The flat top window coefficients are given by the following formula
where N is the length of the filter and k = 0, 1, …, N – 1.
An example flat top window
Consider a finite impulse response (FIR) low pass filter of length N = 201. The following is the flat top 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 flat top window is as follows.
The magnitude response of the same filter is shown on the graph below.
Measures for the flat top window
The following graph shows the discrete Fourier transform of the flat top window against the transform of the rectangular window.
The following are selected measures for the flat top window.