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TOPIC: How calculate biquad coefficients for 6dB filter

How calculate biquad coefficients for 6dB filter 1 month 1 week ago #33035

  • supersteff
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Hi

I own 4 pieces of PWR-ICE125, and I am in the process of building a 3-way speakersystem. I want to create speakers with Duelund Syncron Filters. These filters are different from normal textbook filters. The individual speaker-units need acoustically to follow certain target-curves.

A friend of mine does passive Duelund Syncron Filters for 3-way speakers. He speaks of cascading several 6 dB filters to create hybrid crossovers with several cut-off- frequencies, thereby approaching the desired filter-slopes.

We want to try to translate that approach to the digital domain by using the "Advanced" mode in the crossover-section of the PWR-ICE125 plug-in. But how can I cascade to, three or four 6 dB filters?

I have played with the all-digital-coefs v1.2, and I have not succeeded in finding a way to create a 6dB Butterworth filter. The program only seems to create 2. order filters!? Am I right in that? It would be nice with some explanation to that program, i.e. what does it create, or where to find what Q-value to choose!

In my old 2x4 Plug-in there is a biquad-calculater that can produce coefficients for 6dB filters, though for a different sampling-rate. In the 2x4 Plug-in I managed to create a hybrid crossover with more than one cut-off-frequency.

BUT how do I do that in the PWR-ICE125- Plug-in?

Is there an alternative biquad-calculater somewhere that can be used? Or could the biquad-calculater from the 2x4 be made available for 96kHz in some way?

Loooong story. I hope someone can help.

Regards from Denmark

Steffen
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How calculate biquad coefficients for 6dB filter 1 month 1 week ago #33041

  • dreite
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Your post is somewhat confusing.
6db Butterworth filters all have a Q=0.707.

If I understand your objective correctly, I think the easiest approach would be to use the "basic" function of the GUI to select the a 6db/BW filter at your desired frequency then switch to the advanced mode and copy the coefficients. Repeat that process with your array of desired cutoff frequencies. You can then take the results (up to 8) and paste into the "advanced" portion of the Xover section of your PWR-ICE plugin.

You might also consider purchasing one of the 2x4 software plugins since they have a handy biquad calculator built in.

Dave.
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How calculate biquad coefficients for 6dB filter 1 month 1 week ago #33043

  • supersteff
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Hi Dave

Thank You so far. And sorry for the confusion.

The ideer of purchasing a 2x4 plug-in sounds Ok. As I understand it, I would need the Plug-in for the 2x4 HD version with 96khz samplingrate. This is probably the best choice at the moment.


I tried going from Basic to Advanced in the PWR-ICE 2x2 GUI, and that is also an option, though i really have to maintain focus not to get confused! And it seems, that for simple 6 dB BW filters, the biquad 1 is used for the basic`s Lowpass and the biquad 5 is used for the Highpass. So I need to be very awake here what biquad to copy!

By the way, I compared the coefficients from the GUI and the All-digital-spreadsheet for a High Pass BW 12 dB/oct filter, and they where not exactly the same!? I guess that can be due to the accuracy of decimals in the Q settings?

When I but 1000 Hz and Q=0,707 in the spreadsheet i got coefficients similar to the GUI`s 12dB/oct BW-filter! I think the spreadsheet can only produce 12dB/oct filters with different Q´s, because biquads inherently are 2. order! I produced coefficients in the GUI Basic for a 6dB BW High pass filter, switched to Advanced and noticed that b2 and a2 are zero, only 1.order components. Well and how do I make them?

Well, that got complicated again!!! I keep on looking and learning.

Bedtime for me now.

Steffen
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How calculate biquad coefficients for 6dB filter 1 month 6 days ago #33049

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What you're attempting to do is not uncomplicated and could get tedious. Take your time.

Regarding the difference in coefficients, I'm not sure what you're referring to. Maybe you could elaborate further?
Either utility, if programming the same filter at the same Fs, should generate the same set of coefficients.

Yes, b2 and a2 coefficients would be zero in a first-order filter.

Dave.
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How calculate biquad coefficients for 6dB filter 1 month 3 days ago #33062

  • supersteff
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Hi again

I did purchase the 2x4 HD Plug-IN. It does NOT contain a biquad-calculater as does the old 48 kHz 2x4 Plug-IN. Hmm.

BUT I CAN use the 2x4 HD Plug-IN as a biquad-calculater for 6 dB/oct BW-filters by choosing a filter in the BASIC mode and switch to the ADVANCED mode. The Plug-IN will automatically compute biquad-coefficients for Low-pass filters in the biquads 1-4 and biquad-coefficients for High-pass filters in the biquads 5-8. So again I need to keep focus, and copy the right biquads!

The advantage by using the 2x4 HD Plug-IN to calculate biquad-coefficients for the PWR-ICE-Plug-IN is, that I keep things sepparated and minimize chances for error end confusion! And yes, it still is a complicated affair. But on the other hand, I did by the PWR-ICE125 exactly because it can be programmed so flexible. I just need to know how.


And now to some "Research":

I did evaluate a 12dB/oct BW High-Pass-filter in the 2x4 HD Plug-IN, the PWR-ICE-Plug-IN and the All-digital-coefs v1.2 and compared the b0-coefficient. I evaluated the b0-coefficient in the spreadsheed for Q-values with increased amount of decimals.

2x4 HD
b0=0,9547740306487544

PWR-ICE
b0=0,9547740306487544

All-Digital- Coefs
b0=0,954767656510722 @ Q=0,707
b0=0,945773625922957 @ Q=0,7071
b0=0,954774043721377 @ Q=0,707107
b0=0,954774031784389 @ Q=0,7071068
b0=0,954774030650375 @ Q=0,707106781
b0=0,954774030662312 @ Q=0,7071067812
b0=0,954774030661715 @ Q=0,70710378119
b0=0,954774030661536 @ Q=0,707106781187

2x4 HD
b0=0,9547740306487544

PWR-ICE
b0=0,9547740306487544

So, as You can se: The two 96 KHz Plug-IN´s compute the same b0-coefficients. But the All-digital-coefs does compute different value, but approximating the Plug-IN-values with increasing amount of decimals in the Q-setting!!!!!

I guess, it does not really matter, as long as the coefficients produce a stable biquad!? But it was interesting and educational.

Regards from Denmark

Steffen
Last Edit: 1 month 3 days ago by supersteff.
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