Editing Haar wavelet (section)

=== Introduction ===
The Haar transform is one of the oldest transform functions, proposed in 1910 by the Hungarian mathematician [[Alfréd Haar]]. It is found effective in applications such as signal and image compression in electrical and computer engineering as it provides a simple and computationally efficient approach for analysing the local aspects of a signal.

The Haar transform is derived from the Haar matrix. An example of a 4×4 Haar transformation matrix is shown below.

:<math>H_4 = \frac{1}{2}
\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 1 & -1 & -1 \\ \sqrt{2} & -\sqrt{2} & 0 & 0 \\ 0 & 0 & \sqrt{2} & -\sqrt{2}\end{bmatrix}
</math>

The Haar transform can be thought of as a sampling process in which rows of the transformation matrix act as samples of finer and finer resolution.

Compare with the [[Walsh transform]], which is also 1/–1, but is non-localized.