Introductory resources to mathematical properties of "dynamically recalculable" filters in audio/musical equalizers?
If you want to modulate in time your filter parameters (like cut frequency), you shouldn't use the usual DF1/TDF2 implementations derived from a polynomial fraction in z.
The reason is that they are originally LTI systems (linear time invariant), which is no longer the case now. The state that they have internally, whether an actual state or a function of the past inputs/outputs, is not reliable when the polynomial coefficients change.
Instead, you should use things like TPT schemas (see the Art of VA filter design at https://www.kvraudio.com/forum/viewtopic.php?f=33&amp;t=350246) that will keep a state that is compatible with parameter changes. Basically, if you map an existing analog system, you model the state of the capacitors and coils and keep them continuous. This doesn't happen when using the z transform.