Tape Saturation
Tier: Color | ComponentType: 26 | Params: 5
Asymmetric soft clipping with pre-emphasis, de-emphasis, and magnetic hysteresis modeling, simulating the nonlinear recording characteristics of analog tape.
Overview
TapeSaturation models the way analog tape records and plays back audio. Real tape has several nonlinear characteristics that together create its distinctive warm, compressed sound. The recording head applies pre-emphasis (boosting high frequencies before recording to improve signal-to-noise ratio), the magnetic medium introduces asymmetric saturation (positive and negative magnetization have slightly different limits), and the playback head applies de-emphasis (rolling off the high frequencies that were boosted during recording, restoring flat response while reducing tape hiss).
The asymmetry parameter controls the difference in saturation between positive and negative signal halves. At 1.0, the clipping is symmetric (same limit in both directions). As asymmetry decreases toward 0.5, the negative half is increasingly attenuated relative to the positive half, generating even-order harmonics that add warmth and fullness -- a characteristic of real tape where the magnetic coating saturates differently in each polarity.
Hysteresis models the magnetic memory of tape: the current magnetization depends not just on the current input but also on the previous magnetization state. This creates a subtle smearing or thickening of the sound, especially on transients, where the tape's magnetic state lags behind the signal. Higher hysteresis values increase this lag, producing a softer, more compressed feel.
File Locations
| Path | |
|---|---|
| Header | Sources/FolioDSP/include/FolioDSP/Color/TapeSaturation.h |
| Implementation | Sources/FolioDSP/src/Color/TapeSaturation.cpp |
| Tests | Tests/FolioDSPTests/TapeSaturationTests.swift |
| Bridge | Sources/FolioDSPBridge/src/FolioDSPBridge.mm (TapeSaturationBridge) |
Parameters
| Index | Name | Description | Min | Max | Default Min | Default Max | Default | Unit |
|---|---|---|---|---|---|---|---|---|
| 0 | Drive | Recording level -- higher values push deeper into tape saturation | 1 | 50 | 1 | 10 | 3 | |
| 1 | Asymmetry | Balance between positive and negative saturation (1.0 = symmetric) | 0.5 | 1.0 | 0.6 | 1.0 | 0.8 | |
| 2 | Tone | De-emphasis lowpass cutoff -- controls brightness of the output | 500 | 16000 | 1000 | 8000 | 3000 | Hz |
| 3 | Hysteresis | Magnetic memory -- blends previous output state into current | 0.0 | 0.5 | 0.0 | 0.3 | 0.1 | |
| 4 | Mix | Dry/wet blend | 0 | 100 | 0 | 100 | 100 | % |
Processing Algorithm
The process() function executes these steps for each input sample:
1. Pre-Emphasis
A first-order highpass filter boosts high frequencies before saturation, simulating the recording head's pre-emphasis circuit:
The 0.85 coefficient sets the highpass frequency, and the 30% blend controls how much pre-emphasis is applied.
2. Drive Gain
The pre-emphasized signal is multiplied by the drive factor:
Where \(D\) is the drive parameter (linear, not dB).
3. Asymmetric Saturation
Hyperbolic tangent saturation with different behavior for positive and negative halves:
Where \(A\) is the asymmetry parameter. When \(A = 1.0\), both halves saturate identically. When \(A < 1.0\), the negative half is scaled down, producing even harmonics.
4. Hysteresis
A one-sample feedback blend models the tape's magnetic memory:
Where \(H\) is the hysteresis parameter and \(s_{n-1}\) is the previous hysteresis state. This is equivalent to a weighted average between the current saturated value and the previous output: when \(H = 0\), no memory; when \(H = 0.5\), equal weight between current and previous.
5. De-Emphasis (Tone Filter)
A one-pole lowpass filter rolls off high frequencies, undoing the pre-emphasis and shaping the final tone:
6. DC Blocker
A standard first-order highpass filter removes any DC offset from the asymmetric saturation:
7. Normalization
The output is divided by \(\tanh(D \cdot 0.5)\) to roughly compensate for the level increase from drive:
8. Dry/Wet Mix
Core Equations
Snapshot Fields
| Field | Type | Range | Unit | Description |
|---|---|---|---|---|
| Input Level | Float | 0--1 | Smoothed absolute input level | |
| Output Level | Float | 0--1 | Smoothed absolute output level | |
| Drive Amount | Float | 1--50 | Current drive setting | |
| Saturation Amount | Float | 0--1 | Ratio of saturated to driven level | |
| Tone Frequency | Float | 500--16000 | Hz | Current de-emphasis cutoff frequency |
| Transfer Curve | Float[16] | -1--1 | 16-point input-to-output transfer function |
Implementation Notes
- DC blocker uses the standard first-order highpass:
y = x - xprev + R * ywhereR = 1 - (2π·10/sr). This is the correct form (not the one-pole LP subtraction variant). - Asymmetry clamping: The denominator in the negative-half saturation is clamped to
max(A, 0.01)to prevent division by zero when asymmetry approaches 0.5 (the parameter minimum). - Normalization: The divisor
tanh(drive * 0.5)is clamped to a minimum of 0.1 to prevent excessive gain at very low drive values. - Transfer curve is computed in the snapshot emission path, sampling 16 points from \(x = -1\) to \(x = 1\) through the current drive and asymmetry settings.
- Level tracking uses exponential smoothing with coefficient 0.01 for display-rate visualization.
- Saturation amount in the snapshot is computed as \(|y_s| / \max(|x_d|, 0.001)\), measuring how much the saturation curve has compressed the signal.
- All parameters are marked as smoothed in ParamInfo for bridge-level interpolation.
- Snapshot emission is decimated to ~60 fps (every 735 samples at 44.1 kHz).
Equation Summary
y = tanh(preEmph(x)·drive); deEmph