Measured Period 8 6 4 2 VOICE SIGNAL -2 -4 -6 -8 0.018 0.02 0.022 VOICE SIGNAL -2 -4 -6 Measured Period -8 0.018 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 TIME (SEC) Figure 2.19. Identification of negative peaks for fundamental frequency tracking on a typical original voice signal. The tracking algorithm automatically selects the minima indicated by X and performs a parabolic interpolation to determine the time of minima to a precision of less than one sample. Circles indicate sample points.

275 270 FREQ (HZ) 265 260 255 0.2 0.4 0.6 0.8 1 TIME (SEC) Figure 2.20. A high resolution 1 sec. fundamental frequency track resulting from subsample interpolation. Note lack of fundamental frequency quantization (flat spots) that would occur without interpolation.

275 270 FREQ (HZ) 265 260 0.2 0.4 0.6 0.8 1 TIME (SEC) 4 2 FREQ (HZ) -2 -4 0.2 0.4 0.6 0.8 1 TIME (SEC) Figure 2.21. The fundamental frequency track of Fig 2.20 is low pass filtered (top part A curve) and high pass filtered (bottom part B curve) yielding the tremor and HFPV time series respectively. A cutoff frequency of 10 Hz is selected.

45 40 35 30 25 #OCCURRANCES 20 15 10 5 -1.5 -1 -0.5 0.5 1 1.5 DELT FREQ (%) TOTSKIP=0 FCUT=10 TOTMAN=0 Figure 2.22. Histogram of frequency deviations of the high pass filtered fundamental frequency time series of Fig 2.20. Successful fundamental frequency tracking yields a Gaussian form distribution.

ORIGINAL FUNDAMENTAL FREQ. 250 ORIGINAL FUNDAMENTAL FREQ. 240 RESAMPLED FUNDAMENTAL FREQ. 230 FUNDAMENTAL FREQUENCY (HZ) 220 210 200 190 0.2 0.4 0.6 0.8 1 TIME (SEC) Figure 2.23. Fundamental frequency time series of original voice and voice re-sampled to remove tremor (low frequency variations). Most of the significant fundamental frequency variation is removed

FREQ (Hz) TIME (SEC) DELTA FREQ PERCENT 0.2 0.4 0.6 0.8 1 266.2 266.4 0.2 0.4 0.6 0.8 1 266.2 266.4 266.6 FREQ (Hz) TIME (SEC) -0.1 -0.05 0.05 0.1 DELTA FREQ PERCENT Figure 2.24. Fundamental frequency time series of voice re-sampled to remove all fundamental period variations: both HFPV and tremor. In the upper plot the residual variation after removal is shown in Hz; it is less than 0.4 Hz. In the lower plot the residual is shown in percent.