Paraunitary MIMO Filters

In §D.2, we generalized the allpass property $1=\left\vert H(e^{j\omega})\right\vert^2=H(e^{j\omega})H(e^{-j\omega})$ to the entire complex plane as

$${\tilde H}(z) H(z) = 1,$$

where ${\tilde H}$ is defined as the paraconjugate of $H$. In the MIMO case, the paraconjugate is the same, but including a matrix transpose operation: