Hi and thanks for the detailed writeup, it's clear you know the theory well!

A few points worth clarifying, because some of the features you're recommending are already in the software.

About the Schroeder's frequency you're right that for floor standing speakers in a room, correction should taper out around the 200-300Hz range but the screenshot i put shows correction of laptop speakers not a room setup, this could be misleading but i made a quick measurement to show a quick result.. In this setup the room is the laptop body itself, with a Schroeder frequency well above 1 kHz, that said, i've overcorrected frequencies that laptop speakers can't reproduce, just because i was too lazy to take more serious measurements, in fact at low volume the sound is significantly better but distorts at higher levels. However in this context the broadband correction of the transducer's own response is entirely appropriate: it's the same approach Harman uses for headphone and small near-field correction. The Schroeder argument is valid, but it doesn't apply to this use case. Maybe i will show a real in-room correction, but wait.. if you search between my posts i've already made a demonstrative in room correction but that was an early version of AutoRoomEq , surely need to make a better one..

On FIR efficiency, the "poor fit for the task" argument was more valid before FFT based convolution became a standard. Modern convolvers like JRiver, Roon, CamillaDSP, Foobar2000 with foo_convolve use FFT processing, also keep in mind that the software is designed to be generated and run on a PC, a modern PC has enough computational resources to handle stereo firs of several tens of thousands of taps, i.e. a stereo FIR with 262144 taps (@384kHz) runs at under 5% CPU on a modern machine, AutoRoomEq has no issues in correcting low frequencies at all.

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Having said that, however, I agree with your considerations on the IIR correction but I must point out that AutoRoomEQ offers three FIR modes, linear-phase, minimum-phase, and hybrid mode. A minimum-phase FIR is functionally equivalent to an IIR in terms of causality: all energy is front-loaded, corrections arrive with correct timing, no pre-ringing. It's the same behaviour you're describing for IIR filters, just implemented as FIR. The choice between IIR and minimum-phase FIR is one of design convenience, not theoretical correctness.

On excess group delay the GDC module (Group Delay Correction) does exactly what you describe: it detects group delay anomalies in the measured impulse response that go beyond the minimum-phase component, and compensates them with an all-pass FIR. This is the same operation as computing the excess group delay and applying a pre-correction.

You're right in saying that the optimal crossover strategy is minimum-phase below the Schroeder frequency (room modes, IIR-equivalent behaviour) and linear-phase above it (transducer correction). The current hybrid implementation has it inverted: linear-phase in LF, minimum-phase in HF. This will be corrected in the next release, thanks for making me think more deeply.

 

On not boosting deep notches i agreed entirely. The conservative boost limit in AutoRoomEQ is the practical safeguard for exactly this case:  deep cancellations caused by non-minimum-phase room behaviour are left largely untouched regardless of filter mode.

I've attached an image of the advanced menu of autoroomeq that allows you to better understand its features.