Estimation of cyclic polyspectra

The authors review the definitions of and relations between cyclic cumulants, cyclic moments, and cyclic polyspectra, and consider nonparametric estimation of both cyclic cumulants and cyclic polyspectra. It is shown that cyclic polyspectra can be estimated consistently by first measuring the cyclic cumulant, multiplying it by a tapering window, and then Fourier transforming it. Measurement of cyclic polyspectra directly in the frequency domain is shown to be relatively difficult due to the fact that infinite-strength spectral functions containing Dirac delta functions must be estimated and combined to obtain estimates of finite-strength spectral functions in which all Dirac deltas cancel each other. Examples are provided to illustrate the theory