Walsh function

In mathematical analysis, the set of Walsh functions form an orthogonal basis of the square-integrable functions on the unit interval. The functions take the values -1 and 1 only, on sub-intervals defined by dyadic fractions. They are useful in electronics, and other engineering applications.

The Walsh functions are related to the Haar functionss; but form a complete orthogonal system, which the latter do not.

The order of the function is 2^s, where s is an integer, meaning that there is 2^s (time-)intervals in which the value is -1 or 1.

2^s Potential function
1  ----------
2  -----_____
3  ---____---
4  --__--__--
5  -___--___-
6  -___-_---_

Table of the first six orthogonal functions from the Walsh basis set.

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