An -channel filter bank can be viewed as an MIMO filter
A paraunitary filter bank must therefore obey
We can note the following properties of paraunitary filter banks:
- A synthesis filter bank
to analysis filter bank
is defined as that filter bank
which inverts the analysis filter bank, i.e., satisfies
- The channel filters in a paraunitary filter bank
are power complementary:
is FIR, the corresponding synthesis filter
is also FIR. Note that this implies an FIR
filter-matrix can be inverted by another FIR filter-matrix. This is in
stark contrast to the case of single-input, single-output FIR filters,
which must be inverted by IIR filters, in general.
is FIR, each synthesis filter,
, is simply the of its corresponding
This follows from the fact that paraconjugating an FIR filter amounts to simply flipping (and conjugating) its coefficients.
Note that only trivial FIR filters can be paraunitary in the single-input, single-output (SISO) case. In the MIMO case, on the other hand, paraunitary systems can be composed of FIR filters of any order.
- FIR analysis and synthesis filters in paraunitary filter banks
have the same amplitude response.
Mechanical Equivalent of a Capacitor is a Spring
Properties of Paraunitary Systems