The Haar wavelet is the compactly supported wavelet
 |
(1)
|
Its dyadic rescalings, which are the function-space analogs of geometric dilations, and its integer translations
 |
(2)
|
for 
form an orthonormal
basis of 
.
The factor 
preserves the 
norm under this rescaling. The Haar wavelet is discontinuous
but has zero mean, since 
.
The Wolfram Language represents the Haar wavelet by HaarWavelet[] and computes a discrete Haar transform using DiscreteWaveletTransform[data, HaarWavelet[]].
