### Abstract

A single-threshold detector is derived for a wide class of classical binary decision problems involving the likelihood-ratio detection of a signal embedded in noise. The class of problems considered encompasses the case of multiple independent (but not necessarily identically distributed) observations of a nonnegative (or nonpositive) signal embedded in additive and independent noise, where the range of the signal and noise is continuous. It is shown that a comparison of the sum of the observations with a unique threshold comprises an optimum detector if a weak condition on the noise is satisfied independent of the signal. Examples of noise densities that satisfy and that violate this condition are presented. A sufficient condition on the likelihood ratio which implies that the sum of the observations is also a sufficient statistic is considered.

Original language | English (US) |
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Pages (from-to) | 213-218 |

Number of pages | 6 |

Journal | IEEE Transactions on Information Theory |

Volume | 25 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1979 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Science Applications
- Library and Information Sciences