The Bohman window coefficients are given by the following formula
where N is the length of the filter, M = (N – 1) / 2, and k = 0, 1, …, N – 1.
The Bohman window is the convolution of the sine window with itself.
An example Bohman window
Take a finite impulse response (FIR) low pass filter of length N = 201. The following is the Bohman window.
Given a sampling frequency of 2000 Hz and a filter cutoff frequency of 40 Hz, the impulse response of the filter with a rectangular window (with no window) and with the Bohman window is as follows.
The magnitude response of the same filter is shown on the graph below.
Measures for the Bohman window
The following is a plot of the discrete Fourier transform of the Bohman window against the discrete Fourier transform of the rectangular window.
The measures of the Bohman window are as follows.