Quantifying modulation in the acoustic field of a small-scale rotor using bispectral analysisg

This paper describes a methodology to quantify inter-frequency modulation in the acoustic field of a small-scale rotor. How the blade passing frequency modulates the intensity of the higher-frequency (broadband) noise content is of specific interest, as this modulation is a major factor in the human perception of rotor noise from advanced air mobility vehicles and drones. A proposed modulation-parameter is based on post-processing steps that are applicable to a single acoustic time series. First, an auto-bispectral analysis assesses the dominant nonlinear, quadratic inter-frequency coupling between the blade passing frequency and the higher-frequency noise content. Secondly, the degree of modulation is determined using a robust parameter: a correlation parameter between the (low-frequency) modulating BPF signal and an envelope of the (higher-frequency) carrier signal. Provided that a single parameter is obtained for a given acoustic time series, the directivity pattern of the modulation strength can be inferred from data available from standard acoustic measurement campaigns. For illustration, an 11 inch diameter single-rotor in hover is considered, with acoustic data taken at 420 microphone positions within a plane perpendicular to the rotor disk. It is revealed that modulation is confined to a sector $\theta \approx (10^\circ,-45^\circ)$, where $\theta = 0^\circ$ is the rotor plane and negative angles are in the direction of the rotor-induced flow. The strongest modulation appears around $\theta \approx -15^\circ$. This work aids in quantifying the phenomenological description of modulation, namely that it results from the periodic advance and retreat of certain rotor blade's noise sources, relative to a stationary observer.