The Blackman window is a weighted function that tapers off at both ends, resulting in a smoother transition between segments and reducing the effect of sharp discontinuities
It is named after James W. Blackman, who developed the technique.
The Blackman window is defined as:
$
w(n) =
\begin{cases}
0.42 - 0.5\cos\left(\frac{2\pi n}{M}\right) + 0.08 \cos\left(\frac{4\pi n}{M}\right)& 0 \leq n \lt M \\
0 & \text{otherwise}
\end{cases}
$
![[Window_function_and_its_Fourier_transform_–_Blackman_(n_=_0...N).svg]]
[Wikimedia](https://en.wikipedia.org/wiki/File:Window_function_and_its_Fourier_transform_–_Blackman_(n_%3D_0...N).svg)