Digital resonators in the Klatt synthesizer

Klatt (1980) uses a large number of IIR filters of a very simple kind: IIR filters of the form:

(3.3)    y[t] = Ax[t] + By[t-1] + Cy[t-2].

This is a specific version of (3.2), with b ₀ called A, b₁ to b_k = 0, a ₁ called B, a₂ called C, and a₃ to a _j = 0. Also, he writes nT, meaning sample number n times sample time interval T, instead of t, but that is just a notational difference.

The frequency f and bandwidth w of each filter are determined by the values of the A, B and C coefficients according to the equations:
 

(3.4)	C = -e-2wT
	B = 2e- wT cos(2 fT)
	A = 1-B-C

First, a filter of this kind is applied to an impulse source (a sequence of 0's with 1's at regular intervals). This filtering turns the impulse source into a waveform that looks like the glottal wave and sounds like a glottal buzz . Then, more filters of this kind are applied to the glottal wave model in order to selectively enhance (by bandpass filtering) each of the formants in turn (F1 , F2 , F3 , F4 , F5 ).
 

Next: Exercises