Folding Back or the “Rückfaltung”

One particular challenge in automated processing of acoustic variables – especially formant values – is to deal with measurements, which are obvious “rubbish”. But how to test on “rubbish-ness”?

“Another effective way to check formant readings is to know where to expect them to be” [Thomas 2010, p. 48].

The VokalJäger seeks to extract appropriate acoustic variables by applying a best-fit approach. In the section “curve smoothing” it was explained how the algorithm would pick a set of formant curves (and hence the “target” F1/F2 formant values). But the so-picked values could still produce nonsensical results: Nothing yet ensures that the F1/F2-values lie within the area of the F1/F2-space which is physically possible, given the nature of the human vocal tract.

“folding back” into the “extreme triangle”

The VokalJäger determines the area in the F1/F2-plane where, given a reference universe (here: the Kiel PHONDAT Corpus for High German, separated by gender), most of the samples are located – under the hypothesis that the area is shaped like a triangle. This so-called extreme triangle is used to improve the best-fit curve picking process described in the previous sections: curves with formant readings within the physically reasonable triangle are favored over unreasonable readings outside the triangle. Unrealistic values, respectively Praat-parameter settings yielding those values, are discouraged. As result, values outside the triangle are “folded back” into the triangle. This VokalJäger mechanism – based on a geometric optimization – is called the Rückfaltung (German: for folding back) and described in detail in Keil (2017, p. 93-101 and p. 105-108).

Below pictures exemplify the process:

Figure:  The first picture shows the original situation for one male speaker from the REDE corpus: this process would have allowed for F1/F2-readings, which lie outside the extreme triangle – colored in blue, one the lower left [Keil 2017, figure 28, left, p. 96; colored version].

Figure: The second picture shows the situation after the Rückfaltung: Curves, respectively Praat calibration parameters, are now favored, which produce values within the extreme triangle. The readings formerly outside the triangle (blue points) have now been “folded back” into the triangle [Keil 2017, figure 28, right, p. 96; colored version].