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Fri Apr 19 14:17:26 EDT 2013

All-pole filter designer GUI

Given: some graphical represenation of a frequency response,
e.g. displayed as a log-log plot in a GUI.

In order for the user to be able to incrementally edit the graph, two
parameters should be settable: a gain increment at a specific
frequency (e.g. mouse drag point) and the bandwidth of the gain
increment.  Suppose that the "smoothing" operation can somehow be
defined.

Given a power spectrum, it can be mapped to an all-pole model using
the Schur algorithm after converting the power spectrum to an
autocorrelation sequence.  When the resulting AR model is plotted
again as a power spectrum, this by itself is a smoothing operation.

What about the following: allow the user to pick the filter order.
This will set the "smoothing amount".  Then tugging at different
places is just changing 1 frequency bin.  The effect of this on the
autocorrelation can be computed directly by adding a sinusoidal
component, so an IFFT step is actually not necessary.

Instead of adding a pure sine, which might be too "sharp", it might be
possible to update the autocorrelation directly with the
autocorrelation of a damped exponential.

Given an N (even) order model, the first N/2 damped exponentials added
will be matched exactly.  Impulse at DC is overall gain, not a
parametric EQ.  However, a notch filter can be designed as the inverse
of a peak filter.

Additionally, it might be interesting to look at interpolation between
different transfer functions by setting linear interpolation of
reflection coefficients, or different kinds of non-linear
interpolation where some reflection coefficients are interpolated at a
different rate.




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