Spectral inversion of second order Volterra models based on the blind identification of Wiener models

In this paper, we develop two main results. The first one is a theorem proving that a second order Wiener model can be blindly identified, i.e. using only the mean, the third and fourth order cumulants of the output data. The second result is the application of this theorem to spectral inversion (i.e. the recovering of the power spectrum density) of the input signal of a second order Volterra model to which usual inversion schemes cannot be applied, in particular when the linear kernel has a strong attenuation in frequency range. Numerical results are discussed with respect to the nonlinear energy amount of the output, the time series length and the SNR values.

► We present a method to blind identify a second order Wiener system from noisy data. ► A theorem using only third and fourth order cumulants for blind identification is proved. ► The kernels have minimum phase. Nonminimum phase can never be identified. ► The method is used to estimate the PSD of a second order Volterra model input signal. ► The Volterra kernels have not to verify the usual assumptions of inversion.