Properties of Paraunitary Systems

Paraunitary systems are essentially multi-input, multi-output (MIMO) allpass filters. Let $ \mathbf{H}(z)$ denote the $ p\times q$ matrix transfer function of a paraunitary system. Some of its properties include the following [98]:

  • In the square case ($ p=q$), the matrix determinant, $ \det[\mathbf{H}(z)]$, is an allpass filter.

  • Therefore, if a square $ \mathbf{H}(z)$ contains FIR elements, its determinant is a simple delay: $ \det[\mathbf{H}(z)]=z^{-K}$ for some integer $ K$.

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MIMO Paraunitary Condition