Modulation effects such as phasers, flangers and chorus effects are heavily used in conjunction with the electric guitar. Machine learning based emulation of analog modulation units has been investigated in recent years, but most methods have either been limited to one class of effect or suffer from a high computational cost or latency compared to canonical digital implementations. Here, we build on previous work and present a framework for modelling flanger, chorus and phaser effects based on differentiable digital signal processing. The model is trained in the time-frequency domain, but at inference operates in the time-domain, requiring zero latency. We investigate the challenges associated with gradient-based optimisation of such effects, and show that low-frequency weighting of loss functions avoids convergence to local minima when learning delay times. We show that when trained against analog effects units, sound output from the model is in some cases perceptually indistinguishable from the reference, but challenges still remain for effects with long delay times and feedback.
Model as it appears during training (a) and inference (b). The flanger/chorus variant (FC) uses an interpolated delay line; the phaser variant (P) uses a cascade of all-pass filters. The switch in (b) provides two configurations of the BQ2 filter, either outside (I) or inside (II) the feedback loop.
Citation
@article{Carson2026modfx,title={Gradient-based optimization of modulation effects},author={Carson, Alistair and Wright, Alec and Bilbao, Stefan},year={2026},month=jul,journal={Journal of the Audio Engineering Society},volume={74},pages={533--543},}
Audio Examples
Listen below to outputs from the target analog modulation pedals and our models’ emulations.
Dry audio samples
Clip
Input
Guitar 1
Guitar 2
Bass 1
Bass 2
BF-2 Flanger
The examples below were generated with the flanger/chorus variant of the model for the two different feedback configurations: FC-I and FC-II.
Resonance = 0% (no feedback)
Clip
Target
FC-I
FC-II
Guitar 1
Guitar 2
Bass 1
Bass 2
Resonance = 50% (medium feedback)
Clip
Target
FC-I
FC-II
Guitar 1
Guitar 2
Bass 1
Bass 2
Resonance = 100% (max feedback)
Clip
Target
FC-I
FC-II
Guitar 1
Guitar 2
Bass 1
Bass 2
Small Stone Phaser
The examples below were generated with the phaser variant of the model for the two different feedback configurations: P-I and P-II.
Color OFF , Rate = 75%
Clip
Target
P-I
P-II
Guitar 1
Guitar 2
Bass 1
Bass 2
Color OFF, Rate = 50%
Clip
Target
P-I
P-II
Guitar 1
Guitar 2
Bass 1
Bass 2
Color OFF, Rate = 25%
Clip
Target
P-I
P-II
Guitar 1
Guitar 2
Bass 1
Bass 2
Color ON, Rate = 75%
Clip
Target
P-I
P-II
Guitar 1
Guitar 2
Bass 1
Bass 2
Color ON , Rate = 50%
Clip
Target
P-I
P-II
Guitar 1
Guitar 2
Bass 1
Bass 2
SV-1 Supervibe Chorus
The examples below were generated with the flanger/chorus variant of the model (FC-I), for different number of channels (C) (see paper for more details).
