Complementary envelope estimation for frequency-modulated random signals

The Hilbert envelope is a well-known indicator for amplitude modulation in subband time series. However, frequency modulation estimators typically impose temporal smoothness constraints that limit their general use for stochastic signals. We introduce the complementary envelope as a direct indicator of stochastic phase coherence and frequency modulation. Rooted in the second-order statistics of randomly-phased sinusoids, the complementary envelope is distinct from the Hilbert envelope, and can be estimated easily and separately. We propose a new complementary envelope estimator based on modified multitaper spectral analysis, and use it to reveal previously unseen FM-like behavior in ship propeller noise.