Synthesizer sound generator

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Synthesizer sound generator

Square form :
$\includegraphics{pulsewidth.eps}$
The relation between $pulseWidth\_usp \in Int[0,100]$ and $pw\in Real[0.5,1]$ can be well approximated by the following equation :

$\begin{displaymath}pw = \gamma \times log(\alpha * pulseWidth\_usp + \beta)\end{displaymath}$

where $\alpha = 1.17844$ , $\beta = 11.7539$ and $\gamma = 0.201171$ . Like for the sawtooth form, the square form seems to have a resonnance filter when the pitch goes higher. Filter to determine.
Sawtooth form :
The sawtooth form is describred by the following function :

$\begin{displaymath}st(t) = sq(t) \times cos(w\times t + \epsilon)\end{displaymath}$

where is the square form defined above, the angular frequency ( $w = 2\pi\times f$ ) and $\epsilon$ a slight shifting forward phase that occurs when the pitch is lower. Determine $\bgroup\color{Green}$\epsilon$\egroup$ . In addition there is a sligth resonnance filter when the pitch gets higher. Filter to determine.

Nil Geisweiller