This study uses Fourier analysis to investigate the relationship between the heat release event and the frequency composition of pressure oscillations in a variety of combustion modes. While kinetically-controlled combustion strategies such as HCCI and RCCI offer advantages over CDC in terms of efficiency and NOX emissions, their operational range is limited by audible knock and the possibility of engine damage stemming from high pressure rise rates and oscillations. Several criteria such as peak pressure rise rate, ringing intensity, and various knock indices have been developed to quantify these effects, but they fail to capture all of the dynamics required to form direct comparisons between different engines or combustion strategies. Experiments were performed with RCCI, HCCI, and CDC on a 2.44 L heavy-duty engine at 1300 RPM, generating a significant diversity of heat release profiles. Fourier and statistical analyses were used to examine the effect of both the average heat release as well as cyclic variations on the frequency and amplitude of pressure oscillations, and these were compared to existing knocking criteria. The results indicate that for this engine platform, the first two resonant frequency modes contain the majority of the spectral power contributing to the ringing effect, and that the relative power contained in these modes is strongly influenced by the heat release event and operating conditions when operating with premixed combustion strategies.