Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics and Statistics

First Advisor

Gregory T. Warhola, PhD


The rational resolution analysis RRA is introduced and developed as a generalization of the integer, dilation multiresolution analyses MRA developed by Mallat and Meyer. Rational dilation factors are achieved by relaxing the condition on MRAs that successive approximation spaces be embedded. Conditions for perfect reconstruction are discussed and it is shown that perfect reconstruction is possible with specific constraints on the scaling function the scaling filter must have its roots on the unit circle. Furthermore, the required arrangement of the roots indicate the scaling function must be derived from a B-spline of some degree. It is proven the only compactly supported scaling function which satisfies these constraints is the Haar basis. An algorithmic approach to constructing p-dilation wavelets is presented. The frame properties along with adjoint wavelets of RRAs are is presented. It is shown the adjoint wavelets form a frame for V0 and that the corresponding decomposition is both stable and unique. The redundant representation of the detail coefficients is exploited as a solution to the specific emitter problem. Results demonstrate the RRA is far superior to the traditional MRA and wavepacket approaches when used as a feature extractor in Bayesian classification schemes.

AFIT Designator


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