We haven’t developed a synth filter here yet…
Filters we’ve presented
Biquads. While they are useful for many simple cases of filtering, they are not a good choice for analog synthesizer emulation. Most notably, they are poorly suited to time-varying parameters such as smooth filter sweeps.
Hal Chamberlin’s digital state variable filter, which has the advantage of independent control of filter frequency and resonance (Q), as well as simultaneous output of lowpass, bandpass, highpass, and notch filtering. While this served in many synthesizers over the years, using oversampling to fix its most glaring problem (limited frequency control range before losing stability), more modern design approaches offer far better performance.
What analog synths use
It’s helpful to discuss what most people are used to before getting to digital implementations.
For analog synthesizer emulation, two basic analog designs stand out, having withstood the test of time the best. The 24 dB/octave (“four pole”) Moog style (“transistor ladder”) lowpass filter, and the 12 dB/octave (“two pole”) state variable with its multiple outputs.
There are other designs, including the “diode ladder” design by Roland, the Steiner-Parker filter (basically Sallen-Key)—these are some of the ways voltage control was solved in analog filters, resulting in characteristic sounds. We’ll limit discussion to the two standouts.
Where to start
The state-variable filter is the best place to start—simple and versatile.
And my choice for your first stop, for a simple filter that’s scarcely more complex than a Chamberlin svf is Andrew Simper’s trapezoidally integrated svf. There is enough detail and code in his pdf for anyone to implement a useable, flexible, and good sounding synthesizer filter—also useable for other filtering applications such as equalization.
http://www.cytomic.com/files/dsp/SvfLinearTrapOptimised2.pdf
Dig into that for a start! (And further reading from Andy)
Bonus audio sample
Here is the sound of two of our sawtooth wavetable oscillators, detuned, through the SVF coded directly from Andy’s paper, with frequency swept from 20 kHz down through the audio range by our ADSR; note that such a sweep would blow up the Chamberlin implementation without oversampling:
SVF lowpass sweep from 20 kHz