Rectangular (None) Windows

The rectangular window has a value of one over its time interval. Mathematically, it can be written as

w[n] = 1.0

for n = 0, 1, 2……N – 1,

where N is the length of the window. Applying a rectangular window is equivalent to not using any window. This is because the rectangular function just truncates the signal to within a finite time interval. The rectangular window has the highest amount of spectral leakage.

The rectangular window for N = 32 is shown in the following illustration.

The rectangular window is useful for analyzing transients that have a duration shorter than that of the window. It is also used in order tracking, where the effective sampling rate is proportional to the speed of the shaft in rotating machines. In this application, it detects the main mode of vibration of the machine and its harmonics.