The sine window coefficients are given by the following formula
where N is the length of the filter and k = 0, 1, …, N – 1.
The sine window is a power of cosine window. The convolution of the sine window with itself produces the Bohman window.
Consider a finite impulse response (FIR) low pass filter of length N = 201. The following is the sine 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 sine window is as follows.
The magnitude response of the same filter is shown on the graph below.
Measures for the sine window
The following graph compares the discrete Fourier transform of the sine window with that of the rectangular window.
The sine window measures are as follows.