Sigma Studio peaking filter Q inaccurate?

I'm looking into this. Could you please post the coefficient values you got using Leap? Try the same filter at Fc = 1000 Hz, Q = 1 and Gain = 6 dB.

Hi Brett,

LEAP will export coefficients derived using the following methods:

Matched-Z

Bilinear

Invariant

Convolution

And can use the following "realization forms":

Single Section, Full Order

Parallel Sections, 1st/2nd Order

Cascade Sections, 1st/2nd Order

Which combination would you like me to post?

Paul

L. Paul Hales

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Btw, when Sigma Studio graphs the response of the filter in the parametic EQ object, the graph on the screen matches the response you get from the processor, but not the theoretical response we want. So the software is calculating it this way.

It took a few days of looking around, but I finally figured out the reason for this anomaly.

The filters in SigmaStudio are based on Robert Bristow-Johnson's Audio EQ Cookbook, which is a fairly well-known implementation of Direct Form 1 biquad filters on fixed-point architectures. It looks like the Q is defined in the traditional electrical engineering sense for all filters except for the peaking EQ. Here's the excerpt that shows that minor deviation from the normal definition, and the reasoning for it:

Q (the EE kind of definition, except for peakingEQ in which A*Q is
the classic EE Q. That adjustment in definition was made so that
a boost of N dB followed by a cut of N dB for identical Q and
f0/Fs results in a precisely flat unity gain filter or "wire".)

What ended up happening was that the GUI designer ended up making the control for setting the Q parameter directly, but the equations that follow for computing the actual coefficients use A*Q (where A = 10^(dBgain/40)). So, this was a mistake in the GUI, not in the filter coefficient calculations themselves.

The end result is that for peaking EQ only, the Q value shown in in SigmaStudio's GUI is actually (1 / 2^0.5) times the real Q... in other words, it's 0.707 times the real Q.

The relationship is:

SigmaStudioPeakingGuiQ =
ActualQ / sqrt(2)

So, if you use a Q of 0.707 in SigmaStudio, the results will match your other software when you use a Q of 1.

If you use a Q of 1 in SigmaStudio, the results will match your other software when you use a Q of 1.414.

We're debating what to do about this issue because of the backwards compatibility issues it presents with existing customers.

Brett,

Thanks for the effort and all the information.

I checked your suggested correction factor of Q=Q/SQRT(2) and unfortunately, I don't think it is correct. It works pretty close the 1kHz, Q=1 filter, but for different frequencies and Q's there is still considerable error. The error doesn't appear to be linear.

The attached plot is an actual filter I need for a speaker program: Fo=2715Hz, Ao=-14.75dB, Q=0.914. The LEAP mathematical filter target is shown in Red. The Sigma Studio measured filter when Q=0.914/SQRT(2)=0.914/1.414=0.646 is shown in Blue. There is considerable error.

- Paul

Hi Paul,

Sorry for my very delayed response. You might have noticed that I've been inactive on the forum for a week or so. I'm actually finishing up a very time-critical PCB design and I've unfortuantely had to devote nearly all of my time to the project. I'm finishing the design this week so I will try to get back to you early next week. Sorry again for the delay.

Brett

Brett,

Understood.

I checked and if I multiply theoretical Q by your factor, 10^(gain dB/40), the Sigma Studio filters match the theoretical. Not efficient, but at least it works!

Please let me know if and when AD will change the software to employ the standard Q definition.

Paul

Brett,

In Version 3.92, the General 2nd Order Filter's Parametric window displays a newly adjusted Q setting that appears to address the difference between the two Q methods ("classic" and DSP). Is that what this is for? Only thing, it shows up in the Parametric window, not the Peaking window. I couldn't find anything on this in the wiki.

BTW, I prefer the old help file (which can be accessed by selecting a block and hitting F1) to the wiki, which doesn't have this convenient feature. Not to mention I do a lot while off the Web.

Best regards,

Bob

Robert Blowsky wrote:

In Version 3.92, the General 2nd Order Filter's Parametric window displays a newly adjusted Q setting that appears to address the difference between the two Q methods ("classic" and DSP). Is that what this is for? Only thing, it shows up in the Parametric window, not the Peaking window. I couldn't find anything on this in the wiki.

Hi Bob,

I'm checking on this now. I think this has something to do with the difference between the "Classical EE Q" and the "DSP Q" definitions, as described in the well-known Audio EQ Cookbook by Robert Bristow Johnson. We implement the Q calculation using RBJ's method, which differs subtly from the classical EE definition. You can find the text here: http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt

Robert Blowsky wrote:

BTW, I prefer the old help file (which can be accessed by selecting a block and hitting F1) to the wiki, which doesn't have this convenient feature. Not to mention I do a lot while off the Web.

In the latest version of SigmaStudio, you can highlight a cell and press F1, and it should bring you to the associated Wiki page. We haven't solved the issue of working offline yet, but that's something we're thinking about.

Hi Brett,

I'm very happy about the F1 - to - Wiki feature, but I can't get it to work yet. Are there any particular requirements? When I try it, F1 only takes me to the old help. I'm using SigmaStudio 3.92 and Firefox. I adjusted my firewall to give SigmaStudio full Internet access.

Bob

Hi Bob,

I don't think there are any specific requirements. I just click on a cell to highlight it, and then press F1. That should take you directly to the wiki. I think if you just press F1 (with no cell highlighted) it takes you to the help file. I'll confirm with the software team.

Brett

Actually, I'm incorrect. Pressing F1 in the software should take you directly to the wiki front page.

Are you using the x86 or x64 installer? I'm using x64. I wonder if that is a factor.

The Wiki has been updated, FYI.

https://wiki.analog.com/resources/tools-software/sigmastudio/toolbox/filters/general2ndorder

Brett,

I'm presently using the X64 installer as well.

Bob

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