LP Formulation of Chebyshev Window Design

What we want:

1. Symmetric zero-phase window.
2. Window samples to be positive.

   $$w\left(n\right)\geq 0\qquad \mathrm{for}\quad -\frac{M-1}{2}\leq n\leq \frac{M-1}{2}=L$$ (4.61)

   
   

3. Transform to be 1 at DC.

   $$W\left(0\right)=1$$ (4.62)

   
   

4. Transform to be within $\left[-\delta ,\delta \right]$ in the stop-band.

   $$-\delta \leq W\left(\omega \right)\leq \delta \qquad \mathrm{for}\quad \omega _{sb}\leq \omega \leq \pi$$ (4.63)

   
   

5. And $\delta$ to be small.