  We present a technique that uses noisy broadband pulse bursts generated by
modulational instability to probe nonlinear processes, including
infrared-inactive Raman transitions, in molecular gases. These processes
imprint correlations between different regions of the noisy spectrum, which can
be detected by acquiring single shot spectra and calculating the Pearson
correlation coefficient between the different frequency components. Numerical
simulations verify the experimental measurements and are used to further
understand the system and discuss methods to improve the signal strength and
the spectral resolution of the technique.
