Hann or Hanning or Raised Cosine

The Hann window is defined by the settings
$\alpha=1/2$ and $\beta=1/4$ :

$$\zbox{w_H(n)=w_R(n) \left[ \frac{1}{2} + \frac{1}{2} \cos( \Omega_M n) \right] = w_R(n) \cos^2\left(\frac{\Omega_M}{2} n\right)}$$

Hann window properties:

• Main lobe is $4\Omega_M$ wide
• First side lobe is at $-31$ dB
• Side-lobes roll off at $\approx 18$ dB / octave

Compare to the Rectangular window:

• Main lobe is $2\Omega_M$ wide
• First side lobe at $-13$ dB
• Side-lobes roll off at $\approx 6$ dB / octave