Cortical responses to the 2f1-f2 combination tone measured indirectly using magnetoencephalography

The simultaneous presentation of two tones with frequencies f(1) and f(2) causes the perception of several combination tones in addition to the original tones. The most prominent of these are at frequencies f(2)-f(1) and 2f(1)-f(2). This study measured human physiological responses to the 2f(1)-f(2) combination tone at 500 Hz caused by tones of 750 and 1000 Hz with intensities of 65 and 55 dB SPL, respectively. Responses were measured from the cochlea using the distortion product otoacoustic emission (DPOAE), and from the auditory cortex using the 40-Hz steady-state magnetoencephalographic (MEG) response. The perceptual response was assessed by having the participant adjust a probe tone to cause maximal beating ("best-beats") with the perceived combination tone. The cortical response to the combination tone was evaluated in two ways: first by presenting a probe tone with a frequency of 460 Hz at the perceptual best-beats level, resulting in a 40-Hz response because of interaction with the combination tone at 500 Hz, and second by simultaneously presenting two f(1) and f(2) pairs that caused combination tones that would themselves beat at 40 Hz. The 2f(1)-f(2) DPOAE in the external auditory canal had a level of 2.6 (s.d. 12.1) dB SPL. The 40-Hz MEG response in the contralateral cortex had a magnitude of 0.39 (s.d. 0.1) nA m. The perceived level of the combination tone was 44.8 (s.d. 11.3) dB SPL. There were no significant correlations between these measurements. These results indicate that physiological responses to the 2f(1)-f(2) combination tone occur in the human auditory system all the way from the cochlea to the primary auditory cortex. The perceived magnitude of the combination tone is not determined by the measured physiological response at either the cochlea or the cortex.     

Asymmetry of masking between complex tones and noise: the role of temporal structure and peripheral compression

Thresholds for the detection of harmonic complex tones in noise were measured as a function of masker level. The rms level of the masker ranged from 40 to 70 dB SPL in 10-dB steps. The tones had a fundamental frequency (F0) of 62.5 or 250 Hz, and components were added in either cosine or random phase. The complex tones and the noise were bandpass filtered into the same frequency region, from the tenth harmonic up to 5 kHz. In a different condition, the roles of masker and signal were reversed, keeping all other parameters the same; subjects had to detect the noise in the presence of a harmonic tone masker. In both conditions, the masker was either gated synchronously with the 700-ms signal, or it started 400 ms before and stopped 200 ms after the signal. The results showed a large asymmetry in the effectiveness of masking between the tones and noise. Even though signal and masker had the same bandwidth, the noise was a more effective masker than the complex tone. The degree of asymmetry depended on F0, component phase, and the level of the masker. The maximum difference between masked thresholds for tone and noise was about 28 dB; this occurred when the F0 was 62.5 Hz, the components were in cosine phase, and the masker level was 70 dB SPL. In most conditions, the growth-of-masking functions had slopes close to 1 (on a dB versus dB scale). However, for the cosine-phase tone masker with an F0 of 62.5 Hz, a 10-dB increase in masker level led to an increase in masked threshold of the noise of only 3.7 dB, on average. We suggest that the results for this condition are strongly affected by the active mechanism in the cochlea.     

Cochlear traveling-wave amplification, suppression, and beamforming probed using noninvasive calibration of intracochlear distortion sources

Originally developed to estimate the power gain of the cochlear amplifier, so-called "Allen-Fahey" and related experiments have proved invaluable for probing the mechanisms of wave generation and propagation within the cochlea. The experimental protocol requires simultaneous measurement of intracochlear distortion products (DPs) and ear-canal otoacoustic emissions (DPOAEs) under tightly controlled conditions. To calibrate the intracochlear response to the DP, Allen-Fahey experiments traditionally employ invasive procedures such as recording from auditory-nerve fibers or measuring basilar-membrane velocity. This paper describes an alternative method that allows the intracochlear distortion source to be calibrated noninvasively. In addition to the standard pair of primary tones used to generate the principal DP the noninvasive method employs a third, fixed tone to create a secondary DPOAE whose amplitude and phase provide a sensitive assay of the intracochlear value of the principal DP near its characteristic place. The method is used to perform noninvasive Allen-Fahey experiments in cat and shown to yield results in quantitative agreement with the original, auditory-nerve-based paradigm performed in the same animal. Data obtained using a suppression-compensated variation of the noninvasive method demonstrate that neither traveling-wave amplification nor two-tone suppression constitutes the controlling influence in DPOAE generation at close frequency ratios. Rather, the dominant factor governing the emission magnitude appears to be the variable directionality of the waves radiated by the distortion-source region, which acts as a distortion beamformer tuned by the primary frequency ratio.     

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.     

A second,low-frequency mode of vibration in the intact mammalian cochlea

The mammalian cochlea is a structure comprising a number of components connected by elastic elements. A mechanical system of this kind is expected to have multiple normal modes of oscillation and associated resonances. The guinea pig cochlear mechanics was probed using distortion components generated in the cochlea close to the place of overlap between two tones presented simultaneously. Otoacoustic emissions at frequencies of the distortion components were recorded in the ear canal. The phase behavior of the emissions reveals the presence of a nonlinear resonance at a frequency about a half octave below that of the high-frequency primary tone. The location of the resonance is level dependent and the resonance shifts to lower frequencies with increasing stimulus intensity. This resonance is thought to be associated with the tectorial membrane. The resonance tends to minimize input to the cochlear receptor cells at frequencies below the high-frequency primary and increases the dynamic load to the stereocilia of the receptor cells at the primary frequency when the tectorial membrane and reticular lamina move in counterphase.     

Hybrid measurement of auditory steady-state responses and distortion product otoacoustic emissions using an amplitude-modulated primary tone

A maximum auditory steady-state response (ASSR) amplitude is yielded when the ASSR is elicited by an amplitude-modulated tone (f(c)) with a fixed modulation frequency (f(m) = 40 Hz), whereas the maximum distortion product otoacoustic emission (DPOAE) level is yielded when the DPOAE is elicited using a fixed frequency ratio of the primary tones (f2/f1 = 1.2). When eliciting the DPOAE and ASSR by the same tone pair, optimal stimulation is present for either DPOAE or ASSR and thus adequate simultaneous DPOAE/ASSR measurement is not possible across test frequency f2 or f(c), respectively. The purpose of the present study was to determine whether the ASSR and DPOAE can be measured simultaneously without notable restrictions using a DPOAE stimulus setting in which one primary tone is amplitude modulated. A DPOAE of frequency 2f1-f2 and ASSR of modulation frequency 41 Hz were measured in ten normal hearing subjects at a test frequency between 0.5 and 8 kHz (f2 = f(c)). The decrease in the DPOAE level and the loss in ASSR amplitude during hybrid mode stimulation amounted, on average, to only 2.60 dB [standard deviation (SD) = 1.38 dB] and 1.83 dB (SD = 2.38 dB), respectively. These findings suggest simultaneous DPOAE and ASSR measurements to be feasible across all test frequencies when using a DPOAE stimulus setting where the primary tone f2 is amplitude modulated.     

The mechanical waveform of the basilar membrane. IV. Tone and noise stimuli

Analysis of mechanical cochlear responses to wide bands of random noise clarifies many effects of cochlear nonlinearity. The previous paper [de Boer and Nuttall, J. Acoust. Soc. Am. 107, 1497-1507 (2000)] illustrates how closely results of computations in a nonlinear cochlear model agree with responses from physiological experiments. In the present paper results for tone stimuli are reported. It was found that the measured frequency response for pure tones differs little from the frequency response associated with a noise signal. For strong stimuli, well into the nonlinear region, tones have to be presented at a specific level with respect to the noise for this to be true. In this report the nonlinear cochlear model originally developed for noise analysis was modified to accommodate pure tones. For this purpose the efficiency with which outer hair cells modify the basilar-membrane response was made into a function of cochlear location based on local excitation. For each experiment, the modified model is able to account for the experimental findings, within 1 or 2 dB. Therefore, the model explains why the type of filtering that tones undergo in the cochlea is essentially the same as that for noise signals (provided the tones are presented at the appropriate level).     

Acoustic distortion in the ear canal. I. Cubic difference tones: effects of acute noise injury

Acoustic emissions in the form of cubic difference tones (CDT's), 2f1-f2, were measured in the ear canals of gerbils and cats. The state of the cochlea was manipulated by means of acute exposure to noise and was monitored with the aid of the whole-nerve response to tone pips. The resulting shifts in the levels of emissions generated by pairs of primary tones of equal intensity were then compared to the corresponding threshold shifts of the whole-nerve response across frequency. Data obtained from normal ears before injury indicate that the absolute thresholds of the whole-nerve responses across frequency are not necessarily good predictors of the absolute levels of CDT emissions generated by 70- and 80-dB SPL primaries. While high emission levels were often linked to low whole-nerve thresholds in pre-exposed ears, instances of animals with sensitive whole-nerve thresholds coupled with very weak emissions were also found. Conversely, animals with poor whole-nerve thresholds (shifted by up to 30 dB) could occasionally have high levels of emissions. After acute noise injury, however, the shifts of emission levels as a function of the center frequency of the primary-tone pair largely corresponded to the threshold shifts seen in the whole-nerve response. In other words, the temporary level shift of an acoustic emission largely reflected the acute change to a specific cochlear region associated with the primary frequencies.     

Ear canal acoustic distortion at 2f1-f2 from human ears: relation to other emissions and perceived combination tones

Two aspects of the intermodulation distortion product at 2f1-f2 generated by normal human ears and measured acoustically in the ear canal were studied: (1) its relation to tone-evoked and spontaneous otoacoustic emissions, and (2) its relation to the perceived combination tone at the same frequency. With regard to (1), substantial differences among ears in the detectability of emissions were observed; ears tended to exhibit all or none of the emission types that were sought. Within ears possessing emissions, the magnitudes of tone-evoked emissions and acoustic distortion showed a similar dependence on frequency. With regard to (2), a three-primary-tone stimulus was employed to ask whether the ear canal acoustic distortion tone is canceled under the same stimulus conditions that produce perceptual cancellation. Simultaneous cancellation of perceptual and acoustic distortion was produced rarely. Results are interpreted qualitatively with a model in which primary tones produce distortion at their interaction region within the cochlea; this distortion propagates to the distortion-frequency place where it mediates perception. This same distortion wave produces emission components at additional locations, including the primary-tone interaction region, which sum vectorially to mediate the emitted acoustic distortion product.     

The perception of complex tones by a false killer whale (Pseudorca crassidens)

Complex tonal whistles are frequently produced by some odontocete species. However, no experimental evidence exists regarding the detection of complex tones or the discrimination of harmonic frequencies by a marine mammal. The objectives of this investigation were to examine the ability of a false killer whale to discriminate pure tones from complex tones and to determine the minimum intensity level of a harmonic tone required for the whale to make the discrimination. The study was conducted with a go/no-go modified staircase procedure. The different stimuli were complex tones with a fundamental frequency of 5 kHz with one to five harmonic frequencies. The results from this complex tone discrimination task demonstrated: (1) that the false killer whale was able to discriminate a 5 kHz pure tone from a complex tone with up to five harmonics, and (2) that discrimination thresholds or minimum intensity levels exist for each harmonic combination measured. These results indicate that both frequency level and harmonic content may have contributed to the false killer whale's discrimination of complex tones.     

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.     

Thresholds for hearing mistuned partials as separate tones in harmonic complexes

When a low harmonic in a harmonic complex tone is mistuned from its harmonic value by a sufficient amount it is heard as a separate tone, standing out from the complex as a whole. This experiment estimated the degree of mistuning required for this phenomenon to occur, for complex tones with 10 or 12 equal-amplitude components (60 dB SPL per component). On each trial the subject was presented with a complex tone which either had all its partials at harmonic frequencies or had one partial mistuned from its harmonic frequency. The subject had to indicate whether he heard a single complex tone with one pitch or a complex tone plus a pure tone which did not "belong" to the complex. An adaptive procedure was used to track the degree of mistuning required to achieve a d' value of 1. Threshold was determined for each ot the first six harmonics of each complex tone. In one set of conditions stimulus duration was held constant at 410 ms, and the fundamental frequency was either 100, 200, or 400 Hz. For most conditions the thresholds fell between 1% and 3% of the harmonic frequency, depending on the subject. However, thresholds tended to be greater for the first two harmonics of the 100-Hz fundamental and, for some subjects, thresholds increased for the fifth and sixth harmonics. In a second set of conditions fundamental frequency was held constant at 200 Hz, and the duration was either 50, 110, 410, or 1610 ms. Thresholds increased by a factor of 3-5 as duration was decreased from 1610 ms to 50 ms. The results are discussed in terms of a hypothetical harmonic sieve and mechanisms for the formation of perceptual streams.     

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.     

Near equivalence of human click-evoked and stimulus-frequency otoacoustic emissions

Otoacoustic emissions (OAEs) evoked by broadband clicks and by single tones are widely regarded as originating via different mechanisms within the cochlea. Whereas the properties of stimulus-frequency OAEs (SFOAEs) evoked by tones are consistent with an origin via linear mechanisms involving coherent wave scattering by preexisting perturbations in the mechanics, OAEs evoked by broadband clicks (CEOAEs) have been suggested to originate via nonlinear interactions among the different frequency components of the stimulus (e.g., intermodulation distortion). The experiments reported here test for bandwidth-dependent differences in mechanisms of OAE generation. Click-evoked and stimulus-frequency OAE input/output transfer functions were obtained and compared as a function of stimulus frequency and intensity. At low and moderate intensities human CEOAE and SFOAE transfer functions are nearly identical. When stimulus intensity is measured in "bandwidth-compensated" sound-pressure level (cSPL), CEOAE and SFOAE transfer functions have equivalent growth functions at fixed frequency and equivalent spectral characteristics at fixed intensity. This equivalence suggests that CEOAEs and SFOAEs are generated by the same mechanism. Although CEOAEs and SFOAEs are known by different names because of the different stimuli used to evoke them, the two OAE "types" are evidently best understood as members of the same emission family.     

In search of basal distortion product generators

The 2f1-f2 distortion product otoacoustic emission (DPOAE) is thought to arise primarily from the complex interaction of components that come from two different cochlear locations. Such distortion has its origin in the nonlinear interaction on the basilar membrane of the excitation patterns resulting from the two stimulus tones, f1 and f2. Here we examine the spatial extent of initial generation of the 2f1-f2 OAE by acoustically traumatizing the base of the cochlea and so eliminating the contribution of the basal region of the cochlea to the generation of 2f1-f2. Explicitly, amplitude-modulated, or continuously varying in level, stimulus tones with f2/f1= 1.2 and f2 =8000-8940 Hz were used to generate the 2f1-f2 DPOAE in guinea pig before and after acoustically traumatizing the basal region of the cochlea (the origin of any basal-to-f2 distortion product generators). It was found, based on correlation analysis, that there does not appear to be a basal-to-f2 distortion product generation mechanism contributing significantly to the guinea pig 2f1-f2 OAE up to L1 = 80 dB sound pressure level (SPL).     

Louder sounds can produce less forward masking: effects of component phase in complex tones

The influence of the degree of envelope modulation and periodicity on the loudness and effectiveness of sounds as forward maskers was investigated. In the first experiment, listeners matched the loudness of complex tones and noise. The tones had a fundamental frequency (F0) of 62.5 or 250 Hz and were filtered into a frequency range from the 10th harmonic to 5000 Hz. The Gaussian noise was filtered in the same way. The components of the complex tones were added either in cosine phase (CPH), giving a large crest factor, or in random phase (RPH), giving a smaller crest factor. For each F0, subjects matched the loudness between all possible stimulus pairs. Six different levels of the fixed stimulus were used, ranging from about 30 dB SPL to about 80 dB SPL in 10-dB steps. Results showed that, at a given overall level, the CPH and the RPH tones were louder than the noise, and that the CPH tone was louder than the RPH tone. The difference in loudness was larger at medium than at low levels and was only slightly reduced by the addition of a noise intended to mask combination tones. The differences in loudness were slightly smaller for the higher than for the lower F0. In the second experiment, the stimuli with the lower F0s were used as forward maskers of a 20-ms sinusoid, presented at various frequencies within the spectral range of the maskers. Results showed that the CPH tone was the least effective forward masker, even though it was the loudest. The differences in effectiveness as forward maskers depended on masker level and signal frequency; in order to produce equal masking, the level of the CPH tone had to be up to 35 dB above that of the RPH tone and the noise. The implications of these results for models of loudness are discussed and a model is presented based on neural activity patterns in the auditory nerve; this predicts the general pattern of loudness matches. It is suggested that the effects observed in the experiments may have been influenced by two factors: cochlear compression and suppression.     

Effect of masker harmonicity on informational masking

Detection thresholds for a tone in an unfamiliar tonal pattern can be greatly elevated under conditions of masker uncertainty [Neff and Green, Percept. Psychophys. 41, 409-415 (1987); Oh and Lutfi, J. Acoust. Soc. Am. 101, 3148 (1997)]. The present experiment was undertaken to determine whether harmonicity of masker tones can reduce the detrimental effect of masker uncertainty. Inharmonic maskers were comprised of m=2-49 frequency components selected at random on each presentation within 100-10000 Hz, excluding frequencies between 920-1080. Harmonic maskers were comprised of frequency components selected at random within this same range, but constrained to have a fundamental frequency of 200 Hz. For inharmonic maskers the signal was a 1000-Hz tone. For harmonic-maskers the signal was a tone whose frequency was either harmonically (1000 Hz) or inharmonically (1047 Hz) related to the masker. In all conditions the amount of masking was greatest for m = 20-40 components. At this point, harmonic maskers with harmonic signal produced an average of 9-12 dB less masking than inharmonic maskers. Harmonic maskers with inharmonic signal produced an average of 16-20 dB less masking.     

Evidence against an effect of grouping by spectral regularity on the perception of virtual pitch

Two experiments investigated the role of the regularity of the frequency spacing of harmonics, as a separate factor from harmonicity, on the perception of the virtual pitch of a harmonic series. The first experiment compared the shifts produced by mistuning the 3rd, 4th, and 5th harmonics in the pitch of two harmonic series: the odd-H and the all-H tones. The odd-H tone contained odd harmonics 1 to 11, plus the 4th harmonic; the all-H tone contained harmonics 1 to 12. Both tones had a fundamental frequency of 155 Hz. Pitch shifts produced by mistuning the 3rd harmonic, but not the 4th and 5th harmonics, were found to be significantly larger for the odd-H tone than for the all-H tone. This finding was consistent with the idea that grouping by spectral regularity affects pitch perception since an odd harmonic made a larger contribution than an adjacent even harmonic to the pitch of the odd-H tone. However, an alternative explanation was that the 3rd mistuned harmonic produced larger pitch shifts within the odd-H tone than the 4th mistuned harmonic because of differences in the partial masking of these harmonics by adjacent harmonics. The second experiment tested these explanations by measuring pitch shifts for a modified all-H tone in which each mistuned odd harmonic was tested in the presence of the 4th harmonic, but in the absence of its other even-numbered neighbor. The results showed that, for all mistuned harmonics, pitch shifts for the modified all-H tone were not significantly different from those for the odd-H tone. These findings suggest that the harmonic relations among frequency components, rather than the regularity of their frequency spacing, is the primary factor for the perception of the virtual pitch of complex sounds.     

Inner hair cell responses to the 2f1-f2 intermodulation distortion product

Recordings of dc and ac receptor potentials from pigmented guinea pig inner hair cells indicate strong responses to the 2f1-f2 intermodulation tone when f1 and f2 are greater than the hair cell characteristic frequency and do not cause a response when given individually. The effective magnitude of this cubic distortion product (CDP) was about 25-30 dB below equal sound level primaries over a 20-30-dB range of their sound levels. The relative strength of the CDP declined at a rate greater than 180-dB/oct separation of the primaries. When magnitude of f1 or f2 was held constant, the growth of CDP was nonmonotonic, exhibiting a distinct maximum. With a constant level of f1 or f2, optimal CDP was produced when the level of f2 was 10-15 dB greater than f1. Strong two-tone suppression from the primaries has a role in shaping the CDP growth. The ac receptor potentials of the CDP show a 150 degrees-200 degrees phase shift when the primaries are increased over a 50-dB range. These results support the hypothesis of a propagated CDP in the cochlea and are consistent with the major features of related studies of human psychoacoustic experiments, afferent nerve neural rate functions, and ear canal distortion products.     

突变截面驻波管和极高纯净驻波场的实验研究

突变截面驻波管属于失谐驻波管,即其高阶共振频率不是一阶共振频率的整数倍。通过对STAS的优化设计,利用STAS的失谐性质在一阶和二阶共振频率下激励分别获得了180 dB和177 dB的极高纯净驻波声场。尽管声压级已经很高,但在接下来的对一阶和二阶共振频率激励下的声波波形畸变和谐波饱和情况进行的实验研究中仍然没有观察到谐波饱和现象。与此同时,对三阶共振频率激励下的声场进行了实验研究,由于三阶共振频率激励下的大振幅非线性声场的二次谐波频率接近六阶共振频率,在声压级达到170 dB时观测到了三阶共振频率激励下的声波波形畸变和谐波饱和现象。