Ethan Fenn писал 2016-03-25 20:57:
oscillator. The update step looks like this:
y := p + b0*x
p := -(a1/2)*p + (sigma/2)*q + (b1 - a1*b0)*x
q := -(sigma/2)*p - (a1/2)*q + (1/sigma)*(2*b2 - 2*a2*b0 - a1*b1 +
a1^2*b0)*x
Is there a name for this kind of representation?
This looks like a single (real) Jordan cell of a state-space form. Also,
equivalently, I think "coupled form" oscillator is the name, where here
it's explicitly excited to be used as a filter. Not sure if "magic
circle" means the same.
IIRC, the problem with this form (as with Jordan normal form in
principle) is that it gets ill-conditioned when the poles get close to
each other (upon the first look I'm not sure where this ill-conditioning
appears in your formulas, though, so I might be wrong there, or there
could have been a mistake). So, it's not very practical if the resonance
may be low. I suggest using ZDF (aka TPT, aka trapezoidal) state
variable filter instead.
Regards,
Vadim
--
Vadim Zavalishin
Reaktor Application Architect | R&D
Native Instruments GmbH
+49-30-611035-0
www.native-instruments.com
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