  We show the existence and uniqueness of invariant foliations about invariant
tori in analytic discrete-time dynamical systems. The parametrisation method is
used prove the result. Our theory is a foundational block of data-driven model
order reduction, that can only be carried out using invariant foliations. The
theory is illustrated by two mechanical examples, where instantaneous
frequencies and damping ratios are calculated about the invariant tori.
