We discuss an effective method for detecting and identifying drugs using a high-noise terahertz (THz) signal. We add a noisy THz signal obtained in real conditions to the THz signal transmitted through a sample with the illicit drug methamphetamine. The insufficiency of the standard THz time-domain spectroscopy method is demonstrated, showing that this method detects the spectral features of neutral substances and explosives in a noisy THz signal. The method discussed is based upon time-dependent integral correlation criteria calculated using spectral dynamics of the medium response. We propose a modification of the integral correlation criterion that is less dependent on the spectral characteristics of a noisy signal under investigation.