Pitch Determination

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

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

3. Applications of Pitch Detector • Speaker Identification and Verification • Pitch Synchronous speech analysis and Synthesis • Linguistic and phonetic knowledge acquisition • 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’

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

6. Dyadic Wavelet Transform Properties • Linearity • Time Shift Variance • 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 • Scale Selection • Computation of Wavelet Transformation of each frame at various scales • Locating Position of local maxims for each frame • Locating position of GCIs • 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 2) Segmentation with 50 % Overlapping 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. • 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 a= fci/fco

12. Input and Output bandwidth • Input bandwidth of the wavelet Δfi= 2*fci • Output Bandwidth of the wavelet 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 • 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

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. • 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 it does not match then it is compared with the Wavelet transform at next higher scale

21. Pitch Calculation • 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

22. Acoustic Measures • 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

23. Jitter • 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.

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.

25. Shimmer(%) • 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

26. Conclusion • 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.

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=2 for female voice • Enter the value of x =1 • Fundamental frequency = • 351.4493 • Highest frequency= • 3.3333e+003 • Lowest frequency= • 217.3913 • Jita = • 0.0021 • Jitter in percentage • 72.4864

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

41. QUESTIONS???????