In mathematics, in particular in functional analysis, the Rademacher system, named after Hans Rademacher, is an incomplete orthogonal system of functions on the unit interval of the following form:

${\displaystyle \{t\mapsto r_{n}(t)=\operatorname {sgn}(\sin 2^{n+1}\pi t);t\in [0,1],n\in \mathbb {N} \}.}$

The Rademacher system is stochastically independent, and is closely related to the Walsh system. Specifically, the Walsh system can be constructed as a product of Rademacher functions.