Recent work demonstrates that stochastic fluctuations in molecular populations have consequences for gene regulation. Previous experiments focused on noise sources or noise propagation through gene networks by measuring noise magnitudes. However, in theoretical analysis, we showed that noise frequency content is determined by the underlying gene circuits, leading to a mapping between gene circuit structure and the noise frequency range. An intriguing prediction from our previous studies was that negative autoregulation shifts noise to higher frequencies where it is more easily filtered out by gene networks--a property that may contribute to the prevalence of autoregulation motifs (for example, found in the regulation of approximately 40% of Escherichia coli genes). Here we measure noise frequency content in growing cultures of E. coli, and verify the link between gene circuit structure and noise spectra by demonstrating the negative autoregulation-mediated spectral shift. We further demonstrate that noise spectral measurements provide mechanistic insights into gene regulation, as perturbations of gene circuit parameters are discernible in the measured noise frequency ranges. These results suggest that noise spectral measurements could facilitate the discovery of novel regulatory relationships.