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.