## Detection of Signals in NoiseThe Second Edition is an updated revision to the authors highly successful and widely used introduction to the principles and application of the statistical theory of signal detection. This book emphasizes those theories that have been found to be particularly useful in practice including principles applied to detection problems encountered in digital communications, radar, and sonar. Detection processing based upon the fast Fourier transform |

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### Contents

Random Processes | 39 |

Narrowband Signals | 69 |

Gaussian Derived Processes | 105 |

Hypothesis Testing | 151 |

O Detection of Known Signals | 202 |

Detection of Signals with Random | 247 |

O Multiple Pulse Detection of Signals | 287 |

j Detection of Signals in Colored | 339 |

Estimation of Signal Parameters | 383 |

Extensions | 449 |

483 | |

### Common terms and phrases

amplitude approximation assume autocorrelation function average Bayes Bayes estimator binary carrier phase characteristic function chi-squared density choose coefficients complex envelope compute consider constant correlation corresponding cos(wc cost criterion defined degrees of freedom density Eq density function detection detector Eq eigenvalues elementary outcomes example false alarm FIGURE Fourier transform frequency Gaussian density Gaussian noise Gaussian random Hilbert transform hypotheses impulse response independent input inverse likelihood function linear matched filter maximum likelihood estimate mean and variance modulated narrowband noncentral observation interval orthogonal power spectral density probability density probability of error pulse Px(x py(y quantity radar random variable Rayleigh Rayleigh fading received signal receiver Eq Receiver operating characteristics result ROC curve Rx(T Sect Show shown in Fig signal-to-noise ratio solution specified spectrum stationary statistic sufficient statistic Suppose threshold unbiased unknown parameters vector waveform yields zero zero-mean Gaussian