Haar wavelet

The Haar wavelet is the first known wavelet and was proposed 1909 by Alfred Haar[?]. Note that the term wavelet was coined much later. The Haar wavelet is also the simplest possible wavelet. It looks like that:

            |
      √1/2  ****O
            |    
            |    
    0  *****O-------****
            |        
            |        
     -√1/2  |   ****O
            0  1/2  1

The disadvantage of the Haar wavelet is that it is not continuous and therefore not differentiable.

Remark: The Haar Wavelet can also be described as a step function f(x) with:

f(x) = 1 (if 0 <= x < 1/2)

f(x) = -1 (if 1/2 <= x < 1)