Dolph-Chebyshev Window Main-Lobe Width

Given the window length $M$ and ripple magnitude $r$ , the main-lobe width $2\omega_c$ may be computed as follows [155]:

$$\begin{eqnarray*} x_0 &=& \cosh\left[\frac{\cosh^{-1}\left(\frac{1}{r}\right)}{M-1}\right]\\ \omega_c &=& 2\cos^{-1}\left(\frac{1}{x_0}\right) \end{eqnarray*}$$

This is the smallest main-lobe width possible for the given window length and side-lobe spec.