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Multivariate-State Hidden Markov Models for Simultaneous Transcription of Phones and Formants

This study explores the use of multivariate state hidden Markov models to simultaneously transcribe phones and formants. It addresses the limitations of traditional models in ignoring relational cues and measurement errors. The proposed system uses formants as state variables and introduces hierarchical dependence constraints to improve accuracy. Results show that the system successfully captures long-term, phonetically meaningful parameters while maintaining spectral information.

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Multivariate-State Hidden Markov Models for Simultaneous Transcription of Phones and Formants

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  1. Multivariate-State Hidden Markov Models for Simultaneous Transcription of Phones and Formants Mark Hasegawa-Johnson jhasegaw@uiuc.edu ECE Department University of Illinois at Urbana-Champaign

  2. Outline Problem Statement HMM Ignores Relational Cues Solution #1: Formants as Features The Problem: Measurement Error Multivariate State Models Complexity Issues Application: Plosive Classification Application: MAP Formant Tracking

  3. Background: Recognition Scoring Choose a model which maximizes P( observations | model ) = sum_(Q)(P(O,Q|model))

  4. Background: Plosive Release Three “Places of Articulation:” Lips (b,p) Tongue Blade (d,t) Tongue Body (g,k)

  5. Objective: Model Relational Acoustic Cues w/ HMM

  6. Problem Statement: 1. Short-Term Features: HMM: no long-term relational cues. 2. Phonetic Interpretation: MFCC statistics hard to interpret phonetically --- information gleaned using Baum-Welch never gets into phonetics textbooks. Objective: Measure long-term, phonetically meaningful parameters (e.g. formants) without throwing away spectral information.

  7. Traditional System: Formants as Acoustic Features

  8. Formant Measurement Error • Small Errors: Spectral Perturbation • Large Errors: Pick the Wrong Peak Amp. (dB) Frequency (Hertz)

  9. Std Dev of Small Errors = 45-72 Hz Std Dev of Large Errors = 218-1330 Hz P(Large Error) = 0.17-0.22 Large Errors are 20% of Total LogPDF Measurement Error (Hertz) re: Manual Transcriptions

  10. Measurement Error PredictsClassification Error

  11. Proposed System: Formants as State Variables

  12. Complexity of SolutionWithout Additional Constraints

  13. Useful Constraint #1: State Independence

  14. Useful Constraint #2:Hierarchical Dependence

  15. Useful Constraint #2:Hierarchical Dependence

  16. Hierarchical Dependence Simplifies Baum-Welch

  17. A Posteriori Formant Distribution

  18. Phoneme Classification: Maximize P(O|model)

  19. Description of the Test System:Transitions and Observations

  20. Description of the Test System:Normalized Spectral Amplitude Measurements

  21. Description of the Test System:Spectral Convexity

  22. Spectral Convexity Estimator

  23. Plosive Classification as a Function of Vowel Context

  24. Dependence on Vowel Context is Similar to Human Listeners

  25. Formant Tracking Results:a Posteriori Formant PDFs10ms After /b/ in “Barb” DFT Amplitude DFT Convexity P(F | O, Q) Frequency (0-4000 Hertz)

  26. Formant Tracking Results:a Posteriori Formant PDFs10ms After /d/ in “dark” DFT Amplitude DFT Convexity P(F | O, Q) Frequency (0-4000 Hertz)

  27. Formant Tracking Results:a Posteriori Formant PDFs50ms After /d/ in “dark” DFT Amplitude DFT Convexity P(F | O, Q) Frequency (0-4000 Hertz)

  28. Conclusions Dependence on Vowel Context is similar to that of Human Listeners. MAP formant tracker provides a posteriori “error bars” for each formant track. Complexity is linearly proportional to the number of formants.

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