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.
|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|