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. Author manuscript; available in PMC: 2010 Dec 1.
Published in final edited form as: J Speech Lang Hear Res. 2009 Dec;52(6):1595–1609. doi: 10.1044/1092-4388(2009/07-0283)

Computation of coarticulation, speech sound distortion, searching articulatory behavior, and variability indices.

Legend

Parameter/function Description

CA Coarticulation index
SSD Speech sound distortion index
SAB Searching articulatory behavior index
VAR Variability index
V1j Vowel 1
j = {/a/,/i/,/u/}
Ck Consonant
k = {/b/,/d/,/g/}
V2l Vowel 2
l = {/a/,/i/,/u/}
S = {V1j, Ck, V2l} S = list of all speech sounds
Wj,k,l = V1jCkV2l W = list of all possible words (e.g. W1,1,1 is /aba/; W2,k,l are all words beginning with /i/.)
Fi,m(SWj,k,l〉) Formant i at measurement point m of speech sound S in the context of word W. (Note that the formant values measured in Hz were normalized using a log10(x)-transformation.)
i = {F1,F2,F3}
m = {beginning, middle, end}
T = Target(F) Target value of formant F
StDev=i=1n(xix¯)2n1
Standard deviation of set x with number of elements n
Calculations

Mean formant frequency
V1:Fi(V1jWj,k,l)=1/3m=13Fi,m(V1jWj,k,l)
C:Fi(CkWj,k,l)=1/3m=13Fi,m(CkWj,k,l)
V2:Fi(V2lWj,k,l)=1/3m=13Fi,m(V2lWj,k,l)

Anticipatory coarticulation
V1:CA(V1jWj,k)=1/3i=131/3l,l=13(Fi(V1jWj,k,l)Fi(V1jWj,k,l))withll
C:CA(CkWj,k)=1/3i=131/3l,l=13(Fi(CkWj,k,l)Fi(CkWj,k,l))withll

Carry-over coarticulation
C:CA(CkWk,l)=1/3i=131/3j,j=13(Fi(CkWj,k,l)Fi(CkWj,k,l))withjj
V2:CA(V2lWk,l)=1/3i=131/3j,j=13(Fi(V2lWj,k,l)Fi(V2lWj,k,l))withjj

Speech sound distortion
V1:SSD(V1jWj,k,l)=1/3i=13|Fi(V1jWj,k,l)T(Fi(V1jWj,k,l))|
C:SSD(CkWj,k,l)=1/3i=13|Fi(CkWj,k,l)T(Fi(CkWj,k,l))|
V2:SSD(V2lWj,k,l)=1/3i=13|Fi(V2lWj,k,l)T(Fi(V2lWj,k,l))|

Searching articulatory behavior
V1:SAB(V1jWj,k,l)=1/3i=13StDev({Fi,1(V1jWj,k,l),Fi,2(V1jWj,k,l),Fi,3(V1jWj,k,l)})
C:SAB(CkWj,k,l)=1/3i=13StDev({Fi,1(CkWj,k,l),Fi,2(CkWj,k,l),Fi,3(CkWj,k,l)})
V2:SAB(V2lWj,k,l)=1/3i=13StDev({Fi,1(V2lWj,k,l),Fi,2(V2lWj,k,l),Fi,3(V2lWj,k,l)})

Variability
V1:VAR(V1j)=1/3i=13StDev({Fi(V1jWj,k,l)})withk,l=1,,3
C:VAR(Ck)=1/3i=13StDev({Fi(CkWj,k,l)})withj,l=1,,3
V2:VAR(V2l)=1/3i=13StDev({Fi(V2lWj,k,l)})withj,k=1,,3