Thibaud Necciari

The ERBlet transform: An auditory-based time-frequency representation with perfect reconstruction

This paper describes a method for obtaining a perceptually motivated and perfectly invertible time-frequency representation of a sound signal. Based on frame theory and the recent non-stationary Gabor transform, a linear representation with resolution evolving across frequency is formulated and implemented as a non-uniform filterbank. To match the human auditory time-frequency resolution, the transform uses Gaussian windows equidistantly spaced on the psychoacoustic “ERB” frequency scale. Additionally, the transform features adaptable resolution and redundancy. Simulations showed that perfect reconstruction can be achieved using fast iterative methods and preconditioning even using one filter per ERB and a very low redundancy (1.08). Comparison with a linear gammatone filterbank showed that the ERBlet approximates well the auditory time-frequency resolution.

Additivity of nonsimultaneous masking for short Gaussian-shaped sinusoidsa)

The additivity of nonsimultaneous masking was studied using Gaussian-shaped tone pulses (referred to as Gaussians) as masker and target stimuli. Combinations of up to four temporally separated Gaussian maskers with an equivalent rectangular bandwidth of 600 Hz and an equivalent rectangular duration of 1.7 ms were tested. Each masker was level-adjusted to produce approximately 8 dB of masking. Excess masking (exceeding linear additivity) was generally stronger than reported in the literature for longer maskers and comparable target levels. A model incorporating a compressive input/output function, followed by a linear summation stage, underestimated excess masking when using an input/output function derived from literature data for longer maskers and comparable target levels. The data could be predicted with a more compressive input/output function. Stronger compression may be explained by assuming that the Gaussian stimuli were too short to evoke the medial olivocochlear reflex (MOCR), whereas for longer maskers tested previously the MOCR caused reduced compression. Overall, the interpretation of the data suggests strong basilar membrane compression for very short stimuli.

Perceptual matching pursuit with Gabor dictionaries and time-frequency masking

This paper describes a method to obtain a perceptually relevant sparse representation of a sound signal. Based on matching pursuit (MP) and recent psychoacoustic data on time-frequency masking measured with Gabor atoms, a perceptual matching pursuit (PMP) algorithm is proposed. To obtain a good match between the masking model and the signal representation, a dictionary of Gabor atoms with variable sizes is chosen for MP. In the proposed method, the signal is first decomposed using MP and the masking model is applied on the resulting set of atoms. This allows for isolating the masked components from the residual. Experimental results show that exploiting time-frequency masking allows to remove more atoms than using only spectral masking. Additionally, accounting for masking effects between atoms of different sizes and at different times allows for sparser representations. The objective evaluation of the proposed PMP algorithm indicates imperceptible distortions.

Simultaneous masking additivity for short Gaussian-shaped tones: Spectral effectsa)

Laback et al. [(2011). J. Acoust. Soc. Am. 129, 888-897] investigated the additivity of nonsimultaneous masking using short Gaussian-shaped tones as maskers and target. The present study involved Gaussian stimuli to measure the additivity of simultaneous masking for combinations of up to four spectrally separated maskers. According to most basilar membrane measurements, the maskers should be processed linearly at the characteristic frequency (CF) of the target. Assuming also compression of the target, all masker combinations should produce excess masking (exceeding linear additivity). The results for a pair of maskers flanking the target indeed showed excess masking. The amount of excess masking could be predicted by a model assuming summation of masker-evoked excitations in intensity units at the target CF and compression of the target, using compressive input/output functions derived from the nonsimultaneous masking study. However, the combinations of lower-frequency maskers showed much less excess masking than predicted by the model. This cannot easily be attributed to factors like off-frequency listening, combination tone perception, or between-masker suppression. It was better predicted, however, by assuming weighted intensity summation of masker excitations. The optimum weights for the lower-frequency maskers were smaller than one, consistent with partial masker compression as indicated by recent psychoacoustic data.

Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field.

The role of compression in the simultaneous masker phase effecta)

Peripheral compression is believed to play a major role in the masker phase effect (MPE). While compression is almost instantaneous, activation of the efferent system reduces compression in a temporally evolving manner. To study the role of efferent-controlled compression in the MPE, in experiment 1, simultaneous masking of a 30-ms 4-kHz tone by 40-ms Schroeder-phase harmonic complexes was measured with on- and off-frequency precursors as a function of masker phase curvature for two masker levels (60 and 90 dB sound pressure level). The MPE was quantified by the threshold range [min/max difference (MMD)] across the phase curvatures. For the 60-dB condition, the presence of on-frequency precursor decreased the MMD from 10 to 5 dB. Experiment 2 studied the role of the precursor on the auditory filters bandwidth. The on-frequency precursor was found to increase the bandwidth, an effect incorporated in the subsequent modeling. A model of the auditory periphery including cochlear filtering and basilar membrane compression generally underestimated the MMDs. A model based on two-step compression, including compression of inner hair cells, accounted for the MMDs across precursor and level conditions. Overall, the observed precursor effects and the model predictions suggest an important role of compression in the simultaneous MPE.

Auditory time-frequency masking: psychoacoustical data and application to audio representations

In this paper, the results of psychoacoustical experiments on auditory time-frequency (TF) masking using stimuli (masker and target) with maximal concentration in the TF plane are presented. The target was shifted either along the time axis, the frequency axis, or both relative to the masker. The results show that a simple superposition of spectral and temporal masking functions does not provide an accurate representation of the measured TF masking function. This confirms the inaccuracy of simple models of TF masking currently implemented in some perceptual audio codecs. In the context of audio signal processing, the present results constitute a crucial basis for the prediction of auditory masking in the TF representations of sounds. An algorithm that removes the inaudible components in the wavelet transform of a sound while causing no audible difference to the original sound after re-synthesis is proposed. Preliminary results are promising, although further development is required.

Additivity of auditory masking using Gaussian‐shaped tones

Both temporal and spectral masking have been studied extensively in the literature. Mostly, they have been regarded as separate phenomena. Very little is known about the interaction between these two effects, i.e. masking in the time‐frequency domain. Data on the time‐frequency spread of masking evoked by a single Gaussian‐shaped tone pulse are presented in an accompanying study at the same conference (Necciari et al.). The current study gathers data on the additivity of masking by up to four, approximately equally effective Gaussian maskers (ERB=600 Hz), separated either along the time or the frequency axis. For temporal separation, the amount of masking increases with the number of maskers, with excess masking (exceeding linear additivity) of up to 25 dB. For frequency separation (preliminary data) excess masking amounts up to 15 dB, and the higher‐frequency masker (relative to the target) contributes more to the additivity than the lower‐frequency maskers. Experiments with multiple maskers combining bo...

Measuring the auditory phase response based on interaural time differences

Harmonic complexes are often used as maskers for measuring the cochlear phase response. The phase curvature can affect the masking in order of up to 20 dB, an effect known as the masker-phase effect. There is evidence that signals yielding peaky internal masker representations after passing the cochlear filter produce minimum masking, with the fast-acting cochlear compression as the main contributor to that effect. Thus, in hearing-impaired listeners showing reduced or absent compression, the estimation of phase response using the masking method may be difficult. Here, an alternative method is proposed, which is based on the effect of signal peakedness on the sensitivity to interaural time differences (ITD) in the signal envelope. With the two methods, ITD and masking thresholds were measured, respectively, in seven normal-hearing listeners. The stimuli were 300-ms Schroeder-phase harmonic complexes, ranging from 3400 to 4600 Hz with a 100-Hz fundamental frequency, with the signal phase curvature varied b...

Auditory masking using Gaussian‐windowed stimuli

This study investigates auditory masking with Gaussian‐windowed tones as target and masker stimuli. On the purpose of developing a time‐frequency masking model, such stimuli minimize the time‐frequency uncertainty. Also, as proposed by van Schijndel et al. (1999), they activate a single spectro‐temporal observation window of the auditory system. The study presented here measured auditory masking with Gaussian‐windowed stimuli with an ERB of 600 Hz and an effective duration of 9.6 ms. The masker was centered at 4 kHz. Its level was 60 dB SL. Four experiments were conducted. (1) Absolute thresholds for Gaussian‐windowed and 300‐ms‐sinusoidal targets were measured and compared for 11 frequencies. (2) Masking patterns were obtained with targets of various frequency separations from the masker. (3) Forward masking functions with 4‐kHz targets were measured at 5 temporal separations. (4) Forward masking was measured for different frequency separations between masker and target. These data are compared with thos...