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Positive Window-Sample Constraint

For each window sample, $ h\left(n\right) \geq 0$ , or,

$\displaystyle -h\left(n\right) \leq 0.$ (4.66)

Stacking inequalities for all $ n$ ,

$\displaystyle \left[\begin{array}{ccccc} -1 & 0 & \cdots & 0 & 0\\ 0 & -1 & & & 0\\ \vdots & & \ddots & & \vdots \\ 0 & & & -1 & 0\\ 0 & 0 & \cdots & 0 & -1\end{array} \right]\left[\begin{array}{c} h\left(0\right)\\ h\left(1\right)\\ \vdots \\ h\left(L-1\right)\\ h\left(L\right)\end{array} \right] \le \left[\begin{array}{c} 0\\ 0\\ \vdots \\ 0\\ 0 \end{array} \right]$ (4.67)

or

$\displaystyle \zbox {-\mathbf{I}\, h \le 0.}$ (4.68)

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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