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Rademacher system

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

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