I recently published an article in audioXpress (September 2024) about a new family of loudspeaker crossovers that I call "DFE Crossovers". The filters that make up these crossovers are derived from elliptic filters (giving rise to the DFE name) are characterized by:
The DFE family consists of over 30 examples, having order from 3 to 8. Variations such as "squared" crossovers (like the Linkwitz-Riley crossover) and combinations of all-pole and DFE crossovers (AP-DFE), are included in the "family". The AP-DFE type can be implemented as a mixed passive+active hybrid, with the all-pole part implemented as a passive crossover and the DFE part using analog active or IIR DSP means. This has the advantage of suppressing harmonic distortion within the LP filter passband (see this Purifi tech note for more information).
The audioXpress article provides full details on the DFE crossovers, but I will provide a couple of examples below. I typically present the lowpass filter response, a zoomed-in view of the LP+HP sum, and the group delay of the crossover. The highpass filters is simply the lowpass mirrored about the crossover frequency. Please see the following attachments:
The elliptic-like response of these crossovers is well suited to loudspeaker crossovers because stopband attenuation of more than about 50dB is not necessary. Instead it is better is to quickly transition between passband and stopband (e.g. the transition band is narrow). Most non-FIR filters with such narrow transition bands would produce excessively high group delay that would cause audible phase distortion, but I have used the extra degrees of freedom to design the DFE Family filters to have sufficiently low group delay as to not give rise to audible distortion in the time domain signal.
Overall these filters offer an interesting mix of capabilties that has not yet been available except through FIR filtering. The DFE filters can be implemented with analog active circuits or IIR DSP, and remain easy to use and relatively lightweight. You can download information about the complete DFE Crossover family at the following link:
https://audioxpress.com/files/attachment/2777
.
- steep transition bands, up to ~150dB/octave
- a stopband that is finite in depth, typically 40dB-50dB but sometimes more
- excellent LP+HP summation with very low ripple
- low group delay (below the threshold of audibility reported in the literature)
The DFE family consists of over 30 examples, having order from 3 to 8. Variations such as "squared" crossovers (like the Linkwitz-Riley crossover) and combinations of all-pole and DFE crossovers (AP-DFE), are included in the "family". The AP-DFE type can be implemented as a mixed passive+active hybrid, with the all-pole part implemented as a passive crossover and the DFE part using analog active or IIR DSP means. This has the advantage of suppressing harmonic distortion within the LP filter passband (see this Purifi tech note for more information).
The audioXpress article provides full details on the DFE crossovers, but I will provide a couple of examples below. I typically present the lowpass filter response, a zoomed-in view of the LP+HP sum, and the group delay of the crossover. The highpass filters is simply the lowpass mirrored about the crossover frequency. Please see the following attachments:
Example 1: 5DFE_1.50_A48_P0
Example 2: 6DFE_1.25_A44_P90
Example 3: AP3_4DFE_1.41_A46_P83
The elliptic-like response of these crossovers is well suited to loudspeaker crossovers because stopband attenuation of more than about 50dB is not necessary. Instead it is better is to quickly transition between passband and stopband (e.g. the transition band is narrow). Most non-FIR filters with such narrow transition bands would produce excessively high group delay that would cause audible phase distortion, but I have used the extra degrees of freedom to design the DFE Family filters to have sufficiently low group delay as to not give rise to audible distortion in the time domain signal.
Overall these filters offer an interesting mix of capabilties that has not yet been available except through FIR filtering. The DFE filters can be implemented with analog active circuits or IIR DSP, and remain easy to use and relatively lightweight. You can download information about the complete DFE Crossover family at the following link:
https://audioxpress.com/files/attachment/2777
.
Attachments
Fantastic! Always nice to see somebody developing versions of notched filters. I've liked using passive Type II Chebyshev's (or even m-derived, if I'm feeling like a bit of self-abuse) tracking some initial 'standard' rolloff (e.g. LR-8, LR-12 etc.) for years, providing the baseline electrical ladder order doesn't get too high to keep GD in check. Will look forward to reading -& many thanks, as always! 🙂
Fascinating! Why wouldn’t one want to use the higher-attenuation versions in your examples with little-to-no phase change?
@von Ah BY "phase-change" do you mean the relative phase angle of LP and HP filters at the crossover frequency? When the filter is very steep, this is not as important compared to a less-steep crossover. Sometimes an in-phase crossover is desired, and sometimes one with a 90 degree phase angle (which also has constant power) is desired. Some people might prefer more attenuation in the stop band, and some dont' care that much. So there are many possibilities.
In general, when the crossover is steep it can not also have a very deep stopband. I tried to get at leats 40-50dB in the stopband if the transition band is very narrow. If the transition band is allowed to be wider, the stopband can be deeper. When you make the transition band very wide, the response for the first octave or so looks just like a Butterworth of the same order, and that would not be any better than using the Butterworth. So I concentrated more on the crossovers with narrow transition band.
All of these parameters are limited by the group delay. For Fc=1kHz, you want to keep the group delay below about 1.5 millliseconds. But even if you want very low group delay similar to an LR4 (with max GD of around 0.5msec for Fc=1kHz), I offer a 5th order filter with about the same group delay and a narrower transition band in the 5DFE_1.75_A45_P66. It just has a different relative phase angle between LP and HP and the response is 45dB down at 1.75 times Fc (over only 0.81 octaves).
In general, when the crossover is steep it can not also have a very deep stopband. I tried to get at leats 40-50dB in the stopband if the transition band is very narrow. If the transition band is allowed to be wider, the stopband can be deeper. When you make the transition band very wide, the response for the first octave or so looks just like a Butterworth of the same order, and that would not be any better than using the Butterworth. So I concentrated more on the crossovers with narrow transition band.
All of these parameters are limited by the group delay. For Fc=1kHz, you want to keep the group delay below about 1.5 millliseconds. But even if you want very low group delay similar to an LR4 (with max GD of around 0.5msec for Fc=1kHz), I offer a 5th order filter with about the same group delay and a narrower transition band in the 5DFE_1.75_A45_P66. It just has a different relative phase angle between LP and HP and the response is 45dB down at 1.75 times Fc (over only 0.81 octaves).
Great work, thanks for that. I see the discussion we had about a year back has grown some serious fruits.
Some of the alignments look really nice for my tastes, that is, the ones with flat zero degree phase offset throughout the whole transition band (and some even beyond), very Linkwitz-Riley'ish. Same for some of the 90deg offset Butterworth'ish variants. I found strict phase tracking with a truly constant offset in the transition range one of the key parameters of good coherent sound but that's just me.
Some of the alignments look really nice for my tastes, that is, the ones with flat zero degree phase offset throughout the whole transition band (and some even beyond), very Linkwitz-Riley'ish. Same for some of the 90deg offset Butterworth'ish variants. I found strict phase tracking with a truly constant offset in the transition range one of the key parameters of good coherent sound but that's just me.
Since the platform is so popular, I want to mention that the highpass-notch and lowpass-notch filters that are needed to implement the DFE Crossovers are fully supported in CamillaDSP. Many thanks to @HenrikEnquist. So if you are already using CDSP and want to give them a try, check out the IIR filter type "General Notch" and then use the values from the tables from here:
https://audioxpress.com/files/attachment/2777
https://audioxpress.com/files/attachment/2777
With the latest version of my DSP app "GSASysCon", the user now has access to a variety of the DFE Crossover Filters via easy-to-use shortcut names. All that you need to do is add the shortcut name to the configuration file and supply the crossover frequency as a parameter on the same line. GSASysCon is easy to install and use, too. See the documentation and the files in the "filter_defs" directory for complete info on the DFE filters.
Get GSASysCon here:
Get GSASysCon here: