Some properties of multiple carriers and intermodulation

The statistics of the amplitude of a sum of sinusoids with more-or-less equal spacing in frequency are examined, with emphasis on the short quasi-periodic peaks characteristic of such sums. Various choices of reference phase for the sinusoids are considered, along with their effect on the amplitude peaks. By assuming a small cubic nonlinearity for an amplifier being fed by the sum of sinusoids, the output intermodulation peaking is related to the quasi-periodic peaking of the input amplitude. To explore a possible mechanism for slow variations in the relative reference phases of the sinusoids, the effect of passing flicker noise through the closed loop filter response of a phase-locked loop is considered.