... but the 180° phase response shows clearly the behaviour of a 2nd order allpass and is therefore NOT minimum phase.
That leads me to the conclusion that the impulse responses for sound coming from the front up to an angle of 90° (the preferred use case of this type of mic) are completely linked to the frequency response via f->t or t->f transformation principles.
Thanks for this MicUlli. You have demonstrated exactly the situation I hinted at earlier about 'back response'
possibly being non-MP
I suspected this from working with Prof Angelo Farina, on whether rooms, with their reflections, were MP.
What we found was that when
later arrivals were larger than the first, the transfer function could be
non-MP. It was unclear from our small investigation whether this is
sufficient or just necessary. Definitely worth a PhD
As the 'back response' is usually a small part of the total sound, it isn't important .. unless you record important stuff on the null of your cardioid
The excess phase behaviour for sound coming from behind is not that critical because the group delay is smaller than approx. 100 us and therefore not audible at all...
Thanks also for showing the scale of the problem. 100us might be at the accuracy limits of modern test gear.
I forgot to mention that some
modern test gear will do the Hilbert Transform for you (Clio?) ... including removing the delays etc. The '
Excess Phase' is a measure of
how non-MP something is.
MicUlli, what gear are you using for these supa dupa measurements?
An important point which IIRC, I mention in
Simple Arbitrary IIRs, is that if a Transfer Function is mostly MP but has non-MP bits (as MicUlli's example). you should
only EQ the MP bits. That way you ALWAYS improve the Transient (Impulse) Response.