Customer Support
Customer Support

In this application note, we show you how to use the miniDSP custom biquad programming feature to implement a Linkwitz transform.

What's a Linkwitz transform? [Top]

A loudspeaker driver in a sealed enclosure has a mathematical description that determines its low-frequency response. At some point, the response of the speaker starts rolling off and reduces in level at 12 dB per octave. (Each time the frequency halves, the output level drops by 12 dB.) The shape of this curve can be characterized by two parameters: tuning frequency F, and quality factor Q.

A Linkwitz transform is a mathematical operation that changes the effective F and Q to different values. Typically, this is used to lower F to get more low bass output, or to lower the Q to make the box behave like a larger box.

You can implement the Linkwitz transform using the custom biquad programming feature of miniDSP processors. Check the user manual of your product to confirm that it support custom biquad programming.

Note that the Linkwitz transform only works for sealed boxes. It's not suitable for ported boxes or for open-baffle speakers.

1. Download the biquad programing spreadsheet [Top]

Download the community-contributed biquad programming spreadsheet from the following link, and select the "LT" tab.

2. Determine your speaker's F and Q [Top]

If you have built the speakers yourself, you may already know these parameters from your box design phase. Otherwise, you will need to determine them by performing a nearfield measurement of the woofer - that is, with the microphone placed close to the cone, or about 5 cm (2"). The curves below illustrate a set of curves with a F of 80 Hz and Q of 0.5, 0.7, 1.0, and 1.4 (green, red, purple, black).

Various values of Q for f = 80 Hz

With a measurement taken, you will need to guess at F and Q by comparing the measured response with the curves above. Enter your guesses at F and Q into the spreadsheet and compare the curve displayed in blue with your measurement. If needed, adjust F and Q in the spreadsheet until the curve displayed in blue is reasonably close.

It's not super-critical to get F and Q exactly right the first time around. After applying the transform (steps 3 to 5 below), you can adjust and try again if the result is not what you want.

3. Calculate the biquad parameters [Top]

In the spreadsheet, enter the box F and Q as f(0) and Q(0), the desired F and Q as f(p) and Q(p), and the sample rate of your processor as Fs. For example:

Linkwitz Transform parameters

Note: Fs must be set to the correct sample rate, or your transform will not be at the correct frequency. Fs will be 48000, 96000, or 192000. Check the advanced biquads section of your user manual for the sample rate to use. (Note that some hardware may run at different sample rates; for example, the miniDSP Flex runs at 48 kHz if Dirac Live is enabled, and 96 kHz otherwise.)

The spreadsheet will display the original response, the desired or target response, and the equalization curve:

Linkwitz Transform curves

You will note at this point that you will need to be realistic about the target F and Q as typically the transform will result in significant boost at low frequencies. Set the target F and Q so that the amount of boost is compatible with available amplifier power and the woofer's excursion limits.

4. Enter the parameters [Top]

Scroll down on the spreadsheet to find the biquad coefficients section:

Linkwitz Transform coefficientsto your measurement

In the miniDSP Device Console (or plugin if you are using the older "plugin" style of user interface), set a filter to Advanced mode and enter the five parameters a1, a2, b0, b1, and b2, as shown below. (Note that the order in the spreadsheet is different than the order shown by default in the miniDSP user interface. Just copy each number and paste into the correct location.) Then press the Process and Apply button. The frequency response graph will update to show the transform.

Linkwitz transform loaded into miniDSP

5. Verify your results [Top]

Run the nearfield measurement of the woofer again. If all is well, you will see the target response! If the response is not what is desired, fine-tune your F and Q settings and try again. Here is the before and after response of the example speaker, as measured with Room EQ Wizard:

Linkwitz transform, before and after

Wrapping up [Top]

And that's it! Have fun, and let us know how you go in our forum.