M-Band Multiwavelet Systems

Felix C. A. Fernandes and C. Sidney Burrus Department of Electrical and Computer Engineering, Rice University, Houston, TX 77251{1892, USA ABSTRACT 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 Kth order balancing conditions forM -band multiwavelet systems. These conditions will enable M -band multiwavelet systems to be used for practical digital signal processing applications.

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