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Tue Jan 4 12:47:34 EST 2011

## Practical d-plane formulations

As a continuation of [1].
Given a d-plane formulation, how to implement it?
It's simplest to start from the leaky discrete integrator and see what
it's d-plane formulation looks like. The time domain formulation
y[k+1] - y[k] = a y[k] + b x[k]
y[k+1] += ...
expresses the update of y in terms of the weighted magnitude of y and
x. It corresponds to the frequency domain formulation
d y = a y + b x
(d - a) y = b x
y / x = b / d - a
The non-leaky integrator is then b / d.
Complex poles are handled in exaclty the same way: We take the complex
form of one of the complementary pairs, feed it a real input and
taking only the real part of the integrator as as output.
TODO:
- Make the 2nd order implementation explicit. Handwaving might be
wrong.
- What about d-zeros?
[1] entry://20110104-110954

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