S522, Kewley-Port
Spring , 2008

Assignment #11 (20 Points)

Specific Assignment on KLATT Synthesis, Week 11, due 4/2

The KLATT synthesizer can be simplified as the cascade of three filters, noted in z-transforms as

P(z) = S(Z)T(Z)R(Z)

In this assignment you are asked to interpret the description of each filter in terms of the notation used in the course, and implement the filters in Matlab. Pezdemo, fdatool or any Matlab commands may be used for any part of this assignment. Use T = .0001 s (FS = 10000 Hz) as the sample rate.

1. Start with R(Z) the easiest. Write down the system function, R(z), in the standard formant, and draw the system block diagram. Hand in the pole/zero plot and the magnitude spectrum.

2. Now try T(Z) for a single resonator, F=1000 Hz and BW = 50 Hz as shown in Fig. 5. Carefully calculate the A, B, and C coefficients. Write down the system function and draw the system block diagram using our notation instead of KLATT's. Factor the denominator into two components in the polar notation and plot the pole/zero diagram. Also calculate the rectangular coefficients. Calculate and print out the magnitude spectrum of your resonator including the A coefficent and check it against that of Fig. 5. Also print the impulse response. On the print outs explain the method you used to calculate the magnitude spectrum and impulse response of your filter (or turn in the Matlab script).

3. Implement S(Z). Calculate and hand in the B and C coefficients for the pole, and coefficients A', B' and C' for the anti-resonator using Klatt's Eq. (4) & (5). Write out the system function, S(z), for these coefficients. Using Matlab, check that the output impulse response of the filter is the glottal waveform with the shape shown at top Fig. 7. Keep a lot of precision in calculating your zero coefficients or you will not get the glottal waveform in Fig. 7. Print your glottal waveform.

4. Now, implement the full P(Z) filter from all filter coefficients from 1, 2 and 3. Write out the full P(Z) system equation (i.e. multiply out the CSOS sections) and the difference equation for y(n). Print out the magnitude spectrum and the impulse response for P(Z).

{Updated on 3/23/08}