Abstract
This work proposes a new estimator for higher-order spectra. Higher-order spectra determine periodical properties of data by cross-frequency correlation. They are defined as the decomposition of central moments and cumulants over frequency and form a powerful tool to assess nonlinear, non-Gaussian or non-stationary systems and processes. The estimation theory of higher-order spectra has emerged from the research on power spectral density estimation. The estimator proposed here complements the existing estimators with a generalized theory of frequency-domain smoothing. It represents the domain-reversed counterpart of the popular method of averaging raw spectra from short-time Fourier transforms. The main selling points are the consistent approach to smoothing with a better bias-variance trade-off, its computational efficiency by averaging in the time domain and its flexibility and simplicity. These properties, the mathematical derivation and the analogy to averaging of raw spectra are presented. Numerical studies outline basic properties of the estimator.
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