PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Characterization of turbulence noise in breathy human phonation
Philipp AICHINGER
Medical University of Vienna, Department of Otorhinolaryngology, Division of Phoniatrics-Logopedics, Austria

ABSTRACT
Breathiness is a voice quality type that may be a sign of a voice disorder. It involves the auditory perceptionof additive noise caused by turbulent trans-glottal airflow. Ten normal and ten breathy phonations recorded
during high-speed videolaryngoscopy are analyzed. A method for extracting additive noise from audio
recordings in the presence of modulation noise is presented. It generates quasi-unit pulse trains at a rate equal
to the vocal frequency. The cycle shape is obtained by cross-correlating the pulse train with the audio signal.
The cycle shape is then Fourier transformed and input to a Fourier synthesizer. Other inputs are the estimatesof the instantaneous phase and the amplitude modulation function. The timing and height of the pulses aremodulated so as to minimize the modeling error, which is the difference between the recorded audio signaland the output of the synthesizer. The error is assumed to approximate the additive noise in the voice.
Differences of energy levels and spectral slope with respect to voice quality (breathy/normal) are reported.
No differences with regard to cycle phase (open/quasi-closed) are reported.
Keywords: Dysphonia, breathiness, laryngeal high-speed videos, voice quality typing

1. INTRODUCTION
Voice quality typing is relevant to the clinical care of voice disorders, because it contributes to theindication, selection, evaluation, and optimization of clinical treatment. A particular voice quality typeis breathiness, which is often described as the auditory perception of turbulence noise caused by thetrans-glottal air flow. Typically, it is modelled by random noise that is added to the cyclic componentof the voice source signal, which is caused by the vibration of the vocal folds. Cycle length and cycle
peak modulations, called vocal jitter and shimmer, are frequent in pathological voices. In contrast toadditive noise, which is perceived as breathiness, random modulation noise is perceived as
roughness (1).
Additive noise observed in pathological voices is often modelled as white Gaussian noise that is
low-pass filtered with a spectral slope of –6 dB/octave (2). The filtered noise is multiplied byℎ1 𝑔(𝑛) + ℎ2 , where 𝑔(𝑛) is the magnitude of the trans-glottal airflow rate, and ℎ1 and ℎ2 areconstants that fix the sizes of the pulsatile and stationary noise components. The stationary component
is associated with a residual glottal gap owing to a lack of full contact between the vocal folds during
the closed glottis phase. A residual glottal gap is frequently observed in pathological voices. The
pulsatile noise component is caused by the cyclic evolution of the glottal area and the trans-glottal
airflow.
The purpose of the presentation is to test assumptions regarding additive noise in pathologicalvoices. A signal processing method segregating additive and modulation noise in voiced speech
signals is presented first. The additive noise is described. Energy levels, power spectral densities andprobability density functions of the estimated additive noise are reported with respect to voice quality(breathy/normal) and glottal phase (open/quasi-closed).

2. MATERIAL AND METHODS
2.1 Test signals
Ten breathy and ten normal sustained phonation signals are selected for testing from a database
comprising laryngeal high-speed videos and simultaneous audio recordings of 80 pathological and 40
healthy subjects (3). The subjects are instructed to sustain an /i/ vowel the production of which tilts theepiglottis so as to facilitate sighting of the vocal folds. The phonations sound schwa-like because of theartificially lowered position of the tongue, which co-occurs with rigid video-endoscopy. The test3139signals are between 0.256 and 1.872 sec long (mean 0.786 sec).
Figure 1 shows a midsagittal view of the procedure. For video recordings, a Richard Wolf HRES
Endocam 5562 is used with a frame rate of 4 kHz. The spatial resolution is 256x256 pixels(interpolated from red channel: 64x128, green channel: 128x128, blue channel: 64x128). For audio
recordings, a headworn microphone AKG HC 577 L, a phantom power adapter AKG MPA V L, and aportable audio recorder TASCAM DR-100 are used. The sampling rate is 48 kHz, and the quantization
bit resolution is 24 bits. The uncompressed PCM/WAV file format is used. The microphone is usedwith the original cap (no boost of high frequencies), and the adapter is set to linear response. The low
cut of the audio recorder is switched off.

Figure 1 – Midsagittal illustration of the recording procedure. The endoscopic camera is inserted into themouth of the subject. The vocal folds are illuminated and filmed via the endoscope. A microphone is used torecord radiated sound pressure. 1. Vocal folds, 2. Microphone, 3. Endoscopic camera. Figure adapted from(4).
2.2 ESTIMATION OF THE VOCAL FREQUENCY
Figure 2 shows the block diagram of the estimation of the vocal frequency from the audio signals as𝛾
described in (5) and (6), with a few modifications. First, candidate vocal frequencies 𝑓0 are obtained
from the speech signal 𝑑(𝑛) via spectral peak picking (SPP), and applying the Viterbi algorithm
repetitively (six times). 𝛾 is the index of the candidate, and 𝑛 is the discrete time index. Second, acyclic waveform 𝑑 𝛾 (𝑛) is obtained for each candidate as follows. A unit-pulse train 𝑢𝛾 (𝑛) with𝛾frequency 𝑓0 is cross-correlated with the audio signal to obtain the cycle shape 𝑟 𝛾 (𝑙), where 𝑙 is thediscrete lag time index with respect to the center of the cycle. Fourier coefficients 𝑎𝛾 and 𝑏 𝛾 are
obtained via discrete Fourier transformation (DFT) of the cycle shape 𝑟 𝛾 (𝑙). The cyclic candidate𝛾
waveform 𝑑 𝛾 (𝑛) is obtained via Fourier synthesis (FS), taking 𝑓0 , 𝑎𝛾 , and 𝑏 𝛾 as inputs. Finally, thevocal frequency estimate 𝑓0 is the candidate which minimizes the difference 𝑒(𝑛) = 𝑑(𝑛) − 𝑑 𝛾 (𝑛) ina least squares sense.

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Figure 2 – Block diagram of the vocal frequency estimator, adapted from (6).
2.3

EXTRACTION OF ADDITIVE NOISE IN THE PRESENCE OF MODULATION NOISE
Additive noise is estimated by subtracting a model 𝑑̃ (𝑛) of the modulated cyclic component fromthe speech signal. The modulated cyclic component is obtained as follows. First, a quasi-unit, i.e., anamplitude and frequency modulated pulse train 𝑢̃(𝑛) with average frequency 𝑓0 is generated andcross-correlated with the audio signal 𝑑(𝑛) to obtain the cycle shape 𝑟̃ (𝑙). Fourier coefficients 𝑎̃ and̃ (𝑛) is estimated from𝑏̃ are obtained by DFT of cycle shape 𝑟̃ (𝑙). Second, the instantaneous phase Θ̃the pulse train 𝑢̃(𝑛) by assigning Θ(𝑛) = 𝜋, 3𝜋, 5𝜋, … to the pulse positions and cubic splinẽ(𝑛) isinterpolating at the time instants in between. Third, the amplitude modulation function A
̃ (𝑛) = 𝑢̃(𝑛) at the pulse positions andestimated from pulse train 𝑢̃(𝑛) by assigning A
shape-preserving parabolic interpolating at the time instants in between. The modulated cyclic̃ (𝑛).
component 𝑑̃ (𝑛) is estimated via Fourier synthesis taking as inputs coefficients 𝑎̃, 𝑏̃, and phase Θ̃The output of the Fourier synthesizer is multiplied by amplitude modulation function A(𝑛). Finally,
the noise 𝑒̃ (𝑛) is minimized in a least squares sense via trial modifications of the pulse positions andheights in train 𝑢̃(𝑛). Deviations of timing from periodicity, 𝑗(𝜇) and heights from unity, 𝑠(𝜇) are
estimated using the interior-point optimization algorithm (7,8).

Figure 3 – Block diagram of additive noise extraction, adapted from (6).

3141Figure 4 – Fragment of a speech signal. The overlaid plots in the top panel show the audio signal 𝑑, theestimate of the cyclic component 𝑑̃ and the noise estimate 𝑒̃ = 𝑑 − 𝑑̃ . The middle and bottom panels show
the instantaneous frequency and the amplitude modulation functions of the cyclic component.

2.4 CHARACTERIZATION OF THE ADDITIVE NOISE
Additive noise 𝑒(𝑛) is described as follows. First, the noise energy level 𝐿𝑒 is obtained in dB
relative to the energy level of the cyclic component. Level 𝐿𝑒 is reported with respect to voice quality(breathy/normal) and glottal phase (open/closed). The glottal phase is obtained via analysis of theglottal area observed in the video images, taking into account a delay owing to the time of soundpropagation through the vocal tract. For comparison purposes, the Harmonics-to-Noise ratio (HNR) is
also obtained via Praat (9). Second, the autoregressive power spectral density (PSD) of the noise is
obtained via Burg’s method with respect to voice quality and glottal phase. Finally, the probability
density function (PDF) of the noise is obtained and fitted with a t location-scale distribution, i.e., a
Student’s t-distribution, given by𝜈+1−()
2

𝜈+1𝑥−𝜇 2Γ() 𝜈+()2𝜎𝑆𝑡(𝑥|𝜇, 𝜎, 𝜈) =]𝜈 [𝜈𝜎√𝜈𝜋Γ ( )2(1)where 𝜇 is the location parameter, i.e., the mean, 𝜎 is the deviation parameter, i.e., the scale, and𝜈 is the shape parameter. With 𝜈 = ∞, the distribution equals a normal distribution. Decreasing 𝜈make the main lobe lower and more narrow, and makes the tails heavier.

3. RESULTS
Figure 5 reports relative noise energy levels with respect to voice quality (breathy versus normal)
and glottal phase (open versus closed). The medians of the noise energy levels are close to 0 dB for
breathy voices, which would suggest that the breathy voices’ noise energy is approximately equal tothe energy of the voices’ cyclic components. The energy distributions range from approximately -2 dB
to 0.5 dB. One outlier exists at approximately -4.5 dB. As expected, noise energy levels of normal
voices are lower on average. Their spread is larger, i.e., they range from approximately -10 dB to -1 dB.
No differences between open and closed phases are observed for either breathy or normal voices. The
difference in noise energy levels between breathy and normal voices is statistically significant.

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Figure 5 – Relative noise energy levels with respect to voice quality and cycle phase.
Figure 6 reports the HNR (dB) with respect to voice quality. For breathy voices, the HNR
approximately ranges from 5 dB to 20 dB, with a median close to 14 dB. HNR is higher for normalvoices, and ranges from approximately 18 dB to 29 dB. The median is close to 26 dB. The overlap
between the distributions is small.

Figure 6 – Harmonics-to-Noise ratio with respect to cycle phase (9).
Figure 7 shows 10-th order autoregressive power spectral density estimates of the noise obtained
via Burg’s method and averaged over speakers (solid lines) and linear regression models thereof(dotted lines) with respect to voice quality (10). No relevant difference between the estimates isobserved at low frequencies. The intercepts of the two regression lines are approximately equal (-97.5dB/Hz and -97.7 dB/Hz). The difference in PSD estimates between breathy and normal voices increasewith frequency. In particular, the slope of the regression lines is −0.946 ⋅ 10−3 𝑑𝐵/𝐻𝑧 2 for breathy
voices, and −1.461 ⋅ 10−3 𝑑𝐵/𝐻𝑧 2 for normal voices.

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Figure 7 – Power spectral density (PSD) of the noise with respect to voice quality, and linear regression
models of the PSDs.
Figure 8 (a) shows PSD estimates for breathy voices, and Figure 6 (b) shows PSD estimates fornormal voices. Red and blue solid lines show estimates of open and closed phases respectively, and thedotted lines show linear regression models thereof. No relevant differences are observed betw een theopen and closed phases for either breathy or normal voices.

Figure 8 – Power spectral density (PSD) of the noise with respect to voice quality and glottal phase, andlinear regression models of the PSDs. (a) Breathy voice quality, and (b) Normal voice quality.
Figure 9 shows a cumulative histogram (blue bars) of the model error time series values and aparametric fit (red lines). The solid line reports the overall fit, and the dotted lines report 95%
confidence intervals. A t location-scale distribution is favored for modelling the noise signal over a
Normal distribution, because of a better log likelihood. Table 1 summarizes the parameters of the fitteddistributions.

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Figure 9 – Cumulative histogram (blue bars) of the noise, and its fitted t location-scale distribution (red lines).
Shown are the average cumulative distribution fit (solid line), and 95% confidence intervals (dotted lines).
Table 1 – Minima, medians, and maxima of t location-scale distribution parameters of the model error signal
time series’ probability density distributions. Parameters are obtained subject-wise.
Parameter

Minimum

Median−5Maximum−77.804 ⋅ 10−5Location 𝜇−2.091 ⋅ 10

Scale 𝜎1.655 ⋅ 10−4

6.670 ⋅ 10−4

2.012 ⋅ 10−3

Shape 𝜈

3.165

6.469

12.63−9.957 ⋅ 10

4. DICUSSION AND CONCLUSION
A method for the segregation of additive noise from voiced speech signals produced bypathological and normal subjects is presented. The additive noise is described with respect to voicequality and glottal phase by means of energy levels, power spectral densities, and probability density
functions. The results suggest updates of the existing modeling framework. First, spectral slopes thatdecay linearly with increasing frequencies are observed. The difference between breathy and normal
voices is not only a difference in noise energy, but also in spectral slope. In particular, noise is boosted
at high frequencies in breathy voices as compared to normal voices. No evidence in favor of a pulsatile
additive noise component is observed. A t location-scale distribution is found to better fit the observed
noise data than a normal distribution. Finally, the conventional Harmonics-to-Noise ratio (HNR)
enables distinguishing between breathy and normal voices. The method that is presented here may
enable analysis of additive noise in the presence of strong modulations of the vocal frequency andvocal cycle amplitude, which are frequent in pathological voices.

ACKNOWLEDGEMENTS
This work was supported by the Austrian Science Fund (FWF): KLI 722-B30.

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