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Kalman-based autoregressive moving average modeling and inference for formant and antiformant tracking.

Daryush D Mehta1, Daniel Rudoy, Patrick J Wolfe

  • 1School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA. daryush.mehta@alum.mit.edu

The Journal of the Acoustical Society of America
|September 18, 2012
PubMed
Summary

This study introduces a statistically principled framework for tracking vocal tract resonances, providing accurate formant frequency and bandwidth estimates with uncertainties. The KARMA algorithm demonstrates superior performance in speech analysis.

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Area of Science:

  • Acoustic Phonetics
  • Speech Signal Processing
  • Statistical Modeling

Background:

  • Classical formant tracking relies on point estimates and dynamic programming, lacking uncertainty quantification.
  • Existing methods often use ad hoc cost functions for smoothing formant trajectories.

Purpose of the Study:

  • To develop a statistically principled state-space framework for estimating vocal tract resonance parameters (center frequencies and bandwidths) with associated uncertainties.
  • To improve the accuracy and reliability of formant and antiformant tracking in acoustic speech signals.

Main Methods:

  • Utilized Extended Kalman (K) algorithms within a state-space framework to infer formant and antiformant parameters.
  • Employed autoregressive moving average (ARMA) cepstral coefficients for parameter estimation.
  • Conducted error analysis comparing the KARMA algorithm against Wavesurfer and Praat using a manually marked formant database and synthesized speech.

Main Results:

  • The KARMA algorithm demonstrated lower overall root-mean-square error compared to benchmark algorithms in formant tracking.
  • KARMA showed effective antiformant tracking for nasal phonemes using synthesized and spoken data.
  • The framework allows controlled trade-offs between bias and variance in parameter estimation.

Conclusions:

  • The proposed state-space framework provides statistically principled estimates of vocal tract resonance parameters with uncertainty quantification.
  • KARMA offers improved accuracy and flexibility for formant and antiformant tracking in speech analysis.
  • Simultaneous tracking of uncertainty levels enhances user confidence and allows for adaptive algorithmic adjustments.