Detecting quadratic-type nonlinearities of random processes in the presence of additive noise

The problem of detecting nonlinear effects often arises in investigations of different physical, engineering and other systems. These can be, for example, nonlinear distortions in radio devices, coupling of waves in nonlinear media, or nonlinear mechanisms of their generation. A powerful tool for solving this problem is the use of cumulants or their associated Fourier transforms, known as polyspectra. However, the estimation of cumulants (or polyspectra) of real processes (especially for fairly long realizations) requires considerable computation resources, in particular, RAM. The present paper illustrates the potentials of the so called “1½D-spectra”, Γ(ω), for solving the problem of detecting weak quadratic-type nonlinearities of random processes in the presence of additive noise. This technique is a particular case of the bispectral analysis being, however, it is much easier to use