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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]:

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)

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

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