This Sound file contains copies of my recent Peaking Butterworth Filter blocks. These both depend on the DirectIIR? microsound. The Peaking LPF is similar to the new Kyma VCF, but the Peaking HPF is the high-pass complement to that.

These are both 4-pole Butterworth filters, hence 24 dB/octave roll off. It turns out that you can develop a resonant Butterworth filter in the S-plane and then use a bilinear transform to take us back to the Z-domain where our digital filters operate. Using the bilinear transform means that the design frequency gets warped on the way to the digital domain. But as long as you keep these tuned to around 10 KHz and lower, the frequency error will be slight.

Both filters have cutoff frequency and Q parameters. A Q of 1 is the standard Butterworth 4-pole filter with no peaking. Q's below 1 are even less steep in their filtering, while Q's above 1 produce a resonance bump at the cutoff frequency. I haven't tried ultra-high Q values to see if these filters will self-oscillate. They might. But at Q's of 10 already the peak gain is some 20-30 dB higher than the rest of the pass band.

You can vary the Q and the cutoff with hot parameters. I don't know if these filters are the same as what you find in synthesizers, but they sound very similar. Just be aware that when you boost the Q you might need to drop the input levels to compensate so that you can avoid clipping.

-- DavidMcClain - 23 Sep 2004