Pitch Estimation

1. Pitch Estimation By Chih-Ti Shih Chih-Ti Shih

2. Objective Determine the fundamental frequency of a speech waveform automatically Chih-Ti Shih

3. Automatic Extraction of Fundamental Frequency Methods • Cepstrum-based FΦ determinator (CFD) • Harmonic product spectrum (HPS) • Feature-based FΦ tracker (FBFT) • Parallel processing method (PP) • Integrated FΦ tracking algorithm (IFTA) • Super resolution FΦ determinator (SRFD) Chih-Ti Shih

4. eSRFD eSRFD: Enhanced Super resolution FΦ determinator. 1. Pass the sample through low-pass filter to simplify the temporal structure of the waveform 2. Pass the sample frames through silence detector to identify unvoiced frames. No analysis will be done for the unvoiced frames. if |XNmin or XNmax| + |YNmin or YNmax| < Tsrfd it is a silent frame Equation 1 Chih-Ti Shih

5. eSRFD Each frame is subdivided into 3 consecutive segments, xn,yn and zn. Chih-Ti Shih

6. eSRFD Chih-Ti Shih

7. eSRFD Cross-correlation 3. For the ‘voiced’ frame, the first normalized cross-correlation of Px,y(n) of the frame is determined. Normalization Equation 2 Chih-Ti Shih

8. eSRFD 4. Candidate values of the fundamental period are obtained by locating the peaks in the normalized cross-correlation coefficient for which the value Px,y(n) exceeds a certain threshold Tsrfd If no candidates are found in the frame, the frame is classified as ‘unvoiced’. Chih-Ti Shih

9. 5. For the voiced frame (Px,y(n) > Tsrfd), the second normalized cross-correlation coefficient py,z(n) is determined eSRFD Chih-Ti Shih

10. eSRFD 6. For those candidates with both Px,y(n) and py,z(n) exceeds the threshold Tsrfd are given a score of 2, others are 1. Note: If there are one or more candidates with a score of 2, then all those with a score of 1 are removed from the list of candidates. Chih-Ti Shih

11. eSRFD If there is only one candidate with score 1 or 2, the candidate is assumed to be the best estimate of the fundamental period of that frame. Otherwise, an optimal fundamental period is sought from the set of remaining candidates. The candidate at the end of this list represents a fundamental period is nM, and the m’th candidate represents a period nm. Chih-Ti Shih

12. eSRFD 7. then calculate q(nM) which is a normalized cross-correlation coefficient between sections of length nM spaced nm . q(nM) is defined as: Chih-Ti Shih

13. eSRFD Chih-Ti Shih

14. eSRFD The first coefficient q(n1) is assumed to be the optimal value. If the subsequent q(nm) * 0.77 > the current optimal value , the subsequent q(nm) is the optimal value. Chih-Ti Shih

15. eSRFD If previous frame is ‘unvoiced’: the current value is hold and depends on the next frame. If the next frame is also unvoiced, the current frame will be considered as ‘unvoiced’ Otherwise, the current frame is considered as ‘voiced’ and current held FΦ will be considered as the good estimation for the current frame. If only 1 candidate score 1 but no candidate score2: Chih-Ti Shih

16. eSRFD • The changes reduced the occurrence of doubling and halving in FΦ contour. However, they increase the chance the voiced region been miss-classified as unvoiced. Chih-Ti Shih

17. eSRFD 8. Applying biasing to Px,y(n) and Py,z(n) if: 1. The two previous frames were ‘voiced’ 2. The FΦ value of the previous frame is not being temp held. 3. FΦ of previous frame is less than 7/4 *(FΦ of current frame) and greater than 5/8*(FΦ of current frame) However, the biasing tends to increase the percentage of unvoiced regions of speech being incorrectly classified as ‘voiced’. If the unbiased coefficient Px,y(n) does not exceed the Tsrfd and this candidate is believed to be the best estimate of the frame. The FΦ of this candidate is held until the state of the subsequent frame is known. If the next frame is silent, the current frame is re-classified as silent. Chih-Ti Shih

18. eSRFD • 9. The fundamental period for the frame is estimated by calculate rx,y(n) for n in the region –L < n < L. The maximum within this range corresponds to a more accurate value of the fundamental period. Chih-Ti Shih

19. Comparison of asynchronous frequency contours • Compare Fx which is generated from the laryngograph with the FΦ contours generated by eSRFD • Fxreference refer to reference value from laryngograph. • FΦ refer to the value from eSRFD Chih-Ti Shih

20. Comparison of asynchronous frequency contours • Fxreference and FΦ are zero: both describe a silent or unvoiced region of the utterance and no error result. • FΦ is non-zero but Fxreference is zero: the region is incorrectly classified as voiced by eSRFD • Fxrefernece is non-zero but FΦ is zero: the voice region is incorrectly classified as unvoiced by eSRFD • Fxreference and FΦ are non-zero: both correctly classify the region as voiced. In such case, calculate the ration of: Chih-Ti Shih

21. Gross Error Halving error Doubling error Acceptable accuracy Chih-Ti Shih

22. Comparison of asynchronous frequency contours Female Chih-Ti Shih

23. Comparison of asynchronous frequency contours Female Chih-Ti Shih

24. Comparison of asynchronous frequency contours Male Chih-Ti Shih

25. Comparison of asynchronous frequency contours Male Chih-Ti Shih

26. Comparison of asynchronous frequency contours laryngograph eSRFD Chih-Ti Shih

27. Comparison of asynchronous frequency contours Chih-Ti Shih

28. Comparison of asynchronous frequency contours Chih-Ti Shih

29. Question? Chih-Ti Shih