Any order IIR Bessel LPF, in a MDS configuration, results in a 2nd-order HPF. This more or less fits your description, but I suspect that you want the reverse -- high-order HPF with low-order derived LPF. I don't know if there is any IIR way to do that. The closest that comes to mind is the Linkwitz-Riley + allpass configuration that I described in #855.
Yes, but it's just curiosity that draws me into it, the weirdness of an easy double slope. Else, symmetric would be the way to go.
Yes, LR is probably the configuration that allows so much flexibility.
* As usual, the LR crossovers maybe implemented using FIR techniques.
* LR being a perfect square would always have an exactly phase matching BUT APF of half order, also allowing analogue / IIR implementations irrespective of phase linearisation being used or not.
* Now, if the phase is linearised to 20kHz, the matching APF also allows the straightforward implementation using HPF and LPF using IIR / analogue domain.
* However, if a delay element is available, the LPF phase linearisation need not reach 20kHz but only needs to be 3 or 4 biquads long for resulting in an essentially linear phase HPF that is also symmetric upto -70dB, by means of MDS operation.
I'm not sure it was noticed much, but I had shown this last method for a 100Hz crossing in Charlie's group delay thread:
https://www.diyaudio.com/community/...ing-reverse-iir-filtering.417505/post-7830676
Here is a direct implementation of an LR4 crossover with phase linearisation upto 15kHz, using only analogue / IIR filters. The phase equalisation uses only 10 biquads (for a 4th order filter) and the group delay is only around 700us vs. 450us for the original LPF. With more biquads, the linearisation maybe extended to 20kHz. The phase EQ APFs (2nd order) are as follows.
| Frequency | 2250 | 3650 | 5075 | 6500 | 7925 | 9350 | 10750 | 12150 | 13500 | 14750 |
| Q-factor | 1.6 | 2.6 | 3.6 | 4.6 | 5.6 | 6.6 | 7.65 | 8.75 | 10 | 12.8 |
Impressive, but that's a lot of tuning of resistors, capacitors, and possibly inductors (depending upon how it's implemented).
Yes, but the point is that a global IIR (vs. FIR) linearisation is feasible, in the context of this thread, in addition to the MDS style linear phase version. Also, as correctly mentioned before, the LR4 is a very popular filter in the audio circles.
Indeed it is! Forgive me; it was not my intent to cast aspersions. I should probably have included a smiley.
For anybody who might be interested, a new version of my matched-delay subtractive crossover document is now available. It is about 90% identical to the previous; changes include analysis of linear-phase Butterworth-derived crossovers (thank you @john k... ), just a bit more information about phase equalization via allpass filters, and lots of minor clarifications and embellishments. PM if you'd like a copy.
Greg Berchin
Greg Berchin
