Noise from rotating systems exhibits cyclostationary features whose physical origin is not fully explained. This work analyzes a rotating, compact monopole with a random volume flow rate via retarded-time Green's functions. In the subsonic far field, the leading-order pressure reduces to a time-warped derivative of the source, scaled by geometric and Doppler gains, demonstrating that deterministic motion alone can induce second-order cyclostationarity when the geometric modulation depth is nonzero. An explicit integral representation for the pressure's cyclic autocorrelation is derived. It exhibits a Bessel-weighted harmonic structure governed by modulation depth and rotation rate. Its magnitude is range-independent at leading order. At lags corresponding to zeros of the amplitude modulation (odd half-periods), the phase-driven component is isolated. Convergence holds under mild assumptions, with a factorial Bessel-tail truncation guideline and an error bound—controlled by the third spectral moment—quantifying phase-linearization effects. The resulting theory offers a compact physical and mathematical basis for diagnostics that exploit cyclic features.
Roger Boustany (Sun,) studied this question.