Retrieval of Self-Coupled Harmonics

Presence of coupled harmonics in the data is a symptom attributed to nonlinear mechanisms generating the available time series. Self-coupling amounts to presence of frequency pairs (ω0, kω0) and perhaps phase pairs (ϕ0. kϕ0) as well, with k an integer. It appears in periodic signals, or, when harmonics undergo nonlinear transformations. Self-coupled harmonics observed in additive noise are retrieved from the peaks of diagonal (scaled) polyperiodogram slices, which contrary to existing higher order approaches, do not increase dimensionality and thus computations when dealing with nonlinearities of increasing orders. Performance evaluation of the resulting frequency estimator reveals decreasing variance with slices of polyperiodograms of increasing order, and ability to suppress stationary mixing noise irrespective of its color and distribution. Detection and estimation of self-phase coupling via polyperiodogram slices obviates limitations of existing methods that require availability of multiple independent records. Theory and algorithms are illustrated with simulated and voiced speech data.