Properties of Paraunitary Systems

Paraunitary systems are essentially multi-input, multi-output (MIMO) allpass filters. Let $\bold{H}(z)$ denote the $p\times q$ matrix transfer function of a paraunitary system. In the square case ($p=q$ ), the matrix determinant, $\det[\bold{H}(z)]$ , is an allpass filter. Therefore, if a square $\bold{H}(z)$ contains FIR elements, its determinant is a simple delay: $\det[\bold{H}(z)]=z^{-K}$ for some integer $K$ .