Multitone Complex Research Articles

Crest factor minimization of the multitone complex signal

In this paper we present the most effective algorithm for a crest factor minimization of multitone complex signals. The approach includes complex root selection of the amplitude function for the phase function rebuilding and then Gerchberg-Saxton algorithm application for a fine phase tuning. Phase optimization of a finite sum is fulfilled in case of the complex harmonics with equal amplitudes and equispaced frequencies. We compare our results with the earlier calculated best ones and remark its superiority. The main features of the approach are highlighted to underline the stability and performance capabilities for the global minimum achievement. Finally, we introduce some amplitude functions of multitone signals with lower crest factor than previously reported in the literature.

Echoes from Sensory Entrainment in Auditory Working Memory for Pitch.

Ongoing neural oscillations reflect cycles of excitation and inhibition in local neural populations, with individual neurons being more or less likely to fire depending upon the oscillatory phase. As a result, the oscillations could determine whether or not a sound is perceived and/or whether its neural representation enters into later processing stages. While empirical support for this idea has come from sound detection studies, large gaps in knowledge still exist regarding memory for sound events. In the current study, it was investigated how sensory entrainment impacts the fidelity of working memory representations for pitch. In two separate experiments, an 8 Hz amplitude modulated (AM) entraining stimulus was presented prior to a multitone complex having an f0 between 270 and 715 Hz. This "target" sound could be presented at phases from 0 to 2π radians in relation to the previous AM. After a retention interval of 4 s (Experiment 1; n = 26) or 2 s (Experiment 2; n = 28), listeners were tasked to reproduce the target sound's pitch by moving their finger along the horizontal axis of a response pad. It was hypothesized that if entrainment modulates auditory working memory fidelity, reproductions of a target's pitch would be more accurate and precise when targets were presented in phase with the entrainment. Cosine fits of the average data for both experiments showed a significant entrainment "echo" in the accuracy of pitch matches. There was no apparent echo in the matching precision. Fitting of the individual data accuracy showed that the optimal phase was consistent across individuals, aligning near the next AM peak had the AM continued. The results show that sensory entrainment modulates auditory working memory in addition to stimulus detection, consistent with the proposal that ongoing neural oscillatory activity modulates higher-order auditory processes.

Not fully remembered, but not forgotten: interfering sounds worsen but do not eliminate the representation of pitch in working memory.

Recent research has begun measuring auditory working memory with a continuous adjustment task in which listeners adjust attributes of a sound to match a stimulus presented earlier. This approach captures auditory memory's continuous nature better than standard change detection paradigms that collect binary ("same or different") memory measurements. In two experiments, we assessed the impact of different interference stimuli (multitone complexes vs. white noise vs. silence) on the precision and accuracy of participants' reproductions of pitch from memory. Participants were presented with a target multitone complex stimulus followed by eight successive interference signals. Across trials, these signals alternated between additional multitone complexes, randomly generated white noise samples, or (in Experiment 2) silence. This was followed by a response period where participants adjusted the pitch of a response stimulus using a MIDI touchpad to match the target. Experiment 1 found a significant effect of interference type on performance, with tone interference signals producing the greatest impairments to participants' accuracy and precision compared to white noise. Interestingly, it also found a compression in the participants' responses, with overestimations of low-frequency targets and underestimations for high-frequency targets. Experiment 2 replicated results from Experiment 1, with an additional silence condition showing the best performance, suggesting that non-tonal signals also generate interference. In general, results support a shared resource model of working memory with a limited capacity that can be flexibly allocated to hold items in memory with varying levels of fidelity. Interference does not appear to knock items out of a fixed precision slot, but rather robs a portion of capacity from stored items.

Learning to detect a tone in unpredictable noise

Eight normal-hearing listeners practiced a tone-detection task in which a 1-kHz target was masked by a spectrally unpredictable multitone complex. Consistent learning was observed, with mean masking decreasing by 6.4 dB over five sessions (4500 trials). Reverse-correlation was used to estimate how listeners weighted each spectral region. Weight-vectors approximated the ideal more closely after practice, indicating that listeners were learning to attend selectively to the task relevant information. Once changes in weights were accounted for, no changes in internal noise (psychometric slope) were observed. It is concluded that this task elicits robust learning, which can be understood primarily as improved selective attention.

No Need for Templates in the Auditory Enhancement Effect

The audibility of a target tone in a multitone background masker is enhanced by the presentation of a precursor sound consisting of the masker alone. There is evidence that precursor-induced neural adaptation plays a role in this perceptual enhancement. However, the precursor may also be strategically used by listeners as a spectral template of the following masker to better segregate it from the target. In the present study, we tested this hypothesis by measuring the audibility of a target tone in a multitone masker after the presentation of precursors which, in some conditions, were made dissimilar to the masker by gating their components asynchronously. The precursor and the following sound were presented either to the same ear or to opposite ears. In either case, we found no significant difference in the amount of enhancement produced by synchronous and asynchronous precursors. In a second experiment, listeners had to judge whether a synchronous multitone complex contained exactly the same tones as a preceding precursor complex or had one tone less. In this experiment, listeners performed significantly better with synchronous than with asynchronous precursors, showing that asynchronous precursors were poorer perceptual templates of the synchronous multitone complexes. Overall, our findings indicate that precursor-induced auditory enhancement cannot be fully explained by the strategic use of the precursor as a template of the following masker. Our results are consistent with an explanation of enhancement based on selective neural adaptation taking place at a central locus of the auditory system.

Evaluation of similarity effects in informational masking

The degree of similarity between signal and masker in informational masking paradigms has been hypothesized to contribute to informational masking. The present study attempted to quantify "similarity" using a discrimination task. Listeners discriminated various signal stimuli from a multitone complex and then detected the presence of those signals embedded in a multitone informational masker. Discriminability negatively correlated with detection threshold in an informational masking experiment, indicating that similarity between signal and the masker quality contributed to informational masking. These results suggest a method for specifying relevant signal attributes in informational masking paradigms involving similarity manipulations.

Distortion Product Otoacoustic Emissions Evoked by Tone Complexes

Distortion product otoacoustic emissions (DPOAEs) are traditionally evoked by two-tone stimuli. In this study, emission data from Mongolian gerbils are reported that were obtained with stimuli consisting of six to 10 tones. The stimuli were constructed by replacing one of the tones of a tone pair by a narrowband multitone complex. This produced rich spectra of the ear canal sound pressure in which many of the third-order DPOAEs originated from the interaction of triplets of stimulus components. A careful choice of the stimulus frequencies ensured that none of these DPOAE components coincided. Three groups of DPOAEs are reported, two of which are closely related to DPOAEs evoked by tone pairs. The third group has no two-tone equivalent and only arises when using a multitone stimulus. We analyzed the relation between multitone-evoked DPOAEs and DPOAEs evoked by tone pairs, and explored the new degrees of freedom offered by the multitone paradigm.

Use of perceptual weights to test a model of loudness summation

Leibold et al.[J. Acoust. Soc. Am. 121, 2822-2831 (2007)] examined the perceptual weight subjects assigned to individual components of a multitone complex while performing a loudness-matching task. Weights agreed with the Moore et al. loudness model [J. Audio Eng. Soc. 45, 224-237 (1997)], except when components were widely spaced in frequency. In an effort to account for the data, the just-noticeable-difference (jnd) for intensity discrimination was measured for each component and compared to the weight for that component. The model predicts greater improvement in intensity discrimination with increasing bandwidth than was observed in the data. jnds were not correlated with weights in the widest frequency-spacing condition.

Contributions of individual components to the overall loudness of a multitone complex

The contributions of individual components to the overall loudness of a multitone complex were examined in a two-interval, loudness judgment task. Stimuli were five-tone complexes centered on 1000 Hz, with six different logarithmic frequency spacings, corresponding to bandwidths from 46 to 2119 Hz. Stimuli were presented for 300 ms (10 ms rise/fall). The overall level of the standard complex was fixed at 60 dB SPL (53 dB/component). Levels of the individual components of the comparison complex were selected at random from a rectangular distribution with a range of 20 dB. Perceptual weights were computed by calculating the point-biserial correlation between the difference in the level of each component across the two intervals and the subject's response. When all components fell within the same critical band, weights varied little across components. In contrast, the range of weights increased with increasing frequency separation, with more weight given to the lowest and highest frequency components. A relation between component weight and masked threshold was observed for all but the widest spacing condition. Perceptual weights and masked thresholds were largely in agreement with the loudness model [Moore et al., J. Audio. Eng. Soc. 45, 224-237 (1997)], except at the widest bandwidth.

Use of perceptual weights to test a model of loudness summation

We recently examined the contribution of individual components of a multitone complex to judgments of overall loudness by computing the perceptual weight listeners assign to each component in a loudness-matching task [Leibold et al., J. Acoust. Soc. Am. 117, 2597 (2005)]. Stimuli were five-tone complexes centered on 1000 Hz, with six different logarithmic frequency spacings, ranging from 1.012 to 1.586. When all components fell within the same critical band, weights varied little across components. In contrast, the range of weights increased with increasing frequency separation, with greater weight given to the lowest and highest frequency components. Perceptual weights were largely in agreement with the Moore et al. loudness model [J. Audio Eng. Soc. 45, 224–237 (1997)], except at the widest bandwidth. In the current study we further examined predictions of the loudness model, focusing on the widest frequency-spacing condition. Masked thresholds and jnds for intensity discrimination were measured for each component and were compared to weights. The model predicts more interaction in the widely spaced conditions than simple critical band models, but underestimates the true interactions in conditions where components are widely spaced. Central factors appear to influence loudness, masked thresholds, and intensity discrimination in these conditions. [Work supported by NIH/NIDCD.]

Observer weighting strategies in interaural time-difference discrimination and monaural level discrimination for a multi-tone complex

Two experiments measured listeners' abilities to weight information from different components in a complex of 553, 753, and 953 Hz. The goal was to determine whether or not the ability to adjust perceptual weights generalized across tasks. Weights were measured by binary logistic regression between stimulus values that were sampled from Gaussian distributions and listeners' responses. The first task was interaural time discrimination in which listeners judged the laterality of the target component. The second task was monaural level discrimination in which listeners indicated whether the level of the target component decreased or increased across two intervals. For both experiments, each of the three components served as the target. Ten listeners participated in both experiments. The results showed that those individuals who adjusted perceptual weights in the interaural time experiment could also do so in the monaural level discrimination task. The fact that the same individuals appeared to be analytic in both tasks is an indication that the weights measure the ability to attend to a particular region of the spectrum while ignoring other spectral regions.

Spectral integration and mutliple looks

A fundamental property of hearing is that signals become more detectable as their bandwidth is increased. The rate at which detection improves is reasonably well predicted by models that assume integration of energy at the output of a single auditory filter roughly matched in bandwidth to the signal. This paper tests an alternative account in which detection is mediated by not one but several independent auditory filters whose outputs are combined (multiple-looks model). Listeners detected an increment in the level of a multitone complex whose bandwidth was increased by adding tones at successively higher and lower frequencies. In different conditions the frequencies were fixed (F) or were perturbed at random from trial to trial with the perturbation being the same (PS) or different (PD) for each frequency. The multiple-looks model predicts performance should improve with bandwidth at a faster rate for PD and at a slower rate for PS compared to F; this due to differences in the shared variance in the output of separate auditory filters. The single filter model predicts little effect of frequency perturbation in either case. Individual differences in the results provided partial support for both models. [Work supported by NIDCD.]

Auditory stream segregation with multi-tonal complexes in hearing-impaired listeners

The ability to segregate sounds into different streams was investigated in normally hearing and hearing-impaired listeners. Fusion and fission boundaries were measured using 6-tone complexes with tones equally spaced in log frequency. An ABA–ABA- sequence was used in which A represents a multitone complex ranging from either 250–1000 Hz (low-frequency region) or 1000–4000 Hz (high-frequency region). B also represents a multitone complex with same log spacing as A. Multitonal complexes were 100 ms in duration with 20-ms ramps, and- represents a silent interval of 100 ms. To measure the fusion boundary, the first tone of the B stimulus was either 375 Hz (low) or 1500 Hz (high) and shifted downward in frequency with each progressive ABA triplet until the listener pressed a button indicating that a ‘‘galloping’’ rhythm was heard. When measuring the fusion boundary, the first tone of the B stimulus was 252 or 1030 Hz and shifted upward with each triplet. Listeners then pressed a button when the ‘‘galloping rhythm ended.’’ Data suggest that hearing-impaired subjects have different fission and fusion boundaries than normal-hearing listeners. These data will be discussed in terms of both peripheral and central factors.

On possible cues in profile analysis: identification of the incremented component.

The ability to identify the frequency of the incremented component in a multitone complex was assessed in two conditions, both using the same 11-tone complexes (fixed frequency, equilog spaced, random phases). In the standard-plus-signal complex all components had equal level, except one of the inner nine, which was incremented in level by an in-phase addition of a sinusoid of the same frequency (the signal). The overall level and signal position were randomly varied on each presentation. In the "Standard-absent" condition the standard-plus-signal complex was presented first, and it was followed by a single sinusoid either at the signal frequency or at that of an adjacent component (below or above). In the "Standard-present" condition, a complex with equal-level components (the standard complex) was also presented on each trial, either before or after the standard-plus-signal complex (in random order). These two complexes were followed by the single sinusoid. In both conditions, the subjects had to indicate whether the signal frequency was the same as or different from the frequency of the single sinusoid. In a third condition, the ability to discriminate between the standard complex and the standard-plus-signal complex (with signal frequency uncertainty) was investigated. In all three conditions, thresholds for the increment in level for each signal frequency were estimated by the use of nine independent interleaved adaptive procedures. Results showed that the ability to identify the signal frequency was at least as good as the ability to discriminate between the two complexes. The results suggest that an increase in pitch strength of the incremented component is a possible cue in profile analysis tasks.

Sensitivity to changes in overall level and spectral shape: an evaluation of a channel model.

Two experiments involving level and spectral shape discrimination which test an optimal channel model developed by Durlach et al. [J. Acoust. Soc Am. 80, 63-72 (1986)] are described. The model specifies how the auditory system compares and/or combines intensity information in different frequency channels. In the first experiment, psychometric functions were obtained for the discrimination of changes in level and discrimination of changes in spectral shape for an eight-tone complex sound. A variety of different base spectral shapes were tested. In some conditions, level randomization was introduced to reduce the reliability of across-interval changes in level. Increasing the amount of level variation degraded performance for the level discrimination task but had no effect on the shape discrimination task. In all conditions, sensitivity to changes in spectral shape was superior to sensitivity to changes in level. Consequently, two models of central noise are evaluated in an attempt to explain these results; one in which central noise acts prior to the formation of the likelihood ratio and one in which central noise degrades the likelihood ratio. The former model is more successful in accounting for the data. In a second experiment, the detectability of a level increment to one component of a multitone complex was measured. The frequency content of the complex was varied by systematically removing six components from a 23-component complex. Thresholds were measured for increments at three different signal frequencies. A common trend in the data was that when there was a spectral gap directly above the signal frequency, thresholds were lowest. This result differs from the predictions of a simple channel model, and contrasts with results presented by Green and Berg [Q. J. Exp. Psychol. 43A, 449-458 (1991)].

Efficiency of selective listening by normal‐hearing and hearing‐impaired listeners

A COSS analysis procedure [B. G. J. Berg, J. Acoust. Soc. Am. 88, 149–158 (1990)] was used to estimate the efficiency with which 15 normal‐hearing and 15 hearing‐impaired listeners detected a level increment in a target tone embedded in a multitone complex. The complex was comprised of 6 oct frequencies from 250–8000 Hz and the target tone was selected as either the 250‐, 1000‐, or 4000‐Hz tone. The hearing‐impaired listeners had moderate, sloping, high‐frequency sensorineural hearing impairments. Two efficiency measures were used to account for the listeners’ less than ideal performance on the task; weighting efficiency (ηwgt), which measures how well the listener attends to or weighs the target, and noise efficiency (ηnoise), which accounts for all other factors unrelated to weights. Weighting efficiencies were significantly higher for hearing‐impaired listeners than normal‐hearing listeners for the 4000‐Hz target, which was in the region of hearing loss. No significant ηwgt differences between normal‐hearing and hearing‐impaired listeners were observed for the other two target tones. Even though hearing‐impaired listeners sometimes weighted information more efficiently than normal‐hearing listeners their overall performance on the task was significantly poorer as was reflected by smaller values of ηnoise.

Identification of the incremented component in profile stimuli

The ability to identify the frequency of the incremented component in a multitone complex was assessed in two conditions, both using the same 11‐tone complexes (fixed frequency, equilog spaced, random phases). All components had equal amplitude, except one of the inner 9, which was incremented. The overall level was randomly varied on each presentation. In condition A the tone complex, with the increment position randomized, was followed by a sinusoid either at the increment frequency or at that of an adjacent component (below or above). In condition B the same complex with flat power spectrum was additionally presented on each trial. The sequence of flat and incremented profile stimuli was randomized over the first two presentation intervals, followed by the sinusoid. In both conditions subjects had to indicate whether the frequency of the incremented component was same or different from that of the sinusoid. Thresholds for these two conditions were estimated by the use of an adaptive procedure and compared to the thresholds of the same subjects in discriminating between the flat and an incremented profile (with signal uncertainty). Results indicate that identification ability is at least as good as discrimination. [Work supported by DFG.]

Contralateral suppression of evoked otoacoustic emissions and detection of a multi-tone complex in noise.

Although some findings suggest that auditory efferent fibers are involved in perception in noise, their function remains controversial. The contralateral suppression of evoked otoacoustic emissions (EOAEs) has recently provided a means of exploring the medial olivocochlear system (MOCS) in humans. In an experiment based on this paradigm, the present study examined the relationships between variations of both EOAEs and detection-in-noise thresholds, induced in the same subjects by a contralateral 50-dB-SPL broad-band noise masker. EOAEs were recorded in response to a burst of a multitone complex composed of 1, 1.5 and 2-kHz components. The detection thresholds of this 3-component complex were measured at 2 ipsilateral noise levels: 50 and 70 dB SPL. The main finding was a significant correlation between EOAE suppression and threshold variations under contralateral masking. A relationship was also found between the contralateral suppression of EOAEs and threshold variation induced by the increase in ipsilateral noise level. These findings support the notion that the MOCS is involved in the detection of multicomponent stimuli in noise.

Effects of original phase and time-delay on the HF channel parameter estimation

It is proposed firstly that the original phase and the time-delay are the main factors which affect the measuring resolution of the multitone complex envelope method. The effects of these factors are analysed and checked by the computer simulation. Finally, three possible ways to eliminate these effects are given.

Discriminability of narrow-band sounds in the absence of level cues

Several experiments are described in which the task of the observer was to detect an intensity increment to the center tone of a narrow-band, multitone complex. The sound-pressure levels of the stimuli were equated, then randomized, so that listeners could not detect the signal by using level cues. The primary experimental variables were the number of tones in the masker spectrum, the level of the center tone or "pedestal" relative to the other tones, the center frequency and the sound-pressure level. Both "random-phase" and "fixed-phase" conditions (referring to whether the pattern of starting phases of the nonsignal tones was chosen randomly on every presentation or was held constant throughout each trial and block of trials) were tested. Although no simple detection strategy appeared to account for all of the results, the most plausible explanation for performance in most conditions was that the listeners were able to discriminate between sounds based on subtle differences in the amplitude envelopes of the waveforms.