Hello,

recently I implemented and published a music plugin with faust [1],
which implements the digital model of a bass tone circuit.

A problem encountered during this process is the discretization of the
EQ section, located on the bottom part of the schematic [2], running
from C25 to C20 not included.

This circuit describes as a low-frequency peak filter (+ or - gain),
combined with a high-frequency shelf, parameterized by a pair of coupled
knobs labelled as bass and treble.

I have produced a program for computing the expression for the analog
transfer function [3], and applying the bilinear transform.
While the analog transfer function matches the SPICE results, I observed
the digital filter does not meet the criterion for stability (that is,
poles inside the unit circle).

There is faust source code [4], the unstable EQ is replaced with an
adhoc substitute having a relatively matching transfer function.

Any hints on producing a more valid discretization of this system?
Thank you very much

[1] https://github.com/jpcima/Bass21
[2] https://blog-imgs-91-origin.fc2.com/d/r/u/drugscore/02_49_4SABDsch.png
[3] https://git.io/JcQi5
[4] https://git.io/JcQPy


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