Additive as well as multiplicative noise appears in weather radar returns, or, when acoustic waves propagate through the ocean. Second order spectral methods fail to retrieve frequencies of such random amplitude modulated harmonic time series, especially when the multiplicative noise is broadband. An existing fourth-order method assumes real Gaussian multiplicative and additive noise. A novel approach is proved herein to impose no constraints on the distribution or the color of the disturbances. It relies on fourth-order special cumulant or moment slices. In particular, the fourth-order moment spectrum is shown to offer computational advantages. Extension to multi-component models and generalizations to alternative sixth order moments are also provided.