cochlea. The results suggest that the nonlinearity in cochlear hair cell transduction may be involved in the generation of SOAEs.

Low-frequency modulation of distortion product otoacoustic emissions in humans

Low-frequency modulation of distortion product otoacoustic emissions (DPOAEs) was measured from the human ears. In the frequency domain, increasing the bias tone level resulted in a suppression of the cubic difference tone (CDT) and an increase in the magnitudes of the modulation sidebands. Higher-frequency bias tones were more efficient in producing the suppression and modulation. Quasi-static modulation patterns were derived from measuring the CDT amplitude at the peaks and troughs of bias tones with various amplitudes. The asymmetric bell-shaped pattern resembled the absolute value of the third derivative of a nonlinear cochlear transducer function. Temporal modulation patterns were obtained from inverse FFT of the spectral contents around the DPOAE. The period modulation pattern, averaged over multiple bias tone cycles, showed two CDT peaks each correlated with the zero-crossings of the bias tone. The typical period modulation pattern varied and the two CDT peaks emerged with the reduction in bias tone level. The present study replicated the previous experimental results in gerbils. This noninvasive technique is capable of revealing the static position and dynamic motion of the cochlear partition. Moreover, the results of the present study suggest that this technique could potentially be applied in the differential diagnosis of cochlear pathologies.

Spectral fine-structures of low-frequency modulated distortion product otoacoustic emissions

Biasing of the cochlear partition with a low-frequency tone can produce an amplitude modulation of distortion product otoacoustic emissions (DPOAEs) in gerbils. In the time domain, odd- versus even-order DPOAEs demonstrated different modulation patterns depending on the bias tone phase. In the frequency domain, multiple sidebands are presented on either side of each DPOAE component. These sidebands were located at harmonic multiples of the biasing frequency from the DPOAE component. For odd-order DPOAEs, sidebands at the even-multiples of the biasing frequency were enhanced, while for even-order DPOAEs, the sidebands at the odd-multiples were elevated. When a modulation in DPOAE magnitude was presented, the magnitudes of the sidebands were enhanced and even greater than the DPOAEs. The amplitudes of these sidebands varied with the levels of the bias tone and two primary tones. The results indicate that the maximal amplitude modulations of DPOAEs occur at a confined bias and primary level space. This can provide a guide for optimal selections of signal conditions for better recordings of low-frequency modulated DPOAEs in future research and applications. Spectral fine-structure and its unique relation to the DPOAE modulation pattern may be useful for direct acquisition of cochlear transducer nonlinearity from a simple spectral analysis.

Cochlear compression: Effects of low-frequency biasing on quadratic distortion product otoacoustic emission

Distortion product otoacoustic emissions (DPOAEs) are generated from the nonlinear transduction n cochlear outer hair cells. The transducer function demonstrating a compressive nonlinearity can be estimated from low-frequency modulation of DPOAEs. Experimental results from the gerbils showed that the magnitude of quadratic difference tone (QDT, f2-f1) was either enhanced or suppressed depending on the phase of the low-frequency bias tone. Within one period of the bias tone, QDT magnitudes exhibited two similar modulation patterns, each resembling the absolute value of the second derivative of the transducer function. In the time domain, the center notches of the modulation patterns occurred around the zero crossings of the bias pressure, whereas peaks corresponded to the increase or decrease in bias pressure. Evaluated with respect to the bias pressure, modulated QDT magnitude displayed a double-modulation pattern marked by a separation of the center notches. Loading/unloading of the cochlear transducer or rise/fall in bias pressure shifted the center notch to positive or negative sound pressures, indicating a mechanical hysteresis. These results suggest that QDT arises from the compression that coexists with the active hysteresis in cochlear transduction. Modulation of QDT magnitude reflects the dynamic regulation of cochlear transducer gain and compression.

Constructing a cochlear transducer function from the summating potential using a low-frequency bias tone

A new method is developed to construct a cochlear transducer function using modulation of the summating potential (SP), a dc component of the electrical response of the cochlea to a sinusoid. It is mathematically shown that the magnitude of the SP is determined by the even-order terms of the power series representing a nonlinear function. The relationship between the SP magnitudes and the second derivative of the transducer function was determined by using a low-frequency bias tone to position a high-frequency probe tone at different places along the cochlear transducer function. Two probe tones (6 kHz and 12 kHz) ranging from 70 to 90 dB SPL and a 25-Hz bias tone at 130 dB SPL were simultaneously presented. Electric responses from the cochlea were recorded by an electrode placed at the round window to obtain the SP magnitudes. The experimental results from eight animals demonstrated that the SP magnitudes as a function of bias levels are essentially proportional to the second derivative of a sigmoidal Boltzmann function. This suggests that the low-frequency modulated SP amplitude can be used to construct a cochlear transducer function.

Cochlear hysteresis: observation with low-frequency modulated distortion product otoacoustic emissions.

Low-frequency modulation of distortion product otoacoustic emissions (DPOAEs) can be used to estimate a nonlinear transducer function (fTr) of the cochlea. From gerbils, DPOAEs were measured while presenting a high-level bias tone. Within one period of the bias tone, the magnitudes of the cubic difference tone (CDT, 2f1 - f2) demonstrated two similar modulation patterns (MPs) each resembled the absolute value of the third derivative of the fTr. The center peaks of the MPs occurred at positive sound pressures for rising in bias pressure or loading of the cochlear transducer, and more negative pressures while decreasing bias amplitude or unloading. The corresponding fTr revealed a sigmoid-shaped hysteresis loop with counterclockwise traversal. Physiologic indices that characterized the double MP varied with primary level. A Boltzmann-function-based model with negative damping as a feedback component was proposed. The model was able to replicate the experimental results. Model parameters that fit to the CDT data indicated higher transducer gain and more prominent feedback role at lower primary levels. Both physiologic indices and model parameters suggest that the cochlear transducer dynamically changes its gain with input signal level and the nonlinear mechanism is a time-dependent feedback process.

Deriving a cochlear transducer function from low-frequency modulation of distortion product otoacoustic emissions.

In this paper, a new method is introduced to derive a cochlear transducer function from measuring distortion product otoacoustic emissions (DPOAEs). It is shown that the cubic difference tone (CDT, 2f1-f2) is produced from the odd-order terms of a power series that approximates a nonlinear function characterizing cochlear transduction. Exploring the underlying mathematical formulation, it is found that the CDT is proportional to the third derivative of the transduction function when the primary levels are sufficiently small. DPOAEs were measured from nine gerbils in response to two-tone signals biased by a low-frequency tone with different amplitudes. The CDT magnitude was obtained at the peak regions of the bias tone. The results of the experiment demonstrated that the shape of the CDT magnitudes as a function of bias levels was similar to the absolute value of the third derivative of a sigmoidal function. A second-order Boltzmann function was derived from curve fitting the CDT data with an equation that represents the third derivative of the Boltzmann function. Both the CDT-bias function and the derived nonlinear transducer function showed effects of primary levels. The results of the study indicate that the low-frequency modulated DPOAEs can be used to estimate the cochlear transducer function.