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LP Formulation of Chebyshev Window Design

What we want:

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

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

  3. Transform to be 1 at DC.

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

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

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

  5. And $ \delta $ to be small.


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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2014-06-03 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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