Nuclear quadrupole resonance (NQR) is a spectroscopic technique that can be used to detect many high explosives and narcotics. Unfortunately, the measured signals are weak, thereby inhibiting the widespread use of the technique. Current state-of-the-art detectors, which exploit realistic NQR data models, assume that the complex amplitudes of the NQR signal components are known, to within a multiplicative constant. However, these amplitudes are typically prone to some level of uncertainty, thus leading to performance loss in these algorithms. Herein, we develop a frequency selective algorithm, robust to uncertainties in the assumed amplitudes, that offers a significant performance gain over current state-of-the art techniques.