M-Band Multiwavelet Systems
Burrus, C. Sidney
M-band; multiwavelet systems; time-frequency plane
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 <i>M</i>-band multiwavelet systems. This indicates the existence of tilings of the time-frequency plane that may be obtained with <i>M</i>--band multiwavelet systems but not with two band multiwavelet systems. Hence <i>M</i>--band multiwavelet systems are inherently more powerful than two band multiwavelet systems and deserve a thorough investigation. Finally, we derive K<sup>th</sup order balancing conditions for <i>M</i>--band multiwavelet systems. These conditions will enable <i>M</i>--band multiwavelet systems to be used for practical digital signal processing applications.