Time-varying higher-order cumulant spectra: application to the analysis of composite FM signals in multiplicative and additive noise

Time-varying higher-order spectra (TV-HOS), have recently been proposed for (poly)spectral analysis of non-stationary signals. Two new results are presented here. First, the cumulant TV-HOS (in particular, cumulant Wigner-Ville trispectrum (WVT)), is shown to preserve the essential properties of cumulant higher-order spectra (e.g. eliminate Gaussian additive noise) and at the same time characterise time-variations of the signal´s frequency content. Second, when dealing with composite FM signals, a special kind of “non-oscillating cross-terms” is shown to appear in the moment TV-HOS time-frequency subspace. We show that these cross-terms cannot be eliminated by smoothing the WVT, but rather by an appropriate projection from the full time-multi-frequency space to a time-frequency subspace