Detection of quadratic interaction in signals using the Wigner bispectrum

It is demonstrated that, under certain conditions which may be quite restrictive, the Wigner bispectrum, based on cumulants, may be used to detect quadratic phase couplings in signals generated from a class of time-varying nonlinear systems. It is shown that for the class of systems considered, the Wigner bispectrum yields a shifted bispectrum. Such an analysis would prove useful for analyzing such nonstationary signals.<<ETX>>

[1]  I. Sandberg.  Volterra expansions for time-varying nonlinear systems , 1982, The Bell System Technical Journal.

[2]  E. J. Powers,et al.  Estimation of quadratically nonlinear systems with an i.i.d. input , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[3]  M. Schetzen.  The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[4]  N. L. Gerr.  Introducing a third-order Wigner distribution , 1988, Proc. IEEE.

[5]  C. L. Nikias,et al.  Transient signal detection using the Wigner bispectrum , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[6]  W. Rugh.  Nonlinear System Theory: The Volterra / Wiener Approach , 1981 .

[7]  Vito Volterra,et al.  Theory of Functionals and of Integral and Integro-Differential Equations , 2005 .

[8]  R. Flake.  Volterra series representation of time-varying non-linear systems , 1963 .

[9]  M. Fréchet.  Sur les fonctionnelles continues , 1910 .

[10]  Chrysostomos L. Nikias,et al.  Wigner polyspectra: higher-order spectra in time varying signal processing , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[11]  I. Sandberg.  On Volterra expansions for time-varying nonlinear systems , 1983 .