A binaural model of monotic level discrimination
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A Binaural Model of Monotic Level Discrimination. Daniel E. Shub and H. Steven Colburn Boston University, Hearing Research Center Harvard-MIT, Health Science and Technology. Introduction.

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A Binaural Model of Monotic Level Discrimination

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A Binaural Model of Monotic Level Discrimination

Daniel E. Shub and H. Steven Colburn

Boston University, Hearing Research Center

Harvard-MIT, Health Science and Technology


  • Monaural level discrimination can be degraded by the addition of a second ear [Rowland and Tobias JSHR 1967, Bernstein JASA 2005, and Shub and Colburn ARO 2004]

  • Traditional models cannot predict this degradation

  • Understanding this degradation might be important for bilateral hearing aids and cochlear implants


  • Psychophysical experiment

    • One-interval left-ear level discrimination task with a roving contralateral distractor

    • Extremely limited amount of published data on degradation from the other ear

    • Previous studies used multi-interval adaptive paradigms which increases model complexity

  • Predict results with a detection theoretic model based on binaural information

Psychophysical Experiment

Distractor tone

Roving level: 50-80 dB

Roving phase: ± 90°

Target tone

Level: 50 or 58 dB

Fixed phase: 0°

  • Task is to detect a level increment of a monaural target in the presence of a simultaneous but contra-aural distractor

  • Both target and distractor are 600 Hz tones with 300 ms duration

  • 1-interval, 2-alternative-forced-choice with feedback paradigm

  • Without distractor: traditional monotic level discrimination task

Stimulus Perception

  • Dominant perception: Single image with a salient loudness and position

    • Target level affects loudness and position

    • Distractor level affects loudness and position

    • Distractor phase affects position

  • Additional “fragile” images

    • Time image, image shape/width

Psychophysical Results






  • Overall Performance:

    • With distractor: 73% correct

    • No distractor: 97% correct (not shown)

  • Responded “Incremented” more with intense and lagging distractors

Detection Theoretic Model

  • Observe:

  • Analysis is currently limited to zero-mean Gaussian noise which is independent across the dimensions

  • Variances of the internal noise and value of trading ratio k are fit to previous level discrimination and lateralization experiments

Ideal Observer

  • Ideal (maximum likelihood) observer:

    • Achieves 99% correct discrimination performance

    • Decision rule is defined by a complex surface

      • Divides 3-D space into regions of “Incremented” and “Un-Incremented”

        • Small  and large  fall into the “Un-Incremented” region

      • For some Q and T, there are no values of  which fall into the “Incremented” region

  • ,  and  carry too much information

  •  and  do not carry sufficient information

  • Consider non-ideal observer of ,  and 

Non-Ideal Observer

  • Non-ideal observer modifies the ideal rule:

    • Responds “Incremented” for large , independent of  and 

      • Assumes subjects always respond “Incremented” whenever a “loud” stimulus is heard

    • Decision rule (criterion) is jittered (zero-mean Gaussian noise) to further decrease discrimination performance

      • Assumes subjects have difficulties implementing the multidimensional decision space; imposes cost for complex decisions

  • Non-ideal observer has four free parameters

    • Variances of the criterion jitter (sL, sQ, sT)

    • The  for which the response is always “Incremented” (threshold)

Minimum RMS Error Predications

RMS error of 11%

60% of the variance was accounted for

Maximum Variance Accounted For

RMS error was 17%

73% of the variance was accounted for


Psychophysical Data

RMS error: 11%

60% of variance accounted for

Minimum RMS error predictions

Captures mean, but not shape

RMS error: 17%

73% of variance accounted for

Maximum variance accounted for predictions

Captures shape, but not mean

Monotic Level Discrimination

  • Under monotic conditions our model is a monaural energy detector

  • Level discrimination models are often more complex than simple energy detectors

  • Our model could be modified such that under monotic conditions it reduces to these “better” models of level discrimination

  • Modified models have not been evaluated

    • Current model is run on a 54-processor supercomputer


  • Monaural level discrimination can be degraded by the “other” ear

  • Ideal observer of two dimensions is degraded

    • 2D model does not predict the data accurately

  • Ideal observer of “loudness”, “position” and “time-image” is NOT degraded by the “other” ear

  • Non-ideal observer of the three dimensions predicts a large proportion of the variance of the data



DC00100 and DC004663

Binaural Gang at Boston University

Nat Durlach

Why Three Dimensions?

  • Observe:

  • The ideal observer of two dimensions has an RMS error of 37%

2-D Model Predictions

RMS error was 37% and variance was added

Visually a completely wrong fit

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