Haar transform

Haar transform

The Haar transform is the simplest of the wavelet transforms. This transform cross-multiplies a function against the Haar wavelet with various shifts and stretches, like the Fourier transform cross-multiplies a function against a sine wave with two phases and many stretches. [ [http://sepwww.stanford.edu/public/docs/sep75/ray2/paper_html/node4.html The Haar Transform ] ]

The Haar transform is derived from the Haar matrix. An example of a 4x4 Haar matrix is shown below.

:H_4 = frac{1}{sqrt{4egin{bmatrix} 1 & 1 & 1 & 1 \ 1 & 1 & -1 & -1 \ sqrt{2} & -sqrt{2} & 0 & 0 \ 0 & 0 & sqrt{2} & -sqrt{2}end{bmatrix}

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

References

External links

*http://cnx.org/content/m11087/latest/
*http://math.hws.edu/eck/math371/applets/Haar.html
*http://online.redwoods.cc.ca.us/instruct/darnold/LAPROJ/Fall2002/ames/paper.pdf
*http://scien.stanford.edu/class/ee368/projects2000/project12/2.html


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