Rectangular window

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

Rectangular window 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).

Rectangular window

Measures for the rectangular window

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

Discrete Fourier transform 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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