Additivity of auditory masking using Gaussian-shaped tones a Laback, B., a Balazs, P., a Toupin, G., b Necciari, T., b Savel, S., b Meunier, S., b Ystad, S., and b Kronland-Martinet, R. a Acoustics Research Institute, Austrian Acad. of Sciences, Austria b Laboratoire de Mécanique et d'Acoustique, CNRS Marseille, France MULAC Meeting, Vienna Sept 24rd, Additivity of auditory masking using Gaussian-shaped tones a Laback, B., a Balazs, P., a Toupin, G., b Necciari, T., b Savel, S., b Meunier, S., b Ystad, S., and b Kronland-Martinet, R. a Acoustics Research Institute, Austrian Acad. of Sciences, Austria b Laboratoire de Mécanique et d'Acoustique, CNRS Marseille, France MULAC Meeting, Vienna Sept 24rd, Acoustics Research Institute Austrian Academy of Sciences

Motivation Both temporal and frequency masking have been studied extensively in the literature Very little is known about their interaction, i.e., masking in the time-frequency domain An accompanying study (Necciari et al., this conference) presents data on time-frequency time- frequency masking caused by a Gaussian-shaped tone pulse (“Gaussian”) Our aim is to study the additivity of masking from multiple Gaussian maskers Taken together, these data may serve as a basis to model time-frequency masking in complex signals

Tim-frequency masking time frequency

time frequency Tim-frequency masking

time frequency Tim-frequency masking

Outline 3 steps: Additivity of temporal masking Additivity of frequency masking Additivity of time-frequency masking (not presented today)

Experiment design Both signal and maskers are Gaussian-windowed tones: with Γ: gamma factor: (Γ = α.f 0 ), where f 0 is the tone frequency and α the shape factor Equivalent rectangular bandwidth (  Γ ) : 600 Hz Equivalent rectangular duration: 1.7 ms Good properties of Gaussian in time-frequency domain: Minimal spread in time-frequency Gaussian shape in both time and frequency A study by van Schijndel et al. (1999) has shown that Gaussian-windowed tones with an appropriate alpha factor may fit the auditory time-frequency window.

Procedure: – 3 interval - 3 AFC (oddity task) – Adaptive procedure: 3 down - 1 up rule (estimates the 79.4% threshold) – 12 turnarounds, the last 8 used to calculate the threshold – Stepsize: 5 dB, halved after 2 turnarounds Repeated measurements to have at least three stable values Presented in blocks of equivalent number of maskers Five subjects, normal hearing according to standard audiometric tests Experiment design

Additivity of temporal masking Design – Frequency (target and maskers): 4000 Hz – Four maskers with time shifts: -24, -16, -8, +8 ms – Maskers nearly equally effective (iterative approach) Amount of masking:  8 dB – Combinations: “M 2 -M 3 ”, “M 3 -M 4 ”, “M 1 -M 2 -M 3 ”, “M 2 -M 3 -M 4 ”, “M 1 -M 2 -M 3 -M 4 ” Δt M3M3 TM2M2 time (ms) M1M1 M4M

Waveform of four maskers at equally effective levels (target at masked threshold for single masker) M1 M2 M3 M4 T

Differences between masker levels and masked thresholds for single maskers Five subjects Forward maskingBackward masking Error bars: 95% confidence intervals

Additivity of temporal masking Average results over five subjects p << 0.05 p >> 0.05 Empty symbols: measured data Filled symbols: linear additivity model Error bars: 95% confidence intervals

Additivity of temporal masking Average results over five subjects Error bars: 95% confidence intervals

Summary of temporal masking data (average) No difference between forward and backward maskers Amount of masking increases with number of maskers: – 2 maskers vs. 1 masker: + 18 dB (p << 0.05) – 3 maskers vs. 2 maskers: + 5 dB (p << 0.05) – 4 maskers vs. 3 maskers: + 11 dB (p << 0.05) Amount of excess masking (nonlinear additivity) increases with number of maskers – 2 maskers: 14 dB – 3 maskers: 17 dB – 4 maskers: 26 dB Results qualitatively consistent with literature data using stimuli with no or little temporal overlap of maskers

Additivity of frequency masking Design – Target frequency: 5611 Hz – Four simultaneous maskers with frequency separations: -7, -5, -3, +3 erbs – Maskers nearly equally effective – Amount of masking: 8 dB – Combinations: as for temporal masking Δf M3M3 TM2M2 Frequency (erb) M1M1 M4M

Additivity of frequency masking Design Cochlear distortions (combination tones) could be detection cues Therefore, lowpass-filtered background noise was added The most critical condition (M3+T) was tested with/without noise on two subjects No difference in threshold: so finally NO masking noise!

Masking towards higher frequencies Masking towards lower frequencies Error bars: 95% CI Differences between masker levels and masked thresholds for single maskers Five subjects

Additivity of frequency masking Average results over five subjects Error bars: 95% CI Empty symbols: measured data Filled symbols: linear additivity model

Summary of frequency masking data (average) Amount of masking depends on maskers involved: – M 2 -M 3 vs. single: 3 dB (p < 0.05) – M 3 -M 4 vs. single: 15 dB (p << 0.05) – M 1 -M 2 -M 3 vs. M 2 -M 3 : 5 dB (p < 0.05) – M 2 -M 3 -M 4 vs. M 3 -M 4 : 0 dB (p > 0.05) – M 2 -M 3 -M 4 vs. M 2 -M 3 : 14 dB (p << 0.05) – M 1 -M 2 -M 3 -M 4 vs. M 1 -M 2 -M 3 : 9 dB (p << 0.05) – M 1 -M 2 -M 3 -M 4 vs. M 2 -M 3 -M 4 : 0 dB (p > 0.05) Excess masking (nonlinear additivity) mainly occurring when higher-frequency masker (M4) included – Pairs: 2-3: 0 dB, 3-4: 15 dB – Triples: 1-2-3: 5 dB, 2-3-4: 13 dB – Quadruple: 14 dB

M1 Maskers M1,M2, and M3 overlap with each other, but not with M4 M2 M3 M4 Waveform of four maskers at equally effective levels (target at masked threshold for single masker) T

Discussion and Conclusions Strong excess masking for Gaussian maskers if they are physically non-overlapping Amount of excess masking increases monotonically with number of non-overlapping maskers Excess masking is thought to be related to the compressivity of BM vibration (e.g. Humes and Jesteadt, 1989) Thus, our Gaussians seem to be subject to BM compression, even though they are rather short (ERD = 1.7 ms) This is consistent with the physiological finding that the BM starts to be highly compressive already 0.5 to 0.7 ms after the onset of a signal (Recio et al., 1998)

Modeling of Results Linear Energy Summation Model Assumption: Masked threshold proportional to masker energy at out put of integrator stage Combining two equally effective maskers A and B should produce X + 3 dB of masking Valid for completely overlapping maskers Nonlinear Model Assumption: Compressive nonlinearity in auditory system is preceding the integrator stage Combining maskers A and B results in more than linear additivity (excess masking) Valid for non-overlapping maskers

Modeling of Results General form: where M A, B : Amount of masking produced by maskers A or B M AB : Amount of masking produced by the combination of maskers A and B J: Compressive nonlinearity in peripheral auditory processing

Modeling of Results Power-law model (Lutfi, 1980): – for p = 1: linear model – for p < 1: compressive model MT X : Masked threshold of masker X Modified Power-law model (Humes et al., 1989): – Threshold in quiet (QT) considered as “internal noise”

Start with Temporal Masking: → perfect masker separation Power Model:  best fit for p = 0.2  Mean error: 1.9 dB Modified power model:  Prediction always too low

Include Correction for Quiet Threshold: -7 dB Power Model:  Mean error: 1.9 dB Modified power model:  Mean error: 1.6 dB Why correction required? → Probably, absolute thresholds for Gaussians are no good approximation for internal noise

Spectral Masking: Using same p-value (0.2) and threshold correction Power Model: Good fit only for M3M4 (non-overlapping) Modified power model: too high predictions Adjustment of parameters required!

p-values optimized for Modified Power model

Some questions Can we derive appropriate p-values from amount of overlap between maskers? Can the (modified) power model be included into the Gabor- Multiplier framework to predict time-frequency masking effects for complex signals?

More experiments to test the model

Acknowledgements We would like to thank – the subjects for their patience – Piotr Majdak for providing support in the development of the software for the experiments Work partly supported by WTZ (project AMADEUS) and WWTF (project MULAC)

End of talk

p-values optimized for Power model

Time-frequency conditions time frequency