Fundamentals of FOFs

Formant wave function synthesis is the basic principle of CHANT. CHANT is a singing voice synthesizer which can be also used to model other resonators. The principle behind CHANT is subtractive synthesis, in which a source signal with a broad spectrum passes through a complicated filter.

These filters can be broken down in a set of parallel bandpass filters.

An alternative implementation replaces the filters with a bank of damped sine wave generators. This leads to the following time domain waveform:

$$s(n) = \left\{ \begin{array}{l} 0, n \leq 0 \\ \\ \fr... ... \sin( \omega_c n + \phi), n > \pi/\beta \end{array} \right.$$ (1)

where $\omega_c$ is the frequency of resonance, $\pi / \beta$ = width of the skirts (in seconds) $k$ is the sample index, $\alpha$ is the decay time. The formant skirt is defined as the lower part of the formant peak.