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In applied mathematics, the transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable functions. Refinable functions play an important role in wavelet theory and finite element theory. For the mask , which is a vector with component indexes from to ,the transfer matrix of , we call it here, is defined as More verbosely The effect of can be expressed in terms of the downsampling operator "":
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