1. Pitch Determination by Wavelet Transformation Santhosh Bellikoth ECE 5525- Speech Processing Instructor: Dr Kepuska

2. Pitch Determination Equivalent to fundamental frequency estimation Equivalent to fundamental frequency estimation Essential Component in all Speech Processing system Essential Component in all Speech Processing system

3. Applications of Pitch Detector Speaker Identification and Verification Speaker Identification and Verification Pitch Synchronous speech analysis and Synthesis Pitch Synchronous speech analysis and Synthesis Linguistic and phonetic knowledge acquisition Linguistic and phonetic knowledge acquisition Voice disease diagnosis Voice disease diagnosis

4. Continuous Wavelet transform Continuous Wavelet transform is defined as the convolution of a signal x (t) with a wavelet functionΨ(t) shifted in time by a translation parameter ‘b‘ and a dilation parameter ‘a’ Continuous Wavelet transform is defined as the convolution of a signal x (t) with a wavelet functionΨ(t) shifted in time by a translation parameter ‘b‘ and a dilation parameter ‘a’

5. Dyadic Wavelet Transform Dyadic Wavelet Transform is defined as Dyadic Wavelet Transform is defined as

6. Dyadic Wavelet Transform Properties Linearity Linearity Time Shift Variance Time Shift Variance Detection of sharp and slow variation in the signal, which makes it useful tool for the analysis of Speech Signal. Detection of sharp and slow variation in the signal, which makes it useful tool for the analysis of Speech Signal.

7. Plot of Haar Wavelet and Scaling Function

8. Pitch Detection Steps Segmentation of Speech Signal Segmentation of Speech Signal Scale Selection Scale Selection Computation of Wavelet Transformation of each frame at various scales Computation of Wavelet Transformation of each frame at various scales Locating Position of local maxims for each frame Locating Position of local maxims for each frame Locating position of GCIs Locating position of GCIs Calculation of Pitch Periods Calculation of Pitch Periods

9. Segmentation of Speech Signal 1) Segmentation without Overlapping Speech Signal is segmented using a hamming window of 40 ms duration Speech Signal is segmented using a hamming window of 40 ms duration 2) Segmentation with 50 % Overlapping Rectangular window is used with overlapping of less than 10 % Rectangular window is used with overlapping of less than 10 %

10. Scale Selection Dyalet Wavelet Transform is computed at scales a=2^j for all j. Dyalet Wavelet Transform is computed at scales a=2^j for all j. Number of Scales for computation of can be reduced based on the nature of the speech signal. Number of Scales for computation of can be reduced based on the nature of the speech signal.

11. Number of Scales Selection Wavelet with input center frequency fci and input bandwidth Δfi, Scale parameter ‘a’ corresponding to the required output center frequency fco using the following relation Wavelet with input center frequency fci and input bandwidth Δfi, Scale parameter ‘a’ corresponding to the required output center frequency fco using the following relation a= fci/fco a= fci/fco

12. Input and Output bandwidth Input bandwidth of the wavelet Input bandwidth of the wavelet Δfi= 2*fci Δfi= 2*fci  Output Bandwidth of the wavelet Δfo=2*fco Δfo=2*fco

13. Approximation of ‘a’ If fci/fco is not to some power of 2, then it is rounded off to nearest power If fci/fco is not to some power of 2, then it is rounded off to nearest power For high pitch speakers lower bound is decreased and upper bound is increased for the better results For high pitch speakers lower bound is decreased and upper bound is increased for the better results

14. Computation of Dyadic Wavelet Transform The Dyadic Wavelet Transform is computed for each frame by the following equation The Dyadic Wavelet Transform is computed for each frame by the following equation

15. Speech Signal to be Segmented

16. First Three Frames of Original Speech Signal with 50% overlapping

17. Speech Segment and Dyadic Wavelet Transform

18. Locating Positions of Local maxims For locating the position of local maxims, first all the peaks of the waveform are located. For locating the position of local maxims, first all the peaks of the waveform are located. Positions of local maxims are computed by setting a threshold, which is 80% of the global maximal. Positions of local maxims are computed by setting a threshold, which is 80% of the global maximal.

19. Locating all the upside peaks of a waveform and local maxims

20. Locating the position of GCI’s (Glottal closure Instant) If the position of local maxima at a scale matches the position of local maxima of frame whose wavelet transform has been calculated, then those locations are called GCI’s position If the position of local maxima at a scale matches the position of local maxima of frame whose wavelet transform has been calculated, then those locations are called GCI’s position If it does not match then it is compared with the Wavelet transform at next higher scale If it does not match then it is compared with the Wavelet transform at next higher scale

21. Pitch Calculation Pitch can be computed as Pitch can be computed as d is the difference between two GCI positions in terms of sample and fs is the sampling frequency of the speech signal d is the difference between two GCI positions in terms of sample and fs is the sampling frequency of the speech signal

22. Acoustic Measures Jita Jita Jita is absolute Jitter, which gives an evaluation in msec of the period to period variability of the Pitch period with in the analyzed voice sample Jita is absolute Jitter, which gives an evaluation in msec of the period to period variability of the Pitch period with in the analyzed voice sample

23. Jitter Jitter percent gives an evaluation of the variability of the pitch period within the analyzed voice sample in percent. Jitter percent gives an evaluation of the variability of the pitch period within the analyzed voice sample in percent. P is the pitch period and N is the number of pitch estimated. P is the pitch period and N is the number of pitch estimated.

24. Shimmer (DB) Shimmer in dB gives an evaluation of the period to period variability of the peak to peak amplitude within the analyzed voice sample. Shimmer in dB gives an evaluation of the period to period variability of the peak to peak amplitude within the analyzed voice sample.

25. Shimmer(%) Shimmer percent gives an evaluation in percent of the variability of the peak to peak amplitude within the analyzed voice sample. Shimmer percent gives an evaluation in percent of the variability of the peak to peak amplitude within the analyzed voice sample. Shimmer in percent is given by Shimmer in percent is given by

26. Conclusion Acoustic parameters computed using wavelet transform can be used for the objective analysis of pathological voice. Acoustic parameters computed using wavelet transform can be used for the objective analysis of pathological voice. These Acoustic parameters can be used to differentiate between normal and pathological voice. These Acoustic parameters can be used to differentiate between normal and pathological voice.

27. Final Program clc; clear all; close all; [s,fs]=wavread('U:\speech2_10k.wav'); %s=s1(1:10000); m=400; wL=400; L=length(s); nf=floor(L/wL); j=1; t=10;

28. Final program cmp1=[]; cmp2=[]; cmp3=[]; gci=[]; q=[]; d=[]; a=[]; %b=[]; disp('Enter x=1 for male voice'); disp('Enter x=2 for female voice');

29. Final Program x=input('Enter the value of x ='); switch x case 1 for i=1:nf-1 f(j,:)=f_ovp(s,m,wL,i); g=gne(f(j,:)); c1=cwt(f(j,:),4,'haar'); c2=cwt(f(j,:),8,'haar'); c3=cwt(f(j,:),16,'haar'); c4=cwt(f(j,:),32,'haar');

30. Final Program [p1,q1,d1]=f_shim_max(c1); [p2,q2,d2]=f_shim_max(c2); [p3,q3,d3]=f_shim_max(c3); [p4,q4,d4]=f_shim_max(c4); L1=length(p1); L2=length(p2); L3=length(p3); L4=length(p4); if L1==L2 cmp1=comp_t(p1,p2,t);

31. Final Program elseif L2==L3 cmp2=comp_t(p2,p3,t); elseif L3==L4 cmp3=comp_t(p3,p4,t); end if ~isempty(cmp1) gci=[gci,p1']; q=[q,q1']; d=[d,d1']; elseif ~isempty(cmp2)

32. Final Program gci=[gci,p2']; q=[q,q2']; d=[d,d2']; elseif ~isempty(cmp3) gci=[gci,p3']; q=[q,q3']; d=[d,d3']; elseif isempty(cmp1)& isempty(cmp2) d=[d,zeros(1,1)]; end

33. Final Program end a=[a g]; % b=[b g2]; j=j+1; end %d1=diff(gci); case 2 for i=1:nf-1 f(j,:)=f_ovp3t(s,m,wL,i); c1=cwt(f(j,:),8,'haar'); c2=cwt(f(j,:),16,'haar'); c3=cwt(f(j,:),32,'haar'); c4=cwt(f(j,:),64,'haar'); g=gne(f(j,:)); [p1,q1,d1]=f_shim_max(c1); [p2,q2,d2]=f_shim_max(c2);

34. Final Program [p3,q3,d3]=f_shim_max(c3); [p4,q4,d4]=f_shim_max(c4); L1=length(p1); L2=length(p2); L3=length(p3); L4=length(p4); if L1==L2 cmp1=comp_t(p1,p2,t); elseif L2==L3 cmp2=comp_t(p2,p3,t); elseif L3==L4 cmp3=comp_t(p3,p4,t); end if ~isempty(cmp1) gci=[gci,p1'];

35. Final Program q=[q,q1']; d=[d,d1']; elseif ~isempty(cmp2) gci=[gci,p2']; q=[q,q2']; d=[d,d2']; elseif ~isempty(cmp3) gci=[gci,p3']; q=[q,q3']; d=[d,d3']; elseif isempty(cmp1)& isempty(cmp2) d=[d,zeros(1,1)]; end a=[a g]; % b=[b g2];

36. Final Program d=smooth_d(d); p=d./fs; L5=length(gci); L6=length(p); L7=abs(L5-L6); m=mean(p); fo=1/m; m1=max(p); m2=min(f_wz(p)); fh=1/m2; fl=1/m1; jit=jita(p); jitt=jitter(p); shdB=shimdB(q,L6); sh=shimmer(q,L6); GNE=max(a);

37. Final Program %GNE2=max(b); disp('Fundamental frequency ='); disp(fo); disp('Highest frequency='); disp(fh); disp('Lowest frequency='); disp(fl); disp('Jita ='); disp(jit); disp('Jitter in percentage'); disp(jitt); disp('Shimmer in dB ='); disp(shdB); disp('shimmer in percentage='); disp(sh);

38. Final Program disp('Press any key for plot'); pause; if L5==L6 stairs(gci,p); xlabel('Number of Samples'); ylabel('Pitch period in msec'); title('Pitch contour'); elseif L5<L6 gci=[gci,zeros(1,L7)]; stairs(gci,p); xlabel('Number of Samples'); ylabel('Pitch period in msec'); title('Pitch contour'); else p=[p,zeros(1,L7)]; stairs(gci,p); xlabel('Number of Samples'); ylabel('Pitch period in msec'); title('Pitch contour'); end

39. Results and Observations Enter x=1 for male voice Enter x=1 for male voice Enter x=2 for female voice Enter x=2 for female voice Enter the value of x =1 Enter the value of x =1 Fundamental frequency = Fundamental frequency = 351.4493 351.4493 Highest frequency= Highest frequency= 3.3333e+003 3.3333e+003 Lowest frequency= Lowest frequency= 217.3913 217.3913 Jita = Jita = 0.0021 0.0021 Jitter in percentage Jitter in percentage 72.4864 72.4864

40. Results and observations Jitter in percentage Jitter in percentage 72.4864 72.4864 Shimmer in dB = Shimmer in dB = 3.2017 3.2017 shimmer in percentage= shimmer in percentage= 15.6931 15.6931 Press any key for plot Press any key for plot >> >> Variables created in current workspace. Variables created in current workspace. >> >>

41. QUESTIONS??????? QUESTIONS???????