[PD] amplitude of modal synthesis

[frablanc]

The continous-time equation is : (d²x/dt²)/F² +(dx/dt)/(Q*F)+x
= E, where E stands for the excitation, F the "proper"
pulsation (not
the frequency) of the system, and Q the quality coefficient.

the derivations are discretized using :

 d²/dt² --> (Z - Z^(-1))Fe²,

 and d/dt --> (Z - Z^(-1))Fe/2 (Fe is the samplerate);

After some algebra, this leads to the difference equation:

x(n) = 1/(Fe²/F² + Fe/(2QF))* [ (2Fe²/F² - 1)x(n-1) +
(Fe/(2QF) - Fe²/F²)x(n-2) + E(n-1)];

anyway, i did a mistake in the biquad~ coefficients (the
excitator coefficient), and now highest pulsations are louder
than the lowest, but the difference is smaller ...

here is the new patch.
François.

 
> interesting problem, could you describe the equation you used?
> 
> cyrille
> 

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