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![Page 1: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/1.jpg)
Characterisation of individuals’ formant dynamics using
polynomial equations
Kirsty McDougallDepartment of LinguisticsUniversity of Cambridge
IAFPA 2006
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Speaker characteristics and static features of speech
• Most previous research has focussed on static features- instantaneous, average
• Straightforward to measure
• Natural progression from other research areas – delineation of different languages and language varieties
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• Reflect certain anatomical dimensions of a speaker, e.g. formant frequencies ~ length and configuration of VT
• Instantaneous and average measures - demonstrate speaker differences, but unable to distinguish all members of a population
look to dynamic (time-varying) features
Speaker characteristics and static features of speech
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• More information than static
• Reflect movement of a person’s speech organs as well as dimensions- people move in individual ways for skilled motor activities - walking, running, … and speech
Dynamic features of speech
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Dynamic features of speech
• can view speech as achievement of a series of linguistic ‘targets’
• speakers likely to exhibit similar properties at ‘targets’ (e.g. segment midpoints), but move between these in individual ways
examine formant frequency dynamics
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Time (s)
/aɪ/ in ‘bike’ uttered by two male speakers of Australian English
Frequency (Hz)
Time (s)
Formant dynamics
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Time (s) Time (s)
/aɪ/ in ‘bike’ uttered by two male speakers of Australian English
Frequency (Hz)
10% 10%
Formant dynamics
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Time (s)
/aɪ/ in ‘bike’ uttered by two male speakers of Australian English
Frequency (Hz)
Time (s)
Formant dynamics
![Page 9: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/9.jpg)
• How do speakers’ formant dynamics reflect individual differences in the production of the sequence //?
• How can this dynamic information be captured to characterise individual speakers?
Research Questions
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bike
hike
like
mike
spike
/baIk/
/haIk/
/laIk/
/maIk/
/spaIk/
Target words:
/aIk/
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e.g. I don’t want the scooter, I want the bike now. Later won’t do, I want the bike now.
5 repetitionsx 5 words (bike, hike, like, mike, spike)x 2 stress levels (nuclear, non-nuclear)x 2 speaking rates (normal, fast)= 100 tokens per subject
Data set
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• 5 adult male native speakers of Australian English (A, B, C, D, E)
• aged 22-28
• Brisbane/Gold Coast, Queensland
Subjects
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Speaker A “bike” (normal-nuclear)
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1 2
Speaker A “bike” (normal-nuclear)
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1 2 10 20 30 40 50 60 70 80 90%
Speaker A “bike” (normal-nuclear)
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1 2 10 20 30 40 50 60 70 80 90%
Speaker A “bike” (normal-nuclear)
F3 F2
F1
F3F2
F1
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F1 normal-nuclear
1009080706050403020100
800
700
600
500
400
300
A
B
C
D
E
Fre
quen
cy (
Hz)
+10% step of /a/
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F2 normal-nuclearF
requ
ency
(H
z)
+10% step of /a/ 1009080706050403020100
2000
1800
1600
1400
1200
1000
800
A
B
C
D
E
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F3 normal-nuclearF
requ
ency
(H
z)
+10% step of /a/ 1009080706050403020100
2800
2700
2600
2500
2400
2300
2200
2100
2000
A
B
C
D
E
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Discriminant Analysis
Multivariate technique used to determine whether a set of predictors (formant frequency measurements) can be combined to predict group (speaker) membership
(ref. Tabachnick and Fidell 1996)
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Discriminant Analysis
fast-nuclear
Function 1
6420-2-4-6
Fu
nctio
n 2
6
4
2
0
-2
-4
A
B
C
D
E
Each datapoint represents 1 token
Each speaker’s tokens are represented with a different colour
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Discriminant Analysis
fast-nuclear
Function 1
6420-2-4-6
Fu
nctio
n 2
6
4
2
0
-2
-4
A
B
C
D
E
Each datapoint represents 1 token
Each speaker’s tokens are represented with a different colour
e.g. Speaker E’s 25 tokens of /aɪk/
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Discriminant Analysis
fast-nuclear
Function 1
6420-2-4-6
Fu
nctio
n 2
6
4
2
0
-2
-4
A
B
C
D
E
DA constructs discriminant functions which maximise differences between speakers
(each function is a linear combination of the formant frequency predictors)
![Page 24: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/24.jpg)
Discriminant Analysis
fast-nuclear
Function 1
6420-2-4-6
Fu
nctio
n 2
6
4
2
0
-2
-4
A
B
C
D
E
Assess how well the predictors distinguish speakers by extent of clustering of tokens
+ classification percentage…
![Page 25: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/25.jpg)
Discriminant Analysis
fast-nuclear
Function 1
6420-2-4-6
Fu
nctio
n 2
6
4
2
0
-2
-4
A
B
C
D
E
Assess how well the predictors distinguish speakers by extent of clustering of tokens
+ classification percentage…
95%
![Page 26: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/26.jpg)
normal-nuclear
Function 1
6420-2-4-6-8
Function 2
4
2
0
-2
-4
-6
SpeakerG r o up Ce nt r o d s
5
4
3
2
1
fast-nuclear
Function 1
6420-2-4-6
Function 2
6
4
2
0
-2
-4
SpeakerG r o up Ce nt r o d s
E
D
C
B
A
normal-non-nuclear
Function 1
6420-2-4-6
Function 2
4
3
2
1
0
-1
-2
-3
-4
SpeakerG r oup C en t r o ds
E
D
C
B
A
fast-non-nuclear
Function 1
6420-2-4
Function 2
6
4
2
0
-2
-4
SpeakerG r o up Ce nt r o d s
E
D
C
B
A
normal-nuclear
Function 1
6420-2-4-6-8
Function 2
4
2
0
-2
-4
-6
Speaker
Group Centroids
A
B
C
D
E
A
B
C
D
E
Discriminant Analysis
95%
88%
95%
89%
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Discussion
• DA scatterplots and classification rates promising
• However, not very efficient – method essentially based on a series of instantaneous measurements, probably containing dependent information
• Recall: individuals’ F1 contours of /aɪk/…
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F1 normal-nuclear
1009080706050403020100
800
700
600
500
400
300
A
B
C
D
E
Fre
quen
cy (
Hz)
+10% step of /a/
![Page 29: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/29.jpg)
A new approach…
• Differences in location in frequency range
• Differences in curvature – location of turning points, convex/concave, steep/shallow
• Need to capture most defining aspects of the contours efficiently
linear regression to parameterise curves with polynomial equations
![Page 30: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/30.jpg)
Linear regression
• Technique for determining equation of a line or curve which approximates the relationship between a set of (x, y) points
0
5
10
15
20
0 5 10 15 20
y
x
![Page 31: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/31.jpg)
Linear regression
• Technique for determining equation of a line or curve which approximates the relationship between a set of (x, y) points
0
5
10
15
20
0 5 10 15 20
y
x
![Page 32: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/32.jpg)
Linear regression
• Technique for determining equation of a line or curve which approximates the relationship between a set of (x, y) points
0
5
10
15
20
0 5 10 15 20
y
x
![Page 33: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/33.jpg)
Linear regression
• Technique for determining equation of a line or curve which approximates the relationship between a set of (x, y) points
0
5
10
15
20
0 5 10 15 20
y
x
y = a0 + a1x
![Page 34: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/34.jpg)
Linear regression
• Technique for determining equation of a line or curve which approximates the relationship between a set of (x, y) points
0
5
10
15
20
0 5 10 15 20
y
x
y = a0 + a1x
y-intercept
![Page 35: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/35.jpg)
Linear regression
• Technique for determining equation of a line or curve which approximates the relationship between a set of (x, y) points
0
5
10
15
20
0 5 10 15 20
y
x
y = a0 + a1x
y-interceptgradient
![Page 36: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/36.jpg)
Linear regression
• Can also be used for curvilinear relationships
0
5
10
15
20
0 5 10 15 20
0
5
10
15
20
0 5 10 15 20
y
x
![Page 37: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/37.jpg)
Linear regression
• Can also be used for curvilinear relationships
quadratic:y = a0 + a1x + a2x2
0
5
10
15
20
0 5 10 15 20
y
x
![Page 38: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/38.jpg)
Linear regression
• Can also be used for curvilinear relationships
quadratic:y = a0 + a1x + a2x2
y-intercept
0
5
10
15
20
0 5 10 15 20
y
x
![Page 39: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/39.jpg)
Linear regression
• Can also be used for curvilinear relationships
quadratic:y = a0 + a1x + a2x2
y-interceptdetermine shape and direction of curve
0
5
10
15
20
0 5 10 15 20
y
x
![Page 40: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/40.jpg)
Polynomial Equations
x
x
x
y
y
y
Cubic
y = a0 + a1x + a2x2 + a3x3
Quartic
y = a0 + a1x + a2x2 + a3x3 + a4x4
Quintic
y = a0 + a1x + a2x2 + a3x3+ a4x4 + a5x5
![Page 41: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/41.jpg)
Polynomial Equations
x
x
x
y
y
y
Cubic
y = a0 + a1x + a2x2 + a3x3
Quartic
y = a0 + a1x + a2x2 + a3x3 + a4x4
Quintic
y = a0 + a1x + a2x2 + a3x3+ a4x4 + a5x5
![Page 42: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/42.jpg)
/ak/ data
• fit F1, F2, F3 contours with polynomial equations
• test the reliability of the polynomial coefficients in distinguishing speakers
Quadratic: y = a0 + a1t + a2t2
Cubic: y = a0 + a1t + a2t2 + a3t3
![Page 43: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/43.jpg)
0
100
200
300
400
500
600
700
800
0 1 2 3 4 5 6 7 8 9
Normalised time
actual
quadratic fit
cubic fit
actual data points
Quadratic fit: y = 420.68 + 79.26t - 5.92t2
Cubic fit:y = 478.85 - 46.07t + 35.62t2
- 3.46t3
“bike”, Speaker A (normal-nuclear token 1)
0
100
200
300
400
500
600
700
800
0 1 2 3 4 5 6 7 8 9
Normalised time
Frequency (Hz)
Normalised time
F1 contoury
t
![Page 44: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/44.jpg)
0
100
200
300
400
500
600
700
800
0 1 2 3 4 5 6 7 8 9
Normalised time
actual
quadratic fit
cubic fit
actual data points
Quadratic fit: y = 420.68 + 79.26t - 5.92t2
R = 0.879
Cubic fit:y = 478.85 - 46.07t + 35.62t2
- 3.46t3
R = 0.978
“bike”, Speaker A (normal-nuclear token 1)
0
100
200
300
400
500
600
700
800
0 1 2 3 4 5 6 7 8 9
Normalised time
Frequency (Hz)
Normalised time
F1 contoury
t
![Page 45: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/45.jpg)
600
800
1000
1200
1400
1600
1800
2000
0 1 2 3 4 5 6 7 8 9
Normalised time
“bike”, Speaker A (normal-nuclear token 1)
0
100
200
300
400
500
600
700
800
0 1 2 3 4 5 6 7 8 9
Normalised time
actual
quadratic fit
cubic fit
actual data points
Quadratic fit: y = 876.01 - 53.24t + 22.46t2
R = 0.985
Cubic fit:y = 825.49 + 55.64t - 13.63t2
+ 3.01t3
R = 0.991
Frequency (Hz)
Normalised time
F2 contoury
t
![Page 46: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/46.jpg)
DA on polynomial coefficents
• Quadratic 3 formants x 3 coefficients = 9 predictors
• Cubic3 formants x 4 coefficients = 12 predictors
• Cubic + duration of /a/ 12 + 1 = 13 predictors
![Page 47: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/47.jpg)
0
20
40
60
80
100
normal-nuclear
fast-nuclear normal-non-nuclear
fast-non-nuclear
quadratic
cubic
cubic + dur
direct meas'ts
Comparison of Classification Rates
% Correct Classification
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0
20
40
60
80
100
normal-nuclear
fast-nuclear normal-non-nuclear
fast-non-nuclear
quadratic
cubic
cubic + dur
direct meas'ts
% Correct Classification
No. of predictors:
(9)
(12)
(13)
(20)
Comparison of Classification Rates
![Page 49: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/49.jpg)
0
20
40
60
80
100
normal-nuclear
fast-nuclear normal-non-nuclear
fast-non-nuclear
quadratic
cubic
cubic + dur
direct meas'ts
% Correct Classification
No. of predictors:
(9)
(12)
(13)
(20)
Comparison of Classification Rates
![Page 50: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/50.jpg)
0
20
40
60
80
100
normal-nuclear
fast-nuclear normal-non-nuclear
fast-non-nuclear
quadratic
cubic
cubic + dur
direct meas'ts
% Correct Classification
No. of predictors:
(9)
(12)
(13)
(20)
Comparison of Classification Rates
![Page 51: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/51.jpg)
0
20
40
60
80
100
normal-nuclear
fast-nuclear normal-non-nuclear
fast-non-nuclear
quadratic
cubic
cubic + dur
direct meas'ts
% Correct Classification
96% 92% 89% 90%
No. of predictors:
(9)
(12)
(13)
(20)
Comparison of Classification Rates
![Page 52: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/52.jpg)
0
20
40
60
80
100
normal-nuclear
fast-nuclear normal-non-nuclear
fast-non-nuclear
quadratic
cubic
cubic + dur
direct meas'ts
% Correct Classification
No. of predictors:
(9)
(12)
(13)
(20)
Comparison of Classification Rates
![Page 53: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/53.jpg)
0
20
40
60
80
100
normal-nuclear
fast-nuclear normal-non-nuclear
fast-non-nuclear
quadratic
cubic
cubic + dur
direct meas'ts
% Correct Classification
No. of predictors:
(9)
(12)
(13)
(20)
Comparison of Classification Rates
![Page 54: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/54.jpg)
Summary of findings
• Comparing polynomial-based tests & direct measurement-based tests: reduction in classification accuracy small in return for much smaller no. of predictors required
• Future: aim to develop this approach to enable inclusion of additional information parametrise other dynamic aspects of speech to capture a dense amount of speaker-specific info with a small no. of predictors
![Page 55: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/55.jpg)
Conclusion
• Differences in formant dynamics reflect differences in articulatory strategies (& VT dimensions) among speakers
e.g. speaker-specificity of /ak/ formant dynamics
- differences in shape and frequency for F1, F2 and F3- preserved across changes in speaking rate and stress
![Page 56: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/56.jpg)
Conclusion
• Trialled new technique for characterising individuals’ formant contours using polynomial equations on /ak/ data
• Able to capture almost same amount of speaker-specific information with far fewer predictors
Polynomial approach using formant dynamics should make an important contribution to speaker characterisation techniques in future
![Page 57: Characterisation of individuals’ formant dynamics using polynomial equations Kirsty McDougall Department of Linguistics University of Cambridge kem37@cam.ac.uk.](https://reader035.fdocuments.in/reader035/viewer/2022070323/56649d425503460f94a1d441/html5/thumbnails/57.jpg)
Characterisation of individuals’ formant dynamics using
polynomial equations
Kirsty McDougallDepartment of LinguisticsUniversity of Cambridge
IAFPA 2006