Haar Matrix
The 2×2 Haar matrix that is associated with the Haar wavelet is
Using the discrete wavelet transform, one can transform any sequence of even length into a sequence of two-component-vectors . If one right-multiplies each vector with the matrix, one gets the result of one stage of the fast Haar-wavelet transform. Usually one separates the sequences s and d and continues with transforming the sequence s. Sequence s is often referred to as the averages part, whereas d is known as the details part.
If one has a sequence of length a multiple of four, one can build blocks of 4 elements and transform them in a similar manner with the 4×4 Haar matrix
which combines two stages of the fast Haar-wavelet transform.
Compare with a Walsh matrix, which is a non-localized 1/–1 matrix.
Read more about this topic: Haar Wavelet
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