Apart from the first Walsh function, which is identically 1, all the others are equal to +1 on half of the interval [0,1] and –1 on the remaining half. Also, the product of any two Walsh functions is again a Walsh function (the first 2^n functions form a multiplicative group. It follows that the integral over [0,1] of the product of two Walsh functions is zero. Hence they form an orthogonal set.