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Timothy Place

Building on my previous filter design videos (see below), I use the 

 objects to make a crossover filter that is perfect for use in multi-band EQ's, compressor/limiters or sound design applications. By using these tools to create a Linkwitz-Riley filter system, join me for a 20-minute trip into examining, testing and ultimately building a filter that doesn't otherwise exist in Max.

Make a crossover filter that is perfect for use in multi-band EQ's, compressor/limiters or sound design applications. 
Get the Package used in this tutorial: https://cycling74.com/2016/09/13/crossover-filter-design-video-tutorial/

Crossover Filter Design

Building on my previous filter design videos (see below), I use the filterdesign, filterdetail and gen~ objects to make a crossover filter that is perfect for use in multi-band EQ's, compressor/limiters or sound design applications. By using these tools to create a Linkwitz-Riley filter system, join me for a 20-minute trip into examining, testing and ultimately building a filter that doesn't otherwise exist in Max.

Download the Package used in this tutorial.

Watch other filter design videos: A Tour of Filtering Tools and Demystifying Filters.

crossover-filter-design-video-tutorial

these are a great set of tutorials tim. long may they continue. (do you take requests?!).

i implemented trond's linkwitz-riley in genexpr a while back, and use it for all my multiband processing needs.

last year we released a few additions to the oscillot package including a crossover based on it. attached is a max patch version of this module from the package, in case anyone else is interested.

nowhere near as useful as the one in your tutorial as the coefficients are calculated at signal rate (!!), but maybe someone will find it interesting to rip out the genexp code and take a look. if not should at least be compatible with beap. also paired here with graham's 2-pole crossover from the gen~ examples.

This is fabulous!  Thanks for sharing @STKR!


This filter series is really awesome.  I don't understand the maths, but this series explains filters in a way that focuses on the use and outcome instead of the mathematics at work.

Maybe this is the discussion of a future tutorial, but how could I use the Linkwitz-Riley crossover to divide an audio stream into more than two parts (eg low-mid-high)?  Intuitively, it seems like I could again divide one of the streams, like the low pass stream, and divide it again into a low and high stream, resulting in a low pass, a middle bandpass and a high pass.  Will my three audio streams remain in phase?  Do I need to add delay to the high pass side to compensate for the extra filters on the low-pass side?

more than two bands... just chain the crossovers serial.


Nice article. Is there a way to easily implement other type of filters like Bessel (std and norm), Linkwitz-Riley, Elliptical and All-Pass. Chebyshev 1 and 2 are already included in filterdesign~ I see.

Your video has been incredibly useful for helping me with my studies! I am creating a crossover simulator at the moment and I wondered if you know of a way to implement a Bessel filter? Any information you have would be incredibly useful.  Many thanks.

I haven't implemented a Bessel filter for Max. Depending on your application for the filter you could generate biquad~ coefficients using Octave's besself function ( https://octave.sourceforge.io/signal/function/besself.html ).

The same is true for an elliptical filter.

If you want to have a filter than can be dynamically modified (as the filters in filterdesign are) then it will take some significant math chops. A good starting place (apart from the Octave besself code) is this: https://vibrationdata.wordpress.com/2012/11/11/bessel-lowpass-filter/

Thank you Tim for this very insightful and helpful tutorial. I tried to run the "3 - crossovers - gen~" tutorial patch for the Linkwitz-Riley crossover but I am getting the wrong frequency response as you see from the attached screenshot. The java script seems to be OK as I get the correct response in the "2 - crossovers - lr" tutorial patch  using the filterdetail object. I am running as required at 44100 Hz and have changed the  I/O and signal vector sizes to various values in Audio Status but nothing changes and the problem remains. I am puzzled at what could be causing this. Any insight would be appreciated. (Max 7.3.5, Mac OS 10.12.6). 

i am posting this question here because it is releated to a similar context:

how far away is a "regular" biquad from a butterworth (read: cascades of 2) when it comes to its main property, the absolute frequency flatness at the crossover point / rated frequency?


I updated Max 7.3.5 to 7.3.6 and the  problem I reported above went away. The spectral plot now shows the same curves as in the tutorial.  Does anyone have a clue why?

I found out that the issue with the wrong curves in the spectral plot~ I reported earlier has nothing to do with the version number of Max but rather the signal vector size. For the spectral plot in that tutorial patch to display the correct curves the signal vector size must be 256 or smaller. 

However I now realized that there is another issue, this time with the sound coming out of the gen~ objects in that tutorial (the one about Linkwitz-Riley gen~ based filters). It is best heard with pink noise (but it is detectable with any wideband audio) as the input (as shown in the attached patch). Basically, as you change the XO frequency either continously (e.g. with a flonum object or live.dial) or by entering discrete values, you will hear a thumping noise/click at every change. This thumping noise is most evident for  XO frequency values below 400 Hz and gets very loud at the monitors/speakers (when set to regular listening level) when the XO frequency is lowered below 100 Hz. It is also clear from the audio in the attached patch tab the thumping noise is only on the HF band of the 2-band crossover. 

 I was able to stop it when the XO frequency  is changed  by discrete values by setting a gate~ that stops the output of ten~ from going out to  ezdac~ for about 15 ms, but that trick does not work well when the XO frequency is changed continuously.

Tim, do you know what is causing this noise? Is there any way to avoid it? 

Thanks in advance.

using sqared topology is less accurate than using 2*butter.

Lots here to respond too, but first, the Butterworth is not something to be compared to a biquad. In fact, the typical implementation of a Butterworth filter is performed with 1 or more biquads. You can use the [biquad~] object or the [cascade~] object.

Regarding the spectral plots, yes, the [windowed-fft~] abstraction has some requirements of the vector size. Specifically, your signal vector size must be 1/4 the size of the FFT or smaller. This is documented in the "spectral" tab for the [plot~] object. I am hoping to eventually replace this abstraction with an external object that will remove these undesirable sensitivities.


Regarding the "thumping" or other discontinuities when the frequency of the filters change, this is a known problem with filters, particularly when there is feedback in the filter. Do you clear the history when you change the frequency and induce a pop? Or leave now-wrong data in the history?

The [biquad~] object has an attribute called "Smooth Coefficients" which implements an approach to helping with this problem. It looks like the [cascade~] object does not, which is unfortunate. I'll make a note to research this further to see if we can add it.

Thank you Tim for the reply. 
I am not sure I understand what you mean by "clearing the history". There is not much documentation on the history object in gen. Could you please clarify how to clear the history.  Perhaps in the context of the tutorial "3- Crossover - gen~" that you posted originally. Would clearing the history solve the thumping issue?

"Clearing the history" means setting all variables used for feedback to zero. It will trade the thumping for a popping sound which you probably also don't want. So... yeah... also not ideal...

Thanks Timothy! This really helped me make a multiband compressor in gen and learn a great deal about filterdesign. I ported your JS crossover calc into the new event driven [gen] if anyone would like it. it also dynamically adjusts to your samplerate using dspstatus. 

the 'samplerate' and 'SAMPLERATE' constants don't seem to function correctly in event driven [gen] on my system samplerate = '200.' when set to 44100.

Thanks for this report @lysdexic. I can reproduce and have ticketed for further research. 

I had initially thought that perhaps my scheduler was running at a 5ms interval and so 200 was a sensible response. But I see that my scheduler preference setting is 2ms, so I'm not sure where the 200 is coming from.

This whole lesson has been really informative and I really appreciate it.  One of the questions I still have (and haven't been able to actually find an answer) is no matter what form of LR-4 I've tried, the final gain is always increased.  I've seen one plugin that uses a non linear phase LR-4 filter that doesn't have any change in output gain, but I haven't been able to actually recreate it in max.  

Turning the gain down to compensate for the change also doesn't seem to be the solution because at that point it's not actually preserving the original signal. What is this gain change from and how is it avoidable?  

Hi Tim, I wanted to extend what you did here to an 8th order Linkwitz-Riley, however the code library from which you  took the code for the js crossover-calc.js object in your example has only 2nd and 4th order L-R filters. Any advice on how I can extend to 8th order?
Thanks 
Adam

To make a proper 8th order LR, you must cascade two, 4th order butterworth filters but make sure that the orders have correct Q values when stacked!

https://csserver.evansville.edu/~richardson/courses/EE410_Analog_Circuit_Synthesis/resources/handouts/ButterQValues.pdf

Yo peoples... I made a pretty cool Multiband compressor but no matter how I stack 4 of these filters (to get 5 bands) I get different frequency responses, none of them linear. Im basically going from the highpass of the first pair into the next pair etc which has given me the most even response but its still not flat. I'm assuming this is normal operation as the filters phase response stack up and create these discontinuities in response. Do I need to go searching for another filter coefficient calculator to get a linear response 5 band crossover?

No, you need to understand the theory behind multiband crossover filters.

To that end, check out this link:
https://www.modernmetalproduction.com/linkwitz-riley-crossovers-digital-multiband-processing/ 

There is also an interesting conversation about it on the JUCE forum:
https://forum.juce.com/t/perfect-crossover-filters/36125/9

Basically it boils down to introducing an extra Allpass filter stage every time you introduce an extra band.
That will keep the phases of the different branches coherent, so you'll get perfect reconstruction when you sum the bands together.

There are also a few papers around that describe this technique in more detail and from a more technical point of view. Google is your friend.


hey all, cool topic, thanks for your interesting successive inputs ! 
i need a 3 band crossover ; so using two crossover linkwitz-riley should work, right ? and following @Luigi's link, it seems introducing an allpass filter at the output of the lowest band plus inverting the mid range band phases (am i correct in assuming this just means pluging a [~* -1] for that band?) should do the trick, but how to get the allpass filter to the desired frequency (which seems to be the high cut frequency) ? From max's documentation, we can see the phase change, but there is no direct correlation to a specific frequency. I'm guessing the frequency in  question should have its phase changed by 1 pi ; but how to calculate that from giving allpass only delay and gain parameters ?
Also how to interpret the differential equation "y(n) = -g x(n) + x(n)-(DR/1000) + g y(n)-(DR/1000)" : is it simply "y(n) = -g*x(n) + x(n - delay) + g*y(n - delay)" if you assume the delay time in samples ? 


edit : apparently for 3 bands, if i don't put an allpass and don't touch the phase, using 2 chained Linkwitz ; it's relatively okay if the low and high cutoff frequencies are sufficiently far apart (at least graphically...)


when you only have an example available how to use the allpasses for 2 and 3 bands, it is a bit tricky to construct the same thing for 5 bands.





"but how to get the allpass filter to the desired frequency (which seems to be the high cut frequency)"

i think this rule is correct: 

if you have n bands, A, B, C, ..., A must be donated n-2 allpasses at the same frequencies (and order) of all crossovers except its own (A vs B) (the order of insertion theoretically does not matter)

the more bands you have, you might even be able to save a few filters, some guy built a 10-band design with 40% allpasses saved in flowstone. 
unfortunately until now i was not able to rebuild in max.


you mean he replaced some band filters with allpasses or something ?.. 
but anyway, no idea how to infer allpass's "center frequency" from its gain and delay parameters ?



not replace, you insert it in addition to the crossovers to correct that little bit which is missing to make the sum of A, B and C the original again.

it doesnt do anything but correcting the phase shift the crossover at the other band(s) is applying, too.

an allpass is basically the same as the crossover on the other signal, just with the outputs of hf and lf summed.



Thanks @luigi that makes perfect sense. Pretty sure each time you run a highpassed signal into a lowpassed signal its getting flipped anyway... ? So you only need the allpass filters in this instance. which @vichug you would use the phaseshift~ object, which is a second order all pass and has a parameter for centre frequency. 
The next objective is to get all the Q values correct, as im still getting some very small dips.

I have incredibly close to a flat frequency response with this setup. The crossovers are set to 160hz, 800hz, 4000hz and 11000hz. Q values of 0.7071.


arent you supposed to built the allpass from the same butterworths?


So, the order of the filters might be off. If you have LP and HP filters at the 2Nth order, you need an AP filter at the Nth order to compensate for their phase response. A very common configuration would be to use 4th order Linkwitz-Riley filters (24db/octave) for the LP and HP and a 2nd order AP for the phase compensation stage.

so phaseshift~ is 2d order allpass filter ? and two phaseshift~ in series would be a 4th order allpass ?

Although building an allpass from the LR filters, like Roman said, does make sense. I'm yet to try it though,  in any case phaseshift~ should be much less demanding, cpu wise.

Yes, what Roman said is absolutely correct. You could also build it from the Linkwitz-Riley filters. Actually it would be LESS demanding cpu wise than a [phaseshift~] solution because you could theoretically use the same Linkwitz-Riley lowpass and highpass outputs (at Nth/2 order), so you don't need to recompute a new filter. So you would start with a lowpass 2nd order Butterworth and a highpass 2nd order Butterworth with the same cutoff frequency. From these two filters you create the 2nd order allpass. Then you cascade these two 2nd order Butterworth filters into another set of lowpass and highpass 2nd order Butterworth filters to create your 4th order Linkwitz-Riley filter (that is exactly why a Linkwitz-Riley filter is also called Butterworth squared). Now you have your 2nd order AP, a 4th order LP and a 4th order HP for the price of a 4th order lowpass and highpass. The allpass comes basically for free. Pretty cool, eh?

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