Transfer matrix

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 ${\displaystyle h}$, which is a vector with component indexes from ${\displaystyle a}$ to ${\displaystyle b}$, the transfer matrix of ${\displaystyle h}$, we call it ${\displaystyle T_{h}}$ here, is defined as

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