Neutron and gamma noise measurements of nuclear reactors are powerful tools to infer the kinetic behavior of such systems in a passive, non-perturbing way. Typically correlations in the small fluctuations in the neutron or gamma population of a reactor are used to make these observations. In this work we demonstrate a method for synchronizing different radiation detection systems post measurement using intrinsic pile noise to investigate previously unobservable correlations between neutron and gamma noise in the frequency domain. After synchronization, we observed a threefold reduction in measurement uncertainty compared to using neutron or gamma noise alone, along with a signal-to-noise ratio improvement of more than two and a half orders of magnitude. Additionally, we found that the time lag between our data acquisition systems was not constant, requiring continuous estimation of this lag. This synchronization technique also offers a means to reanalyze historical measurements obtained with unsynchronized acquisition systems and to detect desynchronization in measurements using externally triggered acquisition systems. This decrease in measurement uncertainty allows for more useful experimental data to validate nuclear data and transport methods.