OnePole

Tier: Primitives | ComponentType: 2 | Params: 2

Single-pole lowpass/highpass filter — the simplest IIR filter topology.

Overview

OnePole implements a one-pole filter with selectable lowpass or highpass response. The lowpass mode uses the standard first-order IIR equation with an exponential coefficient. The highpass mode is derived as the complement: HP = input - LP.

This is the fundamental building block for parameter smoothing, envelope following, DC blocking, and simple tone shaping. Extremely efficient — one multiply and one add per sample.

File Locations

	Path
Header	Sources/FolioDSP/include/FolioDSP/Primitives/OnePole.h
Implementation	Sources/FolioDSP/src/Primitives/OnePole.cpp
Tests	Tests/FolioDSPTests/OnePoleTests.swift
Bridge	Sources/FolioDSPBridge/src/FolioDSPBridge.mm (OnePoleBridge)

Parameters

Index	Name	Description	Min	Max	Default Min	Default Max	Default	Unit
0	Frequency	Filter cutoff frequency	1.0	20000.0	20.0	5000.0	1000.0	Hz
1	Type	Filter type: 0=lowpass, 1=highpass	0.0	1.0	0.0	1.0	0.0

Processing Algorithm

1. Coefficient Calculation

\[c = e^{-2\pi f / f_s}\]

2. Lowpass Filter

\[y_{\text{LP}} = (1 - c) \cdot x + c \cdot y[n-1]\]

3. Highpass (complementary)

\[y_{\text{HP}} = x - y_{\text{LP}}\]

4. Output Selection

Type < 0.5 returns LP; type ≥ 0.5 returns HP.

Core Equations

\[c = e^{-2\pi f / f_s}\]

\[y_{\text{LP}}[n] = (1-c) \cdot x[n] + c \cdot y_{\text{LP}}[n-1]\]

Snapshot Fields

Field	Type	Range	Unit	Description
Frequency	Float	1–20000	Hz	Current cutoff
Type	Float	0–1		Current filter type
Output	Float	-1–1		Current output sample

Implementation Notes

• Coefficient recalculated every sample for real-time frequency modulation
• At type = 0.5, output is equal blend of LP and HP (partial cancellation at cutoff)
• No normalization — output may be slightly attenuated at high frequencies (inherent to one-pole topology)

Equation Summary

y = (1-c)·x + c·y[n-1], c = e^(-2πf/sr)