# Tag Archives: complete orthonormal system

## Walsh functions I. Orthonormality and completeness

In this post I summarize some useful properties of Walsh functions. These functions were introduced by Joseph Walsh in

Another paper where many ideas can be found is by Nathan Fine

In this exposition here we only concentrate on the simplest case of base $b = 2$ and dimension $s = 1$.

We write $\mathbb{N}$ for the set of natural numbers $1,2,3, \ldots$ and $\mathbb{N}_0$ for the set of nonnegative integers $0,1,2,\ldots$.