If and only if the original filter is (strictly) minimum-phase, you can cancel out the response (both magnitude and phase) simply using an inverse filter obtained by swapping the poles and zeroes. This is usually the case for peaking and shelving filters.JCJR wrote: ↑Thu Oct 10, 2019 10:33 amIn fact, in my ignorance this caused a woeful misunderstanding only resolved a few years ago. I had read about processes claiming to "un-do" the time-delay of previous layers of phase shifting, and I couldn't understand how one could possibly un-do several additive layers of "negative slope" phase shift curves, if the only stable causal tools available also have the same direction "negative slope" phase shift curves.
Until someone kindly pointed out that filters such as shelving and peaking filters have "positive bump" or "negative bump" phase shift curves, not the continuous negative slope curve. So it was indeed possible to un-do some kinds of "positive bump" phase curves with complementary "negative bump" phase curves, and vice-versa. Doh! The light finally shines, however feebly.
This doesn't work for LP/BP/HP because the zeroes are on the unit circle and it doesn't work for AP because the zeroes are outside the unit circle; in either case the poles would not be stable.
As for equating phase-shift with time-delays, it just doesn't work. The fact that we have multiple concepts such as phase-delay and group-delay should make it pretty obvious that the "time delay" really depends on what aspect of the signal you are looking at.