Cubic Nonlinear Coupling Estimation using Hilbert Transform and Cyclic Statistics in Correlative Multiplicative Noise

H. Dou, S. Wang, and F. Wang (PRC)


Hilbert transform, multiplicative noise, fourth-order time-average moment spectrum, cubic nonlinear coupling


Based on Hilbert transform and cyclic statistics, a new approach is proposed for estimating cubic nonlinear coupling in real domain. First, we convert the real observations into their complex counterpart through Hilbert transform. Then we define a special fourth-order time-average moment spectrum of this complex process. It can be applied to obtain the coupled and coupling frequencies in the noise that multiplicative and additive noise of any mean are mutually independent, the multiplicative noises are correlative. In the meantime, this method needn't constrain the distribution and the color of noises. Simulation examples illustrate the algorithms.

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