# Introduction to Speech Processing : Inverse filtering for glottal activity estimation

Created by Tom Bäckström, last modified on Jun 25, 2020

### Motivation

The main source of speech sounds, where the acoustic signal is first created, are the vocal folds, which oscillate in the airflow generated by the lungs (for details, see Speech production and acoustic properties). The opening between the vocal folds is known as the glottis and the movements of vocal folds as well and the corresponding airflow are jointly known as glottal activity.

Since glottal activity is thus central to speech, it is also important to understand how it works. What makes a "good" voice? If there is a disruption to the vocal folds, how does that affect the voice? These are often medical questions, but they have a large social and societal impact. If you loose your voice, you can easily become isolated since you loose an important mode of communication. If you are in a voice profession such as teaching, sales, singing or acting, also your ability to work relies on your voice such that any disturbance in the voice impedes your ability to work. Studying the glottis is thus paramount.

The vocal folds are located in the neck, covered and surrounded by a cartilage. Accessing them is therefore difficult. Putting a camera in the throat is uncomfortable to say the least and even when it is possible, it impedes normal speech, giving measurements a bias of unknown size. Moreover, since the vocal folds oscillate with a fundamental frequency that can go up to 400 Hz, we need a camera whose frame rate is at least 4000 Hz to get 10 frames per period. In other words, we would need a high-speed camera. While such cameras are today readily available, they need a lot of light, which generates a lot of heat, which is not compatible within the sensitive tissues inside the throat. Imaging with other methods, X-rays or magnetic resonance imaging, generally have a slower frame rate and some imaging like X-rays also generate harmful radiation (esp. at high frame rates).

The cartilage surrounding the vocal folds also prevents ultrasound measurements. The only usable direct measurement is electroglottography (EGG), which measures the impedance through the neck using electrodes. It measures conductivity, which is highly dependent on the contact area of the vocal folds, thus giving information about the position of the vocal folds. However, this information is usually one-dimensional which limits the usability of such measurements. It also sensitive to and requires careful placement of electrodes.

What remains is the acoustic signal. With a microphone, we can record the sound emitted from the mouth, and try to deduce the movements of the vocal folds from the sound. It is minimally invasive, because we do not need to insert any sensors inside or onto the the body. Airflow through the glottis is closely related to the movements of the vocal folds; when the vocal folds are open air can flow and when they are closed, airflow is stopped. Airflow in turn is related to the acoustic signal; sound is a variation in air pressure such that the gradient of airflow approximately translates to the corresponding sound.

When sound is generated in the vocal folds, it is however acoustically shaped by the vocal tract (for details, again, see Speech production and acoustic properties); some frequencies are emphasised and others attenuated. To analyse glottal activity, we therefore need to cancel the acoustic effect of the vocal tract. Recall that the effect of the vocal tract can be efficiently modelled by a linear predictive filter. We can thus estimate a filter corresponding to the effect of the vocal tract, and then invert the effect of that filter. This process is known as inverse filtering.

### Signal Model

In glottal inverse filtering, we follow the source-filter paradigm for speech source modelling, where the acoustic speech signal is modelled as an excitation signal filtered by the vocal tract. The assumption is that these two components are independent. By assuming that we know the effect of the vocal tract, we can therefore remove its effect by inverting its effect. If we further model the vocal tract as a tube-model, its effect corresponds to IIR filtering, such that the inverse process is FIR filtering.

The main difficulty in of glottal inverse filtering is estimation of the filter corresponding to the effect of the vocal tract. The task resembles classical linear predictive modelling, where the parameters of an IIR filter are uniquely estimated from the autocorrelation of the signal. Covertly, this however assumes that the excitation is uncorrelated white noise. However, in voiced speech, the excitation is the glottal excitation, which resembles a half-wave rectified sinusoid. That is, it is a fairly smooth curve with a characteristic comb-structure in the spectrum, as well as a distinct tilt with more energy at low frequencies. Though we know a lot about the glottal excitation, it is hard to model. If we would have the glottal excitation, then the vocal tract would be easy to estimate and vice versa - a typical chicken-and-egg problem.

One of the most popular methods for glottal inverse filtering is iterative adaptive inverse filtering (IAIF), where both the glottal excitation and the vocal tract are modelled with linear predictive filtering, and both filters are estimated in an alternating iteration. Many improvements based on more advanced signal models as well as machine learning have been proposed, but the question is far from solved. A central problem in evaluation such methods is the ground truth. We can estimate curves which look like glottal excitations, but we would need to know the actual movements of the vocal folds to verify the accuracy of the obtained curves. Since we do not have a satisfactory direct method for observing glottal activity, which would not bias results, we cannot verify our models.