Vocal Tract Area Functions Research Articles

Goal-based speech motor control: A theoretical framework and some preliminary data

A theoretical framework for the segmental component of speech production is outlined and some preliminary supporting data are reviewed. According to the framework, articulatory movements are programmed to achieve sequences of goals that are defined in terms of articulatory and acoustic parameters. The goals are correlates of distinctive features. Some feature correlates are determined by quantal (non-linear) relations between articulation and sound. Goals may also be influenced by other principles, such as a compromise between sufficient perceptual contrast and economy of articulatory effort, which leads to the prediction that the goal definitions correspond to regions (as opposed to points) in acoustic and articulatory space. Thus the goals are characterized by some parameter variation, which is possible partly because listeners can understand variable speech. Before utterances are produced, goal specifications are modified by prosodic influences and reduction. The sequence of modified goal specifications is converted to smooth, appropriately-timed articulatory movements by the speech motor control system. This control and the resulting kinematics are constrained in part by the biomechanical properties of the articulators. To help keep acoustic variability within perceptually-acceptable limits, speech motor control mechanisms may include a strategy by which different parts of the vocal-tract area function are adjusted in a complementary (“motor equivalent”) manner. The strategy takes advantage of the fact that for some sounds, a similar acoustic transfer function can be achieved with somewhat different area functions. The existence of such a strategy and the idea that speech motor programming is based in part on acoustic goals are supported by data that show trading relations between lip rounding and tongue-body raising in production of the vowel /u/.

Deriving vocal-tract area functions from midsagittal profiles and formant frequencies: A new model for vowels and fricative consonants based on experimental data

In order to achieve better understanding of the articulatory-acoustic relationships, more data are still very much needed. The two-fold aim of the present study was thus (1) to provide a set of coherent midsagittal functions, area functions and formant frequencies, for a small corpus of vowels and fricative consonants produced by one subject, and (2) to derive a midsagittal profile to area function conversion model optimised for this given subject. Simultaneous tomography and sound recording were available for the subject, as well as some complementary data such as lip geometry or casts of the hard palate. The model is based on Heinz and Stevens' A = αd β area function model, modified so that α varies continuously along the vocal tract midline as a function of the midsagittal distance. The coefficients of the model have been determined with the help of an optimisation algorithm based on a gradient descent technique. The gradient of the error between actual and desired formant values was computed through a back-propagation network implementing both sagittal-to-area conversion and acoustic wave propagation. The fact that the model should work for sounds as different as vowels and consonants and be coherent at both midsagittal and acoustic levels ensures the reliability of the area functions determined in such a way.

On the perceptual characteristics of ‘‘speech gestures.’’

The notion of ‘‘speech gesture’’ or ‘‘phonetic gesture’’ has been developed as a theoretical construct during the past few years. For present purposes, the term is specified as a ‘‘phonologically significant task defined on the vocal tract area function.’’ A given task generally involves the coordination of the movements of several articulators. It appears reasonable to expect speech gestures to have perceptual characteristics like the following: (a) Within certain limits, the time course of speech gestures is not important; (b) within certain limits, the precise synchronization of two, or more, gestures (e.g., constriction displacement and lip opening) is also unimportant; (c) vowel reduction is a natural consequence of speech gesture characteristics. The commands of the distinctive region model were studied as possible speech gestures. Preliminary tests show, as hypothesized, that there are no significant perceptual differences (a) when the shape of a gestural transition is changed to be linear, quadratic, logarithmic, or cosine; (b) when the time separation between two gestures varies from −30 to +30 ms; (c) when gestural dynamics (transitional rate of change) is kept constant but the target is not reached (because of movement undershoot).

Speech stress classification and feature analysis using a neural network classifier

Variability in speech production due to task induced stress contributes significantly to loss in speech processing performance. A new neural network algorithm is formulated which classifies speech under stress using the susas stress database. Five spectral parameter representations (Mel, Δ-Mel, Δ2-Mel, Auto-Corr-Mel, and Cross-Corr-Mel cepstral) are considered as potential stressed speech relayers. Eleven stress conditions are considered which include Angry, Clear, Fast, Lombard, Loud, Normal, Question, Slow, and Soft speech. Stressed speech classification using these features is evaluated with respect to (i) pairwise class separability, (ii) an objective measure of pairwise and global feature separability, and (iii) analysis of articulatory vocal tract area functions. Perturbations in speech production under stress are reflected to varying degrees in the five speech feature representations. A neural network classifier over phoneme partitions can achieve good speaker dependent classification performance (80.6%) when stress conditions are combined into six groups of related stress domains. The implication of reliable stress classification will be discussed for applications such as monitoring speaker state, improving naturalness of speech coding, and increasing robustness of speech recognizers in adverse conditions.

Magnetic resonance imaging (MRI) in vocal tract research: Clinical application

This research demonstrates the application of three-dimensional analysis using MRI to study normal and abnormal aspects of speech and voice production. Subjects who undergo supraglottic laryngectomy often experience changes in vocal quality, even though the larynx is spared. Vocal tract area functions based on pre- and post-operative images and acoustic recordings demonstrate the correspondence between anatomy and acoustic product and quantify these categorical changes. Anatomically, the supraglottis is altered by removal of the base of tongue, epiglottis, and the false vocal folds. The correlation between changes in vocal tract shape and perceptual consequences relative to voice quality were assessed and quantified using three-dimensional reconstruction and computer assisted measurement analysis in addition to computer algorithms for assessment of glottal characteristics. For all subjects, changes in voice quality were highly correlated with specific variation in vocal tract area function and changes in the sound source at the glottis. The development of methods for studying the functional effects of surgical alteration of the vocal tract are highly relevant to clinical study as well as basic studies of the articulatory and acoustic processes. [Work supported in part by NINDCS/NIH Grant Nos. DC-00865, DC-01147, DC-00044, DC-00121.]

Formant frequency estimates for abruptly changing area functions: a comparison between calculations and measurements.

Vocal tract area functions may contain quite abrupt changes in cross-sectional area. In formant frequency calculations for such area functions, an inner length correction (ILC) should be applied. The relevance of this correction was investigated by comparing acoustic measurements obtained from a physical model of the vocal tract with data gathered by means of computer simulations. Calculating formant frequencies without applying internal length corrections caused substantial errors, particularly for area functions representing apical stops just anterior to occlusion. Decentering and axial symmetry in the arrangement of the area elements of the physical model were briefly studied and found to have effects on the formant frequency values.

Determination of vocal tract shape for vowels

The inverse problem for vocal tract shape, area function and articulatory parameters was solved for steady-state vowels by means of an optimization procedure requiring the conditional minimum of work on the part of the articulatory organs. One to four formant frequencies were used as references. The shape of the tongue was measured with an X-ray microbeam system for male and female speakers. The shapes of the vocal tract calculated for the experiments are very similar to the measured shapes.

Vocal Tract Area Function Estimation From Midsagittal Dimensions With CT Scans and a Vocal Tract Cast

The generation of area functions from measurements of the sagittal section is an important step in the study of the relation between vocal tract geometry and speech acoustics. We present a new model to perform this transformation, inspired by the alpha beta model of Heinz & Stevens (1965). Our model is based on analysis of a vocal tract cast for large sagittal dimensions and for small sagittal dimensions on CT scans of the vocal tract constriction zones for the three cardinal vowels [i, a, u] of French. We extracted two sets of coefficients, appropriate for large and small sagittal dimensions respectively. We then compared the predictions of the model with those of other models from the literature. Finally, the usefulness of this dual coefficient procedure for the acoustic simulation of vowels was tested using sagittal sections generated by an acoustic model of the vocal tract.

The geometric vocal tract variables controlled for vowel production: proposals for constraining acoustic-to-articulatory inversion

Studies on vocal tract shape estimation from the speech signal have thoroughly established that no unique inversion from the acoustic speech signal to the vocal tract area function is possible. However, by emphasizing the non-uniqueness of vocal tract shapes, these studies have exaggerated the possibilities of compensatory articulation, which in turn challenges the traditional classification in terms of place of articulation. We suggest, in the light of more recent studies, that this phonetic concept was too hastily discarded. These studies show that certain geometric variables are very important in the process of motor control and in the typology and description of vowel systems. The aim of this paper is to show the possibility and the value of deriving these controlled variables, rather than the entire vocal tract geometry, from acoustic parameters. For this purpose, using a statistical model of the vocal tract integrating articulatory constraints, we generated a 60 000 item look-up table of vocalic configurations. The analysis of 10 French vowels shows that, for the majority of them, it is possible to associate the formant patterns with the well known geometric parameters, namely the lip area and the location and dimension of the tongue constriction. This result seems to confirm that some geometric variables controlled during production can be inferred from the acoustic signal if articulatory constraints are taken into account in the inversion procedure.

Measurements of vocal tract shapes using magnetic resonance imaging

Magnetic resonance imaging is used to determine the vocal tract area functions of a speaker producing five steady vowel sounds. The data is used in an acoustic tube model, formed by concatenating short uniform sections, and the acoustic spectra of the computed output from the model are compared with those of natural speech. For all but one of the vowels good agreement (typically within 120 Hz) is obtained for the first three formant frequencies. To compensate for measurement errors, optimisation procedures are applied, aimed at adjusting the areas to minimise a chosen cost function. A cost function which combines a windowed cepstral error with a Euclidean distance penalty for the areas is effective in finding area functions that gave much closer spectral matches, but which still lie largely within the estimated errors of measurement. These adjusted functions provide suitable root shapes for use in articulatory speech synthesis.

Vocal tract area functions from magnetic resonance (MR) images.

MR equipment was used to obtain axial, coronal, and sagittal images of the vocal tracts of two male subjects during sustained vowel production. Spaced at 0.5-cm intervals, the MR image sections sampled the region from the larynx to the lips. A computer algorithm traced the air-tissue boundaries of the tract sections, and the boundaries of intermediate sections were interpolated at intervals of approximately 1 mm. These boundary data were used in 3-D digital reconstructions of the tract shape. Two methods for determining the area function from a 3-D tract model were applied and the results compared. Based on the assumption that the tract could be approximated by two straight tubes connected by a gradual right-angled bend, method 1 resectioned the model with a systematic combination of radial and parallel gridplanes designed to intersect the tract at equal intervals along its midline [cf. J. M. Heinz and K. N. Stevens, J. Acoust. Soc. Am. 36, 1037 (A) (1964); P. Mermelstein, J. Acoust. Soc. Am. 53, 1070–1082 (1974)]. Method 2 made no assumptions as to tract uniformity and traced the midline with an area minimization algorithm applied to the 3-D data. A sequence of equidistant points along the midline was then found and the area function derived. Several differences between the area functions are found, a major one being tract length which tends to be longer by method 2 than method 1. Also, the precision that can be gained by method 2 depends on the presence of many high definition MR images to ensure minimization stability. [Work supported by NIH Grant DC-00121.]

Vowel–vowel trajectories and region modeling

Trajectories in the formant space of vowel–vowel transitions are analyzed. Results on natural speech are presented. The trajectories have been modeled, taking advantage of a new concept which quantizes the vocal tract area function into Distinctive Regions and Modes.

The acoustic sensitivity of vocal tract constrictions: a preliminary report

A basic premise underlying most recent vocal tract modeling is that the area functions at and near vocal tract constrictions are the ones most critical to the acoustic output; it is also the central point of many hypotheses concerning speech production, that speech targets are coded neurophysiologically with respect to acoustically significant area function features. To determine the relationship between constriction parameters and the acoustic output, we performed a number of vocal tract simulations that perturbed the locations and cross-sectional areas of the points of constriction for the three cardinal vowels, [i], [a] and [u]. The vocal tract area functions of the steady state vowels were approximated by first obtaining midsagittal X-rays of a single speaker’s production of the three vowels. These approximations were then used to construct a set of articulatory-derived acoustic continua that represented systematic perturbations of the cross-dimensions and locations of the constrictions for each sound. Empirically derived coefficients were used to convert the measured cross-dimensions to area functions. A third program calculated the transfer function and formants for each sample. Results of the perturbation analysis showed that formants for each of the vowels were relatively sensitive to minimal changes in crosssectional area but relatively insensitive to larger changes in constriction location. Vowel perception, however, was highly resistant to these step changes, suggesting a many-to-one relationship between articulatory/acoustic and perceptual targets.

A sentence‐level speech training system for hearing‐impaired children

Hearing‐impaired children, or even adults, cannot necessarily pronounce words or sentences fluently, even though they can clearly articulate individual vowels. The system described here aims at helping teachers train hearing‐impaired children by showing the differences between the children's pronunciations and the correct ones given by teachers. The system displays the speech waveform uttered by a trainee, together with several useful correlates including frequency spectra, vocal tract area functions, and the phonetic symbols for estimated vowels. The lateral shapes of the vocal tract are also estimated for vowel segments and displayed together with the correct shapes so that the trainee can practice the correct articulation of vowels referring to the place of articulation and the lip opening. The fundamental frequency contour and the waveform envelope of the trainee's speech are also displayed together with the teacher's, so that the trainee can practice pronunciations with correct prosody. This system is designed so as to be used also for self‐training by older children with hearing impairment.

Speech production models—Constraints and control strategies

Our modeling includes five areas of speech production. (1) Extension of the three-parameter vocal tract area function model of Fant (1960) to include bandwidths and to allow for variations of length and degree of asymmetry of the tongue section, and covariation of these parameters as well as overall VT length and configurations in the laryngeal region. (2) Algorithms for inverse transform, i.e., deriving VT parameters from formant frequencies. (3) Control strategies for synthesis of combinations of vocalic sounds from VT area function parameters. (4) A study of essential cavity structures of fricatives and stops with a discussion of source functions, in part based on data from Fant (1960). (5) Discussion of how source-filter interaction may be implemented and how it affects control strategies in formant synthesis based on underlying vocal tract simulations. [This work has been supported by grants from the Swedish Board of Technical Development and the Swedish Telecom.]

Accuracy of vocal tract area function estimates from acoustic reflection measurements

A broadband dynamic transducer is used to apply a continuous acoustic excitation at the lips for purposes of measuring the vocal tract area function. A pair of closely spaced microphones inside the tube that conveys this excitation signal is used to resolve forward and backward going acoustic wave components. The reflection coefficients of the vocal tract are obtained by a migration operator which transforms wave components measured at the lips into the equivalent causal response to a finite duration wavelet incident at successive depths into the vocal tract. The accuracy of this measurement technique is influenced by (1) the bandwidth limit imposed by the separation of the microphone pair, (2) the stability of microphone gain, and (3) the sensitivity of the microphones to structure borne vibrations. The combined influence of these limits on accuracy is determined experimentally by making acoustic measurements of the area functions of epoxy molds made to the dimensions of vowels derived from Fant's x‐ray data. [Work supported by NIH grants NS 2156 and NS 16377.]

Vocal tract area functions from two point acoustic measurements with formant frequency constraints

A formulation is presented by which the cross-sectional areas of the vocal tract can be computed from the pressure spectrum. The pressure spectrum is the magnitude squared of the transfer function relating acoustic pressure at the glottis to pressure measured in the acoustic radiation field beyond the lips. Two correction parameters are determined using an iterative procedure. One parameter relates to the absolute scaling of the vocal tract areas; the other parameter is the area of the vocal tract at its driving point. This formulation is not robust when applied to a vocal tract with wall losses. The problem results from the effect of wall losses on the amplitudes of pressure spectrum peaks. A correction factor is applied which constrains the formant frequencies of the estimated vocal tract shape to match observed formant frequencies. This correction factor is obtained by a noniterative procedure. The resulting area function estimation procedure is applied to acoustic data computed from the Fant area functions. The area function estimates show the procedure to be robust in the case of lossy vocal tract walls and a free space radiation load.

Vocal tract area functions from autoregressive analysis of two‐point acoustic data

It is well known that the frequencies of the low‐order driving point impedance poles and zeros of the vocal tract can be used to determine a smoothed representation of the vocal tract area function. The impedance poles are congruent with the vocal tract formants; the pole frequencies are specified by the location of peaks in the speech spectrogram. The impedance zero frequencies are indirectly related to formant bandwidths. The bandwidths, however, are difficult to accurately measure from speech. A method is presented for estimating vocal tract impedance zero frequencies directly as the peaks of the transfer function relating the acoustic speech signal to the acceleration signal from a transducer taped to the skin of the neck at the thyroid notch. This transfer function is estimated from pressure and acceleration signals using an autoregressive technique. Area function reconstructions derived from estimated pole and zero frequencies from human speech are presented. [Work supported by NIH.]

Estimation of the vocal tract shape producing fricative consonants.

Estimation of the vocal tract area function producing fricative consonants is performed using the spectral matching technique. The model is composed of an equivalent acoustical tube, a radiation impedance and a noise source which is put in the vocal tract. The estimated area functions for /s/, /∫/, /h/ and /f/ are distinctive, and each shows the unique characteristics which correspond to the articulation of the consonant. Thus, it is verified that the proposed method is beneficial in analyzing the features of fricative consonants.

Vibrotactile identification of vowels

The ability of subjects to identify vowels in vibrotactile transformations of consonant-vowel syllables was measured for two types of displays: a spectral display (frequency by intensity), and a vocal tract area function display (vocal tract location by cross-sectional area). Both displays were presented to the fingertip via the tactile display of the Optacon transducer. In the first experiments the spectral display was effective for identifying vowels in /b/V/ context when as many as 24 or as few as eight spectral channels were presented to the skin. However, performance fell when the 12- and 8-channel displays were reduced in size to occupy 1/2 or 1/3 of the 24-row tactile matrix. The effect of reducing the size of the display was greater when the spectrum was represented as a solid histogram ("filled" patterns) than when it was represented as a simple spectral contour ("unfilled" patterns). Spatial masking within the filled pattern was postulated as the cause for this decline in performance. Another experiment measured the utility of the spectral display when the syllables were produced by multiple speakers. The resulting increase in response confusions was primarily attributable to variations in the tactile patterns caused by differences in vocal tract resonances among the speakers. The final experiment found an area function display to be inferior to the spectral display for identification of vowels. The results demonstrate that a two-dimensional spectral display is worthy of further development as a basic vibrotactile display for speech.