The restoration of nonlinearly distorted audio signals, alongside the identification of the applied memoryless nonlinear operation, is studied. The paper focuses on the difficult but practically important case in which both the nonlinearity and the original input signal are unknown. The proposed method uses a generative diffusion model trained unconditionally on guitar or speech signals to jointly model and invert the nonlinear system at inference time. Both the memoryless nonlinear function model and the restored audio signal are obtained as output. Successful example case studies are presented including inversion of hard and soft clipping, digital quantization, half-wave rectification, and wavefolding nonlinearities. Our results suggest that, out of the nonlinear functions tested here, the cubic Catmull-Rom spline is best suited to approximating these nonlinearities. In the case of guitar recordings, comparisons with informed and supervised methods show that the proposed blind method is at least as good as they are in terms of objective metrics. Experiments on distorted speech show that the proposed blind method outperforms general-purpose speech enhancement techniques and restores the original voice quality. The proposed method can be applied to audio effects modeling, restoration of music and speech recordings, and characterization of analog recording media.
Analog electronic circuits are at the core of an important category of musical devices, which includes a broad range of sound synthesizers and audio effects. The development of software that simulates analog musical devices, known as virtual analog modeling, is a significant sub-field in audio signal processing. Artificial neural networks are a promising technique for virtual analog modeling. While neural approaches have successfully accurately modeled distortion circuits, they require architectural improvements that account for parameter conditioning and low-latency response. This article explores the application of recent machine learning advancements for virtual analog modeling. In particular, we compare State-Space models and Linear Recurrent Units against the more common Long Short-Term Memory networks. Our comparative study uses these black-box neural modeling techniques with various audio effects. We evaluate the performance and limitations of these models using multiple metrics, providing insights for future research and development. Our metrics aim to assess the models' ability to accurately replicate energy envelopes and frequency contents, with a particular focus on transients in the audio signal. To incorporate control parameters into the models, we employ the Feature-wise Linear Modulation method. Long Short-Term Memory networks exhibit better accuracy in emulating distortions and equalizers, while the State-Space model, followed by Long Short-Term Memory networks when integrated in an encoder-decoder structure, and Linear Recurrent Unit outperforms others in emulating saturation and compression. When considering long time-variant characteristics, the State-Space model demonstrates the greatest capability to track history. Long Short-Term Memory networks tend to introduce audio artifacts.
Infinite impulse response filters are an essential building block of many time-varying audio systems, such as audio effects and synthesisers. However, their recursive structure impedes end-to-end training of these systems using automatic differentiation. Although non-recursive filter approximations like frequency sampling and frame-based processing have been proposed and widely used in previous works, they cannot accurately reflect the gradient of the original system. We alleviate this difficulty by re-expressing a time-varying all-pole filter to backpropagate the gradients through itself, so the filter implementation is not bound to the technical limitations of automatic differentiation frameworks. This implementation can be employed within audio systems containing filters with poles for efficient gradient evaluation. We demonstrate its training efficiency and expressive capabilities for modelling real-world dynamic audio systems on a phaser, time-varying subtractive synthesiser, and compressor. We make our code and audio samples available and provide the trained audio effect and synth models in a VST plugin at https://diffapf.github.io/web/.
In this work we present a data-driven approach for predicting the behavior of (i.e., profiling) a given non-linear audio signal processing effect (henceforth "audio effect"). Our objective is to learn a mapping function that maps the unprocessed audio to the processed by the audio effect to be profiled, using time-domain samples. To that aim, we employ a deep auto-encoder model that is conditioned on both time-domain samples and the control parameters of the target audio effect. As a test-case study, we focus on the offline profiling of two dynamic range compression audio effects, one software-based and the other analog. Compressors were chosen because they are a widely used and important set of effects and because their parameterized nonlinear time-dependent nature makes them a challenging problem for a system aiming to profile "general" audio effects. Results from our experimental procedure show that the primary functional and auditory characteristics of the compressors can be captured, however there is still sufficient audible noise to merit further investigation before such methods are applied to real-world audio processing workflows.