Learning Noise with Generative Adversarial Networks: Explorations with Classical Random Process Models

Random noise arising from physical processes is an inherent characteristic of measurements and a limiting factor for most signal processing tasks. Given the recent interest in generative adversarial networks (GANs) for data-driven signal modeling, it is important to determine to what extent GANs can faithfully reproduce noise in target data sets. In this paper, we present an empirical investigation that aims to shed light on this issue for time series. Namely, we examine the ability of two general-purpose time-series GANs, a direct time-series model and an image-based model using a short-time Fourier transform (STFT) representation, to learn a broad range of noise types commonly encountered in electronics and communication systems: band-limited thermal noise, power law noise, shot noise, and impulsive noise. We find that GANs are capable of learning many noise types, although they predictably struggle when the GAN architecture is not well suited to some aspects of the noise, e.g., impulsive time-series with extreme outliers. Our findings provide insights into the capabilities and potential limitations of current approaches to time-series GANs and highlight areas for further research. In addition, our battery of tests provides a useful benchmark to aid the development of deep generative models for time series.