Accuracy of formant measurement for synthesized vowels using the reassigned spectrogram and comparison with linear prediction

Assessing accuracy of resonances obtained with reassigned spectrograms from the "ground truth" of physical vocal tract models

The reassigned spectrogram (RS) has emerged as the most accurate way to infer vocal tract resonances from the acoustic signal [Shadle, Nam, and Whalen (2016). "Comparing measurement errors for formants in synthetic and natural vowels," J. Acoust. Soc. Am. 139(2), 713-727]. To date, validating its accuracy has depended on formant synthesis for ground truth values of these resonances. Synthesis is easily controlled, but it has many intrinsic assumptions that do not necessarily accurately realize the acoustics in the way that physical resonances would. Here, we show that physical models of the vocal tract with derivable resonance values allow a separate approach to the ground truth, with a different range of limitations. Our three-dimensional printed vocal tract models were excited by white noise, allowing an accurate determination of the resonance frequencies. Then, sources with a range of fundamental frequencies were implemented, allowing a direct assessment of whether RS avoided the systematic bias towards the nearest strong harmonic to which other analysis techniques are prone. RS was indeed accurate at fundamental frequencies up to 300 Hz; above that, accuracy was somewhat reduced. Future directions include testing mechanical models with the dimensions of children's vocal tracts and making RS more broadly useful by automating the detection of resonances.

Formants are easy to measure; resonances, not so much: Lessons from Klatt (1986)

Formants in speech signals are easily identified, largely because formants are defined to be local maxima in the wideband sound spectrum. Sadly, this is not what is of most interest in analyzing speech; instead, resonances of the vocal tract are of interest, and they are much harder to measure. Klatt [(1986). in Proceedings of the Montreal Satellite Symposium on Speech Recognition, 12th International Congress on Acoustics, edited by P. Mermelstein (Canadian Acoustical Society, Montreal), pp. 5-7] showed that estimates of resonances are biased by harmonics while the human ear is not. Several analysis techniques placed the formant closer to a strong harmonic than to the center of the resonance. This "harmonic attraction" can persist with newer algorithms and in hand measurements, and systematic errors can persist even in large corpora. Research has shown that the reassigned spectrogram is less subject to these errors than linear predictive coding and similar measures, but it has not been satisfactorily automated, making its wider use unrealistic. Pending better techniques, the recommendations are (1) acknowledge limitations of current analyses regarding influence of F0 and limits on granularity, (2) report settings more fully, (3) justify settings chosen, and (4) examine the pattern of F0 vs F1 for possible harmonic bias.

F0-induced formant measurement errors result in biased variabilities

Many developmental studies attribute reduction of acoustic variability to increasing motor control. However, linear prediction-based formant measurements are known to be biased toward the nearest harmonic of F0, especially at high F0s. Thus, the amount of reported formant variability generated by changes in F0 is unknown. Here, 470 000 vowels were synthesized, mimicking statistics reported in four developmental studies, to estimate the proportion of formant variability that can be attributed to F0 bias, as well as other formant measurement errors. Results showed that the F0-induced formant measurements errors are large and systematic, and cannot be eliminated by a large sample size.

Regional Variation in Fundamental Frequency of American English Vowels

We examined whether the fundamental frequency (f0) of vowels is influenced by regional variation, aiming to (1) establish how the relationship between vowel height and f0 ("intrinsic f0") is utilized in regional vowel systems and (2) determine whether regional varieties differ in their implementation of the effects of phonetic context on f0 variations. An extended set of acoustic measures explored f0 in vowels in isolated tokens (experiment 1) and in connected speech (experiment 2) from 36 women representing 3 different varieties of American English. Regional differences were found in f0 shape in isolated tokens, in the magnitude of intrinsic f0 difference between high and low vowels, in the nature of f0 contours in stressed vowels, and in the completion of f0 contours in the context of coda voicing. Regional varieties utilize f0 control in vowels in different ways, including regional f0 ranges and variation in f0 shape.

Comparing measurement errors for formants in synthetic and natural vowels

The measurement of formant frequencies of vowels is among the most common measurements in speech studies, but measurements are known to be biased by the particular fundamental frequency (F0) exciting the formants. Approaches to reducing the errors were assessed in two experiments. In the first, synthetic vowels were constructed with five different first formant (F1) values and nine different F0 values; formant bandwidths, and higher formant frequencies, were constant. Input formant values were compared to manual measurements and automatic measures using the linear prediction coding-Burg algorithm, linear prediction closed-phase covariance, the weighted linear prediction-attenuated main excitation (WLP-AME) algorithm [Alku, Pohjalainen, Vainio, Laukkanen, and Story (2013). J. Acoust. Soc. Am. 134(2), 1295-1313], spectra smoothed cepstrally and by averaging repeated discrete Fourier transforms. Formants were also measured manually from pruned reassigned spectrograms (RSs) [Fulop (2011). Speech Spectrum Analysis (Springer, Berlin)]. All but WLP-AME and RS had large errors in the direction of the strongest harmonic; the smallest errors occur with WLP-AME and RS. In the second experiment, these methods were used on vowels in isolated words spoken by four speakers. Results for the natural speech show that F0 bias affects all automatic methods, including WLP-AME; only the formants measured manually from RS appeared to be accurate. In addition, RS coped better with weaker formants and glottal fry.

Kalman-based autoregressive moving average modeling and inference for formant and antiformant tracking

Vocal tract resonance characteristics in acoustic speech signals are classically tracked using frame-by-frame point estimates of formant frequencies followed by candidate selection and smoothing using dynamic programming methods that minimize ad hoc cost functions. The goal of the current work is to provide both point estimates and associated uncertainties of center frequencies and bandwidths in a statistically principled state-space framework. Extended Kalman (K) algorithms take advantage of a linearized mapping to infer formant and antiformant parameters from frame-based estimates of autoregressive moving average (ARMA) cepstral coefficients. Error analysis of KARMA, wavesurfer, and praat is accomplished in the all-pole case using a manually marked formant database and synthesized speech waveforms. KARMA formant tracks exhibit lower overall root-mean-square error relative to the two benchmark algorithms with the ability to modify parameters in a controlled manner to trade off bias and variance. Antiformant tracking performance of KARMA is illustrated using synthesized and spoken nasal phonemes. The simultaneous tracking of uncertainty levels enables practitioners to recognize time-varying confidence in parameters of interest and adjust algorithmic settings accordingly.