(1) |

(2) |

Letting in the first part therefore gives

(3) |

Rewriting (2) using (3) gives

(4) |

Integrating the first part and using the integral

(5) |

(6) |

where is the Sinc Function. The peak (in units of ) is 1. The function is always positive, so there are no Negative sidelobes. The extrema are given by letting and solving

(7) |

(8) |

(9) |

(10) |

(11) |

(12) |

(13) |

**References**

Bartlett, M. S. ``Periodogram Analysis and Continuous Spectra.'' *Biometrika* **37**, 1-16, 1950.

© 1996-9

1999-05-26