State Variable Filter

Tier: Primitives | ComponentType: 7 | Params: 3

Chamberlin state variable filter with 2x oversampling and simultaneous LP/HP/BP/Notch outputs.

Overview

The State Variable Filter (SVF) uses the Chamberlin topology with 2x oversampling for improved stability at high resonance. Unlike the Biquad which offers one output type at a time, the SVF computes all four filter outputs (lowpass, highpass, bandpass, notch) simultaneously from the same integrator state. The output selector chooses which response to emit.

Resonance approaching 1.0 drives the filter toward self-oscillation, producing a singing tone at the cutoff frequency. The 2x oversampling prevents instability that would occur in a naive single-pass implementation at high frequencies and resonance.

File Locations

	Path
Header	Sources/FolioDSP/include/FolioDSP/Primitives/StateVariableFilter.h
Implementation	Sources/FolioDSP/src/Primitives/StateVariableFilter.cpp
Tests	Tests/FolioDSPTests/StateVariableFilterTests.swift
Bridge	Sources/FolioDSPBridge/src/FolioDSPBridge.mm (StateVariableFilterBridge)

Parameters

Index	Name	Description	Min	Max	Default Min	Default Max	Default	Unit
0	Frequency	Filter cutoff frequency	20.0	20000.0	200.0	8000.0	1000.0	Hz
1	Resonance	Resonance amount (0.999 approaches self-oscillation)	0.0	0.999	0.0	0.8	0.0
2	Output	Output type: 0=LP, 1=HP, 2=BP, 3=Notch	0.0	3.0	0.0	3.0	0.0

Processing Algorithm

1. Coefficient Calculation

\[f = 2 \sin\!\left(\frac{\pi f_c}{f_s}\right), \quad q = 1 - \text{resonance}\]

2. Chamberlin SVF (2x oversampled, run twice per sample)

\[\text{hp} = x - \text{lp} - q \cdot \text{bp}\]

\[\text{bp} \mathrel{+}= f \cdot \text{hp}\]

\[\text{lp} \mathrel{+}= f \cdot \text{bp}\]

3. Notch Output

\[\text{notch} = \text{hp} + \text{lp}\]

Core Equations

\[\text{hp} = x - \text{lp} - q \cdot \text{bp}; \quad \text{bp} \mathrel{+}= f \cdot \text{hp}; \quad \text{lp} \mathrel{+}= f \cdot \text{bp}\]

Snapshot Fields

Field	Type	Range	Unit	Description
Frequency	Float	20–20000	Hz	Current cutoff
Resonance	Float	0–1		Current resonance
Output	Float	0–3		Selected output type
LP	Float	-1–1		Lowpass output
HP	Float	-1–1		Highpass output
BP	Float	-1–1		Bandpass output

Implementation Notes

• 2x oversampling: two SVF iterations per input sample for stability at high resonance
• All four outputs computed internally; only one is selected for return, but all are in the snapshot
• Resonance maps inversely to damping: q = 1 - resonance
• No DC blocker — SVF structure is inherently AC-coupled for BP and Notch; LP passes DC normally

Equation Summary

hp = x-lp-q·bp; bp += f·hp; lp += f·bp