Phase selection of synthetic discriminant function filters

In this paper, we address the problem of correlation peak phase selection for synthetic discriminant function filters. We show that the minimization of the output variance and the optimization of the correlation peak form are problems of the same complexity (analogous to the determination of the ground state of a magnetic disordered system). We propose a general framework and, with examples, we show that, although the variance reduction by a proper selection of the correlation peak phases can be interesting in some situations, the optimization of the sharpness of the correlation peak is often more fruitful.