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Monotonicity Constraint

We can constrain the positive-time part of the window to be monotonically decreasing:

$\displaystyle \Delta h_{i}=h\left(i+1\right)-h\left(i\right)\leq 0\qquad i=1,\ldots ,L-1$ (4.77)

In matrix form,
$\displaystyle \left[\begin{array}{ccccc} -1 & 1 & & & 0\\ & -1 & 1 & & \\ & & \ddots & \ddots & \\ 0 & & & -1 & 1\end{array}\right]h$ $\displaystyle \le$ $\displaystyle 0,$  

or,

$\displaystyle \zbox {\mathbf{D}\,h \le 0.}$ (4.78)

See Fig.3.38.

Figure 3.38: Monotonic Chebyshev Window
\includegraphics[width=\twidth,height=6.5in]{eps/print_monotonic_chebwin}

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