Theory and Design of Signal--Adapted FIR Paraunitary Filter Banks

	by Pierre Moulin and M. Kivanc Mihcak

We study the design of signal--adapted FIR paraunitary filter banks,
using energy compaction as the adaptation criterion.
We present some important properties that {\em globally optimal}
solutions to this optimization problem satisfy.
In particular, we show that the optimal filters
in the first channel of the filter bank are spectral factors of the solution
to a linear semi--infinite programming (SIP) problem.
The remaining filters are related to the first through
a matrix eigenvector decomposition. 
We discuss uniqueness and sensitivity issues.
The SIP problem is solved using a discretization method and
a standard simplex agorithm.
We also show how regularity constraints may be incorporated
into the design problem so as to obtain globally optimal
(in the energy compaction sense) filter banks with specified regularity.
We also consider a problem in which the polyphase matrix implementation
of the filter bank is constrained to be DCT--based.  Such constraints
may also be incorporated into our optimization algorithm,
so we are able to obtain globally optimal filter banks subject
to regularity and/or computational complexity constraints.
Numerous experiments are presented to illustrate
the main features that distinguish adapted and nonadapted filters,
as well as the effects of the various constraints.
The conjecture that energy compaction and coding gain optimization
are equivalent design criteria, is shown not to hold for FIR filter banks.