Background Simulation and Filter Design Using Iterated Function Systems
NAVAL RESEARCH LAB WASHINGTON DC
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Design of filters which detect known signals in unknown backgrounds are considered from a deterministic viewpoint. Backgrounds which appear in Nature rather than being smooth, may appear fractal within a given waveband of interest. In this paper, derivations are given for the design of filters for both smooth backgrounds, and fractal backgrounds. The main theoretical tool for the fractal design is the Iterated Function System IFS. It is shown how the IFS models generalize the smooth models of the background and the corresponding filters. Derivations of the false alarm rate in terms of the filters are given. Numerical examples demonstrating background simulation as well as convolution of the filters with signals embedded in noise having fractal dimension are presented.
- Electricity and Magnetism