AN EXPECTATION MAXIMIZATION APPROACH FOR FORMANT TRACKING USING A PARAMETER-FREE NON-LINEAR PREDICTOR Issam Bazzi, Alex Acero, and Li Deng Microsoft Research.

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Presentation transcript:

AN EXPECTATION MAXIMIZATION APPROACH FOR FORMANT TRACKING USING A PARAMETER-FREE NON-LINEAR PREDICTOR Issam Bazzi, Alex Acero, and Li Deng Microsoft Research One Microsoft Way Redmond, WA, USA 2003

Ts'ai, Chung-Ming, Speech Lab, NTUST, 20072/14 Outline Introduction The Model EM Training Format Tracking Experiment Results Conclusion

Ts'ai, Chung-Ming, Speech Lab, NTUST, 20073/14 Introduction Traditional methods use LPC or matching stored templates of spectral cross sections In either case, formant tracking is error-prone due to not enough candidates or templates This paper uses a predictor codebook of MFCC to present formant relationships Also, this method explores the complete formant space, avoiding premature elimination in LPC or template matching

Ts'ai, Chung-Ming, Speech Lab, NTUST, 20074/14 The Model o t = F(x t ) + r t o t is observed MFCC coefficients x t is vocal tract resonances (VTR) and corresponding bandwidths F(x t ) is the quantized frequency and bandwidth of formants, named predictor codebook r t is the residual signal

Ts'ai, Chung-Ming, Speech Lab, NTUST, 20075/14 Constructing F(x) All-pole model Assume there are I formants x = (F 1, B 1, F 2, B 2,……, F I, B I ) Then use z-transfrom to get H(z): Finally, each quantized VTR x can be transformed into a MFCC series F(x)

Ts'ai, Chung-Ming, Speech Lab, NTUST, 20076/14 EM Training (1/2) Use a single Gaussian to model r t T frames utterance, θ is parameters (mean and covariance) of Gaussian Assume formant values x are uniformly distributed, and can take any of C quantized values

Ts'ai, Chung-Ming, Speech Lab, NTUST, 20077/14 EM Training (2/2)

Ts'ai, Chung-Ming, Speech Lab, NTUST, 20078/14 Formant Tracking (1/2) Frame-by-Frame Tracking  Formants in each frame are estimated independently  One-to-one Mapping (MAP)  Minimum Mean Squared Error (MMSE)

Ts'ai, Chung-Ming, Speech Lab, NTUST, 20079/14 Formant Tracking (2/2) Tracking with Continuity Constraints  First Order State Model: x t = x t-1 + w t  w t is modeled as a Gaussian with zero mean and diagonal Σ w  MAP method below can be estimated using Viterbi search  MMSE is more much complex and this paper uses an approximate method to obtain, which is not well described here

Ts'ai, Chung-Ming, Speech Lab, NTUST, /14 Experiment Settings Track 3 formants  Frequencies are first mapped on mel-scale then uniformly quantized  Bandwidths are simply uniformly quantized  F1 < F2 < F3, so totally entries in codebook Gain = 1 MFCC is 12 dimension, without C 0 20 utterances of one male speaker are used for EM

Ts'ai, Chung-Ming, Speech Lab, NTUST, /14 Experiment Results, “they were what”

Ts'ai, Chung-Ming, Speech Lab, NTUST, /14 Experiment Results, with bandwidth

Ts'ai, Chung-Ming, Speech Lab, NTUST, /14 Experiment Results, residual

Ts'ai, Chung-Ming, Speech Lab, NTUST, /14 Conclusion This method is totally unsupervised, needless of any labeling Works well in unvoiced frames No gross errors May be applied to speech recognizing system