Filters

Filter

A topology-preserving state-variable filter with simultaneous lowpass, highpass, bandpass, and notch outputs - the most flexible filter shape in modular synthesis.

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What is a Filter?

A state-variable filter (SVF) is a filter topology that produces lowpass, highpass, bandpass, and notch responses *simultaneously* from the same circuit. It does this by wrapping two integrators in a feedback loop and tapping the signal at three different points: before any integration (HP), after one (BP), after two (LP). The notch is just HP + LP summed back together. One filter, four colored windows on the same audio.

The architecture has a long history. It originates in analog computers of the 1950s and 60s, where engineers used integrators in feedback to solve differential equations - the math of resonant systems. When synthesizer designers realized those same equations describe a filter, the topology jumped into music. The Oberheim SEM shipped a state-variable filter in 1974, the Doepfer A-121 brought it into Eurorack, and software developers have been studying its discrete-time equivalents ever since.

The two parameters that matter are cutoff (where the filter acts) and resonance (how sharply). Cutoff sets the corner frequency for all four outputs simultaneously. Resonance feeds the bandpass output back into the input - low resonance gives a smooth response, high resonance creates a sharp peak at cutoff, and at maximum the filter self-oscillates as a pure sine wave. That's not a defect; it's a feature. A self-oscillating SVF is a clean, V/Oct-trackable sine source.

Compared to the Moog ladder, an SVF is brighter, more analytical, and more flexible - but warmer character and that famous bass-eating resonance behavior come from the ladder. SVFs and ladders are the two great filter lineages of subtractive synthesis. Pick by feel: SVF for clarity and morphing, ladder for vintage thickness.

Our Filter

Our state-variable filter is a topology-preserving transform (TPT) SVF based on Andrew Simper's design. TPT is the modern way to discretize an analog filter: instead of bilinear-transforming the transfer function (which detunes resonance and goes unstable near Nyquist), TPT keeps the integrator structure of the analog circuit intact at every sample rate. The result is a filter that stays stable up to 21 kHz cutoff and self-oscillates as a clean, V/Oct-tracking sine.

The cutoff knob runs 20 Hz to 20 kHz exponentially, with 1V/Oct tracking on the CV input - so you can play the filter melodically as a sine source. All three primary parameters (cutoff, resonance, drive) have CV inputs with attenuverters. The drive stage is a tanh soft-clipper *before* the filter input, so you can saturate harmonics that the filter then carves - distortion-into-filter, the classic acid signal flow.

And because it's an SVF, all four outputs (LP, HP, BP, notch) are live simultaneously. No mode switch, no tradeoff - patch any combination, route any of them anywhere. 10 HP, 6 parameters, the most flexible filter in the rack.

In a patch

In a typical subtractive voice the filter sits right after the oscillator: VCO -> VCF -> VCA -> output. The oscillator generates harmonics; the filter carves them; the VCA shapes amplitude. Patch an ADSR into the cutoff CV input and you have classic envelope-controlled filter sweeps - the basis of plucks, basses, and brass-like sounds.

Because an SVF gives you four outputs at once, you can route them to different destinations. Send the LP to the main mix, the BP to a delay, the HP into a distortion - one filter splits a single voice into three texturally distinct streams. Modulate cutoff with one LFO for slow movement and resonance with another for evolving character.

At maximum resonance the filter self-oscillates as a pure sine. Send a 1V/Oct signal to the cutoff CV input and you have a sine-wave VCO, free of charge. Useful for FM carriers and sub-bass when oscillator slots are tight.

Inputs

Audio In (audio) — Signal input. Feed in audio from an oscillator, noise source, or any other signal you want to filter.
Cutoff CV (cv) — Cutoff frequency CV input. Tracks 1V/Oct so you can play the filter melodically. Amount scaled by the Cutoff attenuverter.
Resonance CV (cv) — Resonance CV input. Modulate resonance for evolving timbral effects. Amount scaled by the Resonance attenuverter.
Drive CV (cv) — Drive amount CV input. Modulate the saturation level. Amount scaled by the Drive attenuverter.

Outputs

Lowpass (audio) — Lowpass output. Passes frequencies below the cutoff, removes highs. The most commonly used filter type - warm and full-sounding.
Highpass (audio) — Highpass output. Passes frequencies above the cutoff, removes lows. Good for removing rumble or creating thin, bright textures.
Bandpass (audio) — Bandpass output. Passes a band of frequencies around the cutoff, removes both highs and lows. Creates nasal, vowel-like tones, especially with resonance.
Notch (audio) — Notch (band-reject) output. Removes a narrow band at the cutoff and passes everything else. Creates phaser-like effects when the cutoff is swept.

Controls

Cutoff — Cutoff frequency (20Hz to 20kHz). The frequency where the filter starts to take effect. Low values darken the sound, high values brighten it.
Resonance — Resonance (0-100%). Boosts frequencies at the cutoff point. Low values are subtle; high values create a sharp peak. At maximum, the filter self-oscillates as a sine wave.
Drive — Drive (0-100%). Adds tanh soft-clipping saturation before the filter. Subtle warmth at low settings, aggressive distortion when cranked.
Cutoff Atten — Attenuverter for the Cutoff CV input (-1 to +1). Controls how much and in which direction the CV modulates the cutoff.
Resonance Atten — Attenuverter for the Resonance CV input (-1 to +1).
Drive Atten — Attenuverter for the Drive CV input (-1 to +1).

Inspired by

The state-variable topology dates to the analog computer era: two integrators in a feedback loop produce LP, HP, and BP outputs simultaneously, with notch as the sum of LP and HP. The Oberheim SEM made the sound famous; Doepfer's A-121 carried the same idea into Eurorack. Our DSP uses Andrew Simper's modern topology-preserving transform (TPT) discretization, which stays stable up to Nyquist and self-oscillates as a clean sine.

Doepfer A-121
Oberheim SEM filter
classic state-variable topology

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