In this paper we introduce three weighting algorithms for performing shift-invariant heterogeneous phase-restricted correlation filters that are capable of identifying an object as belonging to a certain class while rejecting any object that is not a member ofthat class. We compare the performance ofthese highly discriminative filters to the performance of the phase-only filter, and the non-discriminative matche4 correlation filter, in similar circumstances. Even when the proposed filters achieved proper classification, the intensities ofthe correlations from heterogeneous targets (hetero-correlations) were much smaller than those from homogeneous targets (autocorrelation). To increase the intensities ofthese hetero-correlation peaks relative to the autocorrelation peaks, we also introduced a fractional power law into the filter's transfer function, thereby controlling the rejection capability of the filter.