The Hann window coefficients are given by the following formula
where N is the length of the filter and k = 0, 1, …, N – 1.
The Hann window belongs to the family of Hamming windows. The derivation of the Hann window is shown in the topic Hamming window. The Hann window is also a poiwer of cosine window (α = 2). When the Hann window is multiplied by the Poisson window, the result is the Hann-Poisson window.
An example Hann window
Consider a finite impulse response (FIR) low pass filter of length N = 201. The following is the Hann 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 Hann window is as follows.
The magnitude response of the same filter is shown on the graph below.
Measures for the Hann window
The following is a comparison of the discrete Fourier transform of the Hann window and the rectangular window.
The Hann window measures are as follows.