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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:

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

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.

References

"Orthogonal system". Encyclopaedia of Mathematics.
Heil, Christopher E. (1997). "A basis theory primer" (PDF).

Mathematics Encyclopedia