## Abstract

Triple-correlation-based cancelers are derived for enhancing noisy signals. The filter impulse response is obtained by solving a set of linear equations involving second-order statistics of the available data. It is shown that the filter thus derived attempts to cancel the noise by essentially matching the cross-correlation between the reference signal and the unknown noise and that between the reference signal and the estimate of the noise. As an extension of this property a filter is derived that matches the triple cross-correlation between the reference signal and the unknown noise with the triple cross-correlation between the reference signal and the estimate of the noise. The impulse response of this filter is obtained by solving a set of linear equations involving third-order statistics of the observations. It is shown that if the noise and the reference signal are related by a linear time-invariant transformation then cancelers based on the true, second-order and higher-order statistics are equivalent and cancel the noise exactly. In other cases the second-order canceler cancels the noise in the mean-square sense. The triple-correlation-based noise canceler outperforms the classical design when the reference signal is corrupted by additive Gaussian noise of unknown covariance. Simulation results illustrating the performance of the second-order and higher-order canceler implemented in batch form are presented.

Original language | English (US) |
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Title of host publication | Workshop Higher Order Spectral Anal |

Editors | Anon |

Publisher | Publ by IEEE |

Pages | 212-216 |

Number of pages | 5 |

State | Published - Dec 1 1989 |

Event | Workshop on Higher-Order Spectral Analysis - Vail, CO, USA Duration: Jun 28 1989 → Jun 30 1989 |

### Other

Other | Workshop on Higher-Order Spectral Analysis |
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City | Vail, CO, USA |

Period | 6/28/89 → 6/30/89 |