ADAU1467 Parametric EQ coefficient calculation

Hello,

The Toolbox Wiki shows the coefficients for parametric (peaking EQ) filters as:

The calculation for alpha highlighted above is correct.

Best regards,

Bob

Hi Bob,

Thanks for your reply.

I confirmed.

There is one additional question.

In the filter GUI, there is an element " Q' " is displayed as below.

What does this mean?

Please tell me the exact definition.

Thanks and Regards,

Q is short for Quality factor, a measure of the resonant quality of a circuit or system.. This Wikipedia article describes Q in detail. In a parametric filter, a higher Q provides a sharper peak in the frequency response, as shown in the graph below. Each of the three filters shown has a center frequency of 1 KHz and a boost of +10 dB, the only difference is their Q. We see that the higher Q filter has the sharpest curve:

Parametric filters are often specified by bandwidth (BW) in octaves instead of Q. We see from the graph that the higher the Q, the lower the BW. To find the Q required to achieve a desired BW, use this formula:

For example, a 1/3 octave bandwidth corresponds to a Q of 4.32.

Best regards,

Bob

Hi Bob,

Thanks.

What I wanted to confirm is regarding to not " Q " but " Q' "(Q-apostrophe) mainly.

This(Q apostrophe) value appears to be dependent on Q and gain.

Please let me know the correct definition.

Thanks and Regards,

Sorry for my confusion. Experimenting with the settings suggests this relation:

Q' = Q * ( 10**( boost / 40 ) ) Yet I don't know what Q' is used for.

Best regards,

Bob

Hi Bob,

Thanks a lot.

Do you know where is the documentation for Q' ?

Thanks and Regards,

Hello takumi3952,

There is some on the Wiki, I found this:

By default, the Q is shown with the value adjusted (from the classical EE definition) 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”. This is equal to A*Q, where A = 10^(dBgain/40).

The “Classic EQ” version of Q can optionally be shown by clicking the small circular button next to the Q control.

Then there are also some details on the forum.

This discussion was a long time ago and I think this lead to the addition of the little button to click on for the classical EQ version of Q. This would keep the cell backwards compatible.

https://ez.analog.com/dsp/sigmadsp/f/q-a/66932/sigma-studio-peaking-filter-q-inaccurate/234701#234701

Dave T

Good find, Dave. I tried searching both EZ and the wiki without success.