  We show that combining vibrational spectroscopy with signal processing can
result in a scheme for ultrasensitive detection of molecules. We consider the
vibrational spectrum as a signal on the energy axis and apply a matched filter
on that axis. On the example of a nerve agent molecule, we show that this
allows detecting a molecule by its vibrational spectrum even when the recorded
spectrum is completely buried in noise, when conventional spectroscopic
detection is impossible. Detection is predicted to be possible with
signal-to-noise ratios in recorded spectra as low as 0.1. We study the
importance of spectral range used for detection as well as of the quality of
the computed spectrum used to program the filter, specifically, the role of
anharmonicity, of the exchange correlation functional, and of the basis set.
The use of the full spectral range rather than of a narrow spectral window with
key vibrations is shown to be advantageous, as well as accounting for
anharmonicity.
