# Window Function

**Posted:**May 3, 2009

**Filed under:**dsp, signal processing, window |

**Tags:**blackman, dsp, fswind, hamming, signal processing, window Leave a comment

Window function an important term in signal processing. It also called apodization or tapering function. It is useful for various operations, like separtion of band frequences etc.

Several different windows are available. Only two are worth using, the Blackman window and the Hamming window.

Blackman window are defined as,

**w(n)= a0 – a1*cos((2*pi*n)/(N-1)) + a2*cos((4*pi*n)/(N-1)); **

where, **0<=n<=N .**

and

**a0=(1-@)/2, a1=1/2, a2=@/2.** in blackman window **@** equal to 0.16

Now , in case of Hamming windows coefficient are computed from following equation,

**w(n)=0.54 – 0.46cos((2*pi*n)/N);** where, **0<=n<=N**.

Now for sample 74-point Blackman window’s time and frequency domain representation are given below,

For the same point Hamming window’s time and frequency domain is

In this case of blackman window Leakage factor is 0%, sidelobe attenuation -58.1dB and mainlobe width is (-3dB) : 0.0449.

for hamming, Leakage factor is 0.04%, sidelobe attenuation -42.5 dB and mainlobe width is (-3dB) : 0.0351.

After convolution this two windows we will get time and frequency domain like this,

Leakage factor is 0%, sidelobe attenuation -72.2dB and mainlobe width is (-3dB) : 0.0273.

so this result is more better than before. I called it FSwind đź™‚