Nuclear quadrupole resonance (NQR) is a technique that discriminates mines from clutter by exploiting unique properties of explosives, rather than the attributes of the mine that exist in many forms of anthropic clutter. After exciting the explosive with a properly designed electromagnetic-induction (EMI) system, one attempts to sense late-time spin echoes, which are characterized by radiation at particular frequencies. It is this narrow-band radiation that indicates the presence of explosives, since this effect is not seen in most clutter, both natural and anthropic. However, this problem is complicated by several issues. First, the late-time radiation if often very weak, particularly for TNT, and therefore the signal-to-noise ratio must be high for extracting the NQR response. Further, the frequency at which the explosive radiates is often a strong function of the background environment, and therefore in practice the NQR radiation frequency is not known a priori. Finally, at the frequencies of interest, there is a significant amount of background radiation, which induces radio frequency interference (RFI). In this paper we discuss several signal processing tools we have developed to enhance the utility of NQR explosives detection. In particular, with regard to the RFI, we exposure least-mean-squares algorithms which have proven well suited to extracting background interference. Algorithm performance is assessed through consideration of actual measured data. With regard to the detection of the NQR electromagnetic echo, we consider a Bayesian discrimination algorithm. The performance of the Bayesian algorithm is presented, again using measured NQR data.