Optimal Wavelets for Signal Decomposition and the Existence
		 of Scale-Limited Signals

	J. E. Odegard R. A. Gopinath C. S. Burrus
  Department of Electrical and Computer Engineering -- MS366
            Rice University, Houston, TX-77251
		email: odegard@rice.edu


		        ABSTRACT

Wavelet methods give a flexible alternative to Fourier methods in
non-stationary signal analysis. The concept of band-limitedness
plays a fundamental role in Fourier analysis. Since wavelet theory
replaces frequency with scale, a natural question is whether there
exists a useful concept of scale-limitedness. Obvious definitions of
scale-limitedness are too restrictive, in that there would be few or
no useful scale-limited signals. This paper introduces a viable
definition for scale-limited signals, and shows that the class is rich
enough to include bandlimited signals, and impulse trains, among
others. Moreover, for a wide choice of criteria, we show how to design
the optimal wavelet for representing a given signal, and how to design
robust wavelets that optimally represent certain classes of signals.