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Characterizing fundamental frequency in Mandarin: A functional principal component approach utilizing mixed effect models
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10.1121/1.4714345
/content/asa/journal/jasa/131/6/10.1121/1.4714345
http://aip.metastore.ingenta.com/content/asa/journal/jasa/131/6/10.1121/1.4714345

Figures

Image of FIG. 1.
FIG. 1.

The first four eigencomponents (top row) are used to construct the final syllable estimate of F0 (bottom row). The individual component magnitude (third row) is calculated by using the weight estimates (w i ) obtained as the sum of the relevant utterance covariates from the LME model and the component specific random intercept (second row). Subsequently, these components added together produce the centralized syllable estimate (row 4). Finally, the addition of the sample mean (row 5) produces the final syllable estimate of F0 (bottom row).

Image of FIG. 2.
FIG. 2.

Mean function and first, second, third, fourth, fifth, and sixth functional principal components. Together these account for 99.994% of the sample variance, but only the first four have linguistic meaning (99.933 % of samples variation) and as such the fifth and sixth were not used in the subsequent analysis.

Image of FIG. 3.
FIG. 3.

Example tone estimates produced by the model utilizing all four FPC’s. Tone 5 is not represented as it lacks a general estimate, always being significantly affected by non-standardized down-drift effects. Phonologically, toneless syllables do not specify a pitch target.

Image of FIG. 4.
FIG. 4.

One randomly selected syllable for each of the five tones; the functional estimates (bold) for each different tone are shown as well as the corresponding original speaker interpolated data over a dimensionless rhyme time interval t. [Estimated vowel rhymes: [uei, oŋ, əŋ, uan, ə] for each of the five tones, respectively. See supplementary material (Ref. 16) for contextual covariate information.]

Image of FIG. 5.
FIG. 5.

Randomly chosen F0 trajectory over (normalized) time. Here six concurrent F0 tracks for rhymes are shown for speaker F03. As can be seen, the match is fairly close for most syllables, with the estimates associated with the break information controlling the temporal down drift effects [Tonal sequence: 2-1-4-4-2-5; estimated vowel rhymes: [i, ɿ, ai, ə, yɛn, ə]. See supplementary material (Ref. 16) for contextual covariate information.]

Tables

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TABLE I.

Individual and cumulative variation percentage per FPC.

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TABLE II.

Actual auditory variation per FPC (in Hz) (human speech auditory sensitivity threshold ≈ 10 Hz).

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TABLE III.

COSPRO break annotation.

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TABLE IV.

Covariates examined in relation to F0 production in Taiwanese Mandarin. Tone variables in a five-point scale representing tonal characterization, 5 indicating a toneless syllable, with 0 representing the fact that no rhyme precedes the current one (such as at the sentence start).

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TABLE V.

Random effects and 95% highest posterior density confidence intervals for the first, second, third, and fourth FPC scores models as produced by using 10 000 samples.

Generic image for table
TABLE VI.

Adjusted R 2 scores for the selected linear models before and after the inclusion of speaker and sentence related random effects.

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/content/asa/journal/jasa/131/6/10.1121/1.4714345
2012-06-14
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Characterizing fundamental frequency in Mandarin: A functional principal component approach utilizing mixed effect models
http://aip.metastore.ingenta.com/content/asa/journal/jasa/131/6/10.1121/1.4714345
10.1121/1.4714345
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