[sdiy] Filter slopes

ASSI Stromeko at nexgo.de
Mon Jun 11 21:50:42 CEST 2018

On Monday, June 11, 2018 7:43:22 AM CEST Elain Klopke wrote:
> I was reading an article about the spectral content of various instruments
> (woodwinds and strings) and while they didn't have any circuits, there were
> some tables showing cutoff frequencies and high and low slopes. Several of
> the pictures looked like bandpass filter responses with different slopes on
> each side. How would I go about doing that? Is the slope determined by the
> gain of the op amp in an active filter? If it's that easy, would it be a
> highpass filter followed by a lowpass filter each with their own gain
> settings?

Both woodwinds and string instruments (among others) can be modeled with 
coupled resonators.  The characteristic timbre of each is related to the modes 
of these resonators and the transfer of energy between them.  The slopes of 
the bandpass skirts depend on both the quality factor of the resonator and the 
coupling strength to other resonators or resonator modes.  Generally speaking, 
losing energy (e.g. into another mode) is a reduction in Q and hence shows up 
as a flattening of the slope.  If you just want to approximate the magnitude 
response, a filter bank with a high enough number of filter bands is as good 
as any other method and relatively easy to implement, it just uses many de-
coupled resonators instead of few(er) coupled ones.

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