By viewing discrete-time amplitude-modulated signals and processes with missing observations as cyclostationary signals, nonparametric, mean-square sense consistent, and asymptotically normal single record estimators are developed for their kth-order cumulants and polyspectra, along with the asymptotic covariances. The proposed estimation schemes use cyclic cumulants and polyspectra, and are theoretically insensitive to any additive stationary noise. In addition, schemes of order k 3 convey complete phase information and are insensitive to additive cyclostationary Gaussian noise of unknown co-variance. The conventional approaches cannot recover mixed-phase linear processes, are susceptible to additive noise, and are a special case of the proposed schemes. Simulations demonstrate superior performance of the proposed algorithms.
- Nonstationary spectral estimation
- amplitude-modulated cyclostationary time series
- asymptotic distribution and variance
- cyclic moment and cumulant estimation
- higher order statistics
- missing observations
- nonparametric cyclic-polyspectrum estimation