The rectangular window of length N, defined for k = 0, 1, …, N – 1 is given by the formula

The window has no effect when applied to a filter or a signal. It is, however, a benchmark window, against which other windows are often compared. For example, a standard low pass filter with finite impulse response will have the shortest transition band with the rectangular window.

The following is a graph of the rectangular window (N = 100).

## Measures for the rectangular window

The following is a discrete Fourier transform of 500 points of the rectangular window.

The window measures are as follows.

Coherent gain | 1.0 |

Equivalent noise bandwidth | 1.0 |

Processing gain | 0.0 dB |

Scalloping loss | -3.92 dB |

Worst case processing loss | -3.92 dB |

Highest sidelobe level | -13.3 dB |

Sidelobe falloff | -6.0 dB / octave, -20 dB / decade |

Main lobe is -3 dB | 0.88 bins |

Main lobe is -6 dB | 1.20 bins |

Overlap correlation at 50% overlap | 0.500 bins |

Amplitude flatness at 50% overlap | 1.000 bins |

Overlap correlation at 75% overlap | 0.752 bins |

Amplitude flatness at 75% overlap | 1.000 bins |

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