1. 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

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

3. 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

4. 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

5. 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)

6. 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

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

8. 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)

9. 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

10. Ts'ai, Chung-Ming, Speech Lab, NTUST, 200710/14 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 767500 entries in codebook Gain = 1 MFCC is 12 dimension, without C 0 20 utterances of one male speaker are used for EM

11. Ts'ai, Chung-Ming, Speech Lab, NTUST, 200711/14 Experiment Results, “they were what”

12. Ts'ai, Chung-Ming, Speech Lab, NTUST, 200712/14 Experiment Results, with bandwidth

13. Ts'ai, Chung-Ming, Speech Lab, NTUST, 200713/14 Experiment Results, residual

14. Ts'ai, Chung-Ming, Speech Lab, NTUST, 200714/14 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