Parametric (Peaking) EQ variations

[Chester]

Hi; I have been using various programs to design EQ filters over the years including REW WinISD Pro, Crown Audio's IQ for Windows, Aixcoustic's Electri-Q, the UFX plugin (on KX drivers) etc. One thing I have noticed over time is how the Q of Parametric EQ filters varies from program to program; ideally the graph of one parametric EQ in a program (given the same ranges on the frequency and db axes) would look the exact same in another program. This rarely is the case. WinISD Pro (which every released version I know of there is a bug with 'negatively' gained parametric EQ's (ex. 2 parametrics both centered at 1000 hz, both a q of 2, one negative with a negative gain and one with positive (but same) gain will not cancel out). I have found formulas to correct this (and in the 'next release' of Win ISD it should be fixed) however this just goes to show how important it is to double check graphs.

I am currently working on a conversion from REW to Crown Audio's IQ for Windows; if anyone else has any information on this sort of thing it would be greatly appreciated. I am guessing that there hasn't been any discussion about how the Q is calculated on various programs though...

[Chester]

A quick example of this (on a commonly used program):
1. Using WinISD Pro; go to the Transfer Function Magnitude (EQ Filter) menu (after loading a speaker file)
2. Using REW; load look at the Modal EQ with a measurement loaded, check so you can see just the filter response
3. In both programs, load a parametric EQ, with a Frequency: 1000 hz, 24 db gain, and a Q of 1.
4.Pick a frequency (I will use 2000 hz) and note the gain in each program, I get:

WinISD Pro: +18.92 db @2khz
REW: +8.9 db @ 2khz

So clearly both programs are using different methods of calculating the shape of the filter even though they both are using "Frequency" "Gain" and "Q".

EDIT: I realize that this is all in 'software' however depending on the calculation method of the device you are programing you could have a large difference between what you 'should be getting' (according to REW) and what you are actually getting; at least at frequencies other than the center frequency

EDIT/addition 2: I have noticed also that as the frequency is increased on the filter and approaches the Nyquist limit (the maximum frequency representable by the sampling rate) the symmetry is not maintained by the filter (make a filter at 10khz and notice how the half on the 20khz side is 'steeper' than the 5khz side; this is a simulation of how most digital filters work however some manufacturers/products do correct for this (the Crown USM-810 I use being one of them... I called and asked ) so that is just another thing to be aware of when designing filters.

[Wayne A. Pflughaupt]

Chester wrote:

So clearly both programs are using different methods of calculating the shape of the filter even though they both are using "Frequency" "Gain" and "Q".

Yes. I’m sure brucek will be along eventually with the mathematical formulas, but basically there is no universal standard for filter Q. It’s different from one equalizer to the next, and one would have to assume, one equalizing program to the next.

To give you an example, here are graphs from three popular parametric EQs. All show the electrical response of filters set for 1/3-octave, which typically translates to ~4.3-4.5Q

Behringer DSP1124



Velodyne SMS-1



Behringer FBQ2496

Regards,
Wayne

[Chester]

Ohh, so perhaps I can find (based upon the various Equalizer presets) one that uses the same calculation method as my software (if I can find one that matches WinISD it would be great because I already have a 'formula' based on the gain and Q of the filter to 'convert' from WinISD to everything else I use )... Thanks for the tip! If anyone knows what the different methods used to calculate the filters are called it would probably be helpful to others interested to know what they are called.

... or if there is a way to add the USM-810 to the list that would be great too (I just noticed that the 'supported devices' have quite a few limitations on various parameters (TMREQ only allows +6 db gain, SMS-1 only goes to 120 hz, etc.)

[Wayne A. Pflughaupt]

Chester wrote:

... or if there is a way to add the USM-810 to the list that would be great too (I just noticed that the 'supported devices' have quite a few limitations on various parameters (TMREQ only allows +6 db gain, SMS-1 only goes to 120 hz, etc.)

That's because REW is programmed for the built-in limitations and parameters of those equalizers. What good would it do for REW to show a +10 gain for the TMREQ if it won't do that?

Regards,
Wayne

[Chester]

Wayne,
Thats completely understandable (and makes perfect sense) I am just saying that for me to 'use' those settings to simulate my setup (assuming one of the graphing algorithms matched) doesn't work well

-Matt

[Wayne A. Pflughaupt]

Understood. This site has the formulas - maybe it will be helpful.

Regards,
Wayne

[Chester]

Thanks man, I've seen that site before it uses the -3db frequency method which can have some trouble with gains <3db; I typically (in my conversions) measure the gain/2 frequencies and figure out what Q will make that a constant at different gains (usually takes ~10 measurements once a commonality is found) and then create equations to interpolate the values in-between. These are then entered into excel worksheets to make things easier to work with

[brucek]

The problem is that every graphics equalizer may calculate bandwidth differently.

As an example, some EQ's (such as the DSP1124P) define bandwidth as:

Bandwidth (Hz) = centre frequency*(BW/60)*sqrt(2)

So, the Q formula becomes: Q = 60/[(BW/60)*sqrt(2)].

For the R-DES eq, the bandwidth is defined as (1.766*centre frequency/Q).

Many are just the standard Bandwidth = centre frequency/Q.

So for each equalizer you would need to know how bandwidth is defined in relation to the standard Q calculation (√2/BW). One equalizer may define its 2/3 octave as the total width of the filter at its -3dB endpoints, (so a 2/3 octave filter would formulate to Q of 2.12). Another may define only the positive half gain endpoint, so a 2/3 octave filter actually covers 4/3 octave overall. There are many different definitions of bandwidth.

brucek

[Chester]

Hmm, it would be cool if we could measure our equipment like we do sound cards; however we could have 5 or 6 eq's we could set on the device so REW could 'calibrate' itself so things would all be on the same calculation

[brucek]

REW could 'calibrate' itself

REW allows the selection of various EQ's, so that the filters comply with that specific equalizer.

brucek

[Chester]

True however I have not seen any settings for the USM-810

Anyways; I came up with a conversion to for the REW filters (on a Generic EQ) to a filter in WinISD Pro (WinISD Pro filters use the same equation as Crown's IQ software):
if Gain=X
and the REW "Q" =Y

(WinISD Q)=Y*(1.000009391*exp(0.05756459995*X)-0.000005486433537*exp(-1.355976474*X))

basically the larger the gain, the greater the 'correction' is need to make the Q's equal; then that correction factor is multiplied by the original Q