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.

here, is defined as

More verbosely

can be expressed in terms of the downsampling":

Properties

See also

• Hurwitz determinant

References

• (contains proofs of the above properties)