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.
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.
|Equivalent noise bandwidth||1.50|
|Processing gain||-1.77 dB|
|Scalloping loss||-1.42 dB|
|Worst case processing loss||-3.19 dB|
|Highest sidelobe level||-31.5 dB|
|Sidelobe falloff||-20.7 dB / octave, -68.9 dB / decade|
|Main lobe is -3 dB||1.44 bins|
|Main lobe is -6 dB||2.00 bins|
|Overlap correlation at 50% overlap||0.165|
|Amplitude flatness at 50% overlap||1.000|
|Overlap correlation at 75% overlap||0.658|
|Amplitude flatness at 75% overlap||1.000|