##
Paraunitary
Filters^{C.4}

Another way to express the allpass condition
is to
write
**Definition:**The

*paraconjugate*of a transfer function may be defined as the

*analytic continuation of the complex conjugate*from the unit circle to the whole plane:

*coefficients only*of

*and not the powers of*. For example, if , then . We can write, for example,

**Examples:**

*invert*, which

*is*analytic, and which reduces to complex conjugation on the unit circle. The paraconjugate may be used to characterize allpass filters as follows:

**Theorem:**A causal, stable, filter is allpass if and only if

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Multi-Input, Multi-Output (MIMO) Allpass Filters

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Allpass Examples