and ripple magnitude 
, the main-lobe
width 
may be computed as follows [155]:
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Given the window length
and ripple magnitude
, the main-lobe
width
may be computed as follows [155]:
![\begin{eqnarray*}
x_0 &=& \cosh\left[\frac{\cosh^{-1}\left(\frac{1}{r}\right)}{M-1}\right]\\
\omega_c &=& 2\cos^{-1}\left(\frac{1}{x_0}\right)
\end{eqnarray*}](img550.png)
This is the smallest main-lobe width possible for the given window length and side-lobe spec.
