$M$-Band Multiwavelet Systems
Felix C. A. Fernandes (felixf@rice.edu)
Electrical and Computer Engineering, Rice University
C. Sidney Burrus (csb@rice.edu)
Electrical and Computer Engineering, Rice University
In this paper we investigate multiwavelet systems whose scaling
functions have disjoint support. We demonstrate that, with the exception
of a trivial case, this property
may not be attained by two band multiwavelet systems. We show that to enjoy
this property, it is indeed
necessary to invoke $M$-band multiwavelet systems.
This indicates the
existence of tilings of the time-frequency plane that may be obtained
with $M$-band multiwavelet systems but not with two band multiwavelet
systems. Hence $M$-band multiwavelet systems are inherently more
powerful than two band multiwavelet systems and deserve a thorough
investigation. Finally, we derive $K^{th}$ order balancing conditions
for $M$-band multiwavelet systems. These conditions will enable
$M$-band multiwavelet systems to be used for
practical digital signal processing applications.