Rademacher functions

Rademacher functions

(mathematics)
The functions ƒn , with n = 1, 2, 3, …, defined on the closed interval [0, 1] by the equation ƒn (x) = sgn [sin (2 n π x)], where sgn represents the signum function and sin represents the sine function.
References in periodicals archive ?
The Rademacher functions are in [L.sup.2] [0, 1] and are defined by
By definition of the Rademacher functions, ipn has at most [2.sup.n] values, since [r.sub.k] is defined on [2.sup.k] subdivisions of the same length of [0, 1] for k = 1, ..., n.
It is also well known that the Walsh functions may be evaluated using Rademacher functions [1]-[3].
We found that the original Walsh functions, defined in terms of products of Rademacher functions can be used to transform the information into frequency domain faster than FHT and thus leads to speed up the DSP process.
We preferred definition of Walsh transform based upon derivation of Walsh functions from Rademacher functions which is found to be more appropriate for hardware implementation.
Consider the Rademacher functions [f.sub.i] := sgn(sin([2.sup.i][pi]x), i [member of] N.