Investigation of building an Electronic Mode Filter (EMF) using a microstrip design. First step is to approximate the
mode function (more precisely the time reversed mode function) with a rational H(s). For H(s) to be realizable as a
discreet lumped RLC filter, H(s) must have both poles and zeros in LHP (left half-plane of the s-lane).

Mode functions:

soft_exp_decay(t, a, decayDur): model what Jonas Neergaard described as desirable on Slack, October 2025. Starts with
     an exponential rise, then smothly reaching a top, falling down x2 faster than rising, and smoothly doing back to
     zero.


Functions returning H(s) as a MATLAB 'tf' object, given an input function:

optimize_ct_impulse(@soft_exp_decay): with 8th order able to approximate 'soft_exp_decay' very well, BUT return
     strongly non-minphase transfer function, where all zeros are in RHP.



codex resume 0199f27d-1c34-7020-a915-893b768e19e2