Paraunitary systems are essentially multi-input, multi-output (MIMO) allpass filters. Let denote the matrix transfer function of a paraunitary system. Some of its properties include the following [98]:

- In the square case (), the matrix determinant,
, is an
*allpass filter*. - Therefore, if a square
contains FIR elements, its
determinant is a simple delay:
for some
integer .

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