Statistical performance of cascaded linear shift-invariant processing

The cascaded correlator architecture comprises a series of traditional linear correlators separated by nonlinear threshold functions, trained with neural-network techniques. We investigate the shift-invariant classification performance of cascaded correlators in comparison with optimum Bayes classifiers. Inputs are formulated as randomly generated sample members of known statistical class distributions. It is shown that when the separability of true and false classes is varied in both the first and the second orders, the two-stage cascaded correlator shows performance similar to that of the optimum quadratic Bayes classifier throughout the studied range. It is shown that this is due to the similar decision boundaries implemented by the two nonlinear classifiers.