Unitary and paraunitary systems in finite fields

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Abstract
Unitary and paraunitary matrices have found a number of applications in signal processing. A paraunitary matrix H(z) in the complex field is nothing but a rational function of z (with complex coefficients), which is unitary for z=e/sup jw/. When computations are performed in a finite field, it is important to deal with this class of matrices in a finite field. Unitary and paraunitary matrices in finite fields are introduced. Various properties are studied, including the possibility of factorizations in terms of Householder building blocks. For the case of FIR (finite impulse response) systems, state-space manifestation of the paraunitary property is also considered.