# Band-Limited Gaussian Processes: The Sinc Kernel

arXiv: https://arxiv.org/abs/1909.07279 · HTML: https://mlsanity.com/paper/1909.07279/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2019.

## Built on by (most cited first, 8 of 8)

- [Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processes](https://mlsanity.com/paper/2106.10210/) (2021)
- [Hida-Mat'ern Kernel](https://mlsanity.com/paper/2107.07098/) (2021)
- [The Minecraft Kernel: Modelling correlated Gaussian Processes in the Fourier domain](https://mlsanity.com/paper/2103.06950/) (2021)
- [Gaussian process deconvolution](https://mlsanity.com/paper/2305.04871/) (2023)
- [Asymptotic Performance of Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2505.13012/) (2025)
- [CatBOX: A Categorical-Continuous Bayesian Optimization with Spectral Mixture Kernels for Accelerated Catalysis Experiments](https://mlsanity.com/paper/2505.17393/) (2025)
- [Universal Modelling of Autocovariance Functions via Spline Kernels](https://mlsanity.com/paper/2506.21953/) (2025)
- [ALAS: Additive Learnable Alpha-Stable Kernels for Flexible Bayesian Optimization](https://mlsanity.com/paper/2607.18282/) (2026)

## Abstract (arXiv)

We propose a novel class of Gaussian processes (GPs) whose spectra have compact support, meaning that their sample trajectories are almost-surely band limited. As a complement to the growing literature on spectral design of covariance kernels, the core of our proposal is to model power spectral densities through a rectangular function, which results in a kernel based on the sinc function with straightforward extensions to non-centred (around zero frequency) and frequency-varying cases. In addition to its use in regression, the relationship between the sinc kernel and the classic theory is illuminated, in particular, the Shannon-Nyquist theorem is interpreted as posterior reconstruction under the proposed kernel. Additionally, we show that the sinc kernel is instrumental in two fundamental signal processing applications: first, in stereo amplitude modulation, where the non-centred sinc kernel arises naturally. Second, for band-pass filtering, where the proposed kernel allows for a Bayesian treatment that is robust to observation noise and missing data. The developed theory is complemented with illustrative graphic examples and validated experimentally using real-world data.