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Assessing bispectrum estimator performance for deterministic real-valued signals observed in additive Gaussian noise and random signal shifts environment

Jaakko Astola, Karen Egiazarian, Vladimir V. Lukin, Alexander V. Totsky and Alexander A. Zelensky.

Three conventional methods intended on improving the bispectrum estimator performance are investigated and compared for the case of a real-valued time deterministic signal for finite-length data records, limited sample size of statistics, additive white Gaussian noise and random signal shifts. The performance of bispectrum estimators is studied by numerical simulation. The accuracy of the bispectrum estimates is investigated for different signal waveforms and lengths as well as for different variances of additive white Gaussian noise. The analysis is performed for the signals with zero and non-zero DC components and using windowing of input sequence. It is shown that due to noise and spectral leakage, inherent in discrete Fourier transform, the bispectrum estimates have relatively high variances for typical situations encountered in practice. Time-domain windowing results only in a slight decrease of the errors in bispectrum estimates.
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