  Partial information decomposition (PID) partitions the information that a set
of sources has about a target variable into synergistic, unique, and redundant
contributions. This information-theoretic tool has recently attracted attention
due to its potential to characterize the information processing in multivariate
systems. However, the PID framework still lacks a solid and intuitive
interpretation of its information components. In the aim to improve the
understanding of PID components, we focus here on Boolean gates, a much-studied
type of source-target mechanisms. Boolean gates have been extensively
characterised via Fourier analysis which coefficients have been related to
interesting properties of the functions defining the gates. In this paper, we
establish for Boolean gates mechanisms a relation between their PID components
and Fourier coefficients.
