Hi
@j_j thanks for hanging around the thread and answering questions
I have another question for you. It is known that the output of minphase filters can not reconstruct a square wave input. For linphase filters, the summation of the low pass and high pass will reconstruct the square wave. A transient is the closest thing we have in music to a square wave. I have heard people say that minphase filters smear the transient in the same way a square wave is smeared across time. The audible consequence is less "attack" of the transient. In your opinion, is this true?
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This goes back to a very simple issue, the length of the impulse response of a filter. The resolution (in frequency) of a filter determines how long the impulse response must be.
I forget where, but there is a set of examples here where I posted a minimum phase, constant delay, and maximum phase trio of filters that all have exactly the same frequency (magnitude, not phase) response.
If you use an IIR (typically minimum phase) filter, the peak of the filter response is near the start. If you use a constant delay filter, it's in the middle. But, for the same frequency response, you're going to have the same overall length.
So, you trade off things like potential pre-echo vs. potential audible phase-shift. It is entirely possible to build a mixed-phase filter, some IIR and minimum phase, some FIR of any phase you choose.
BUT, IIR filters must always have minimum phase pole roots. Otherwise they aren't stable. It's not just a good idea, as they say, it's the MATH.
FIR filters can be anything they want. You can take a constant delay filter, use standard cepstrum techniques and make it minimum phase, for instance. You can take the roots of the filter (this is a much more "high-precision" effort and hard to do past very short filter lengths) identify the zero pairs and quads (for a symmetric filter, there will always be quads for complex roots, one is the inverse of the other in the root value), and swap pairs back and forth between the root and 1/root to make things more minimum phase, or more maximum phase, or whatever you choose. Some people call this apodizing, I call it math.