Linear Programming (LP)

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Index: Spectral Audio Signal Processing

Spectral Audio Signal Processing

Optimal Window Design by linprog

LP Formulation of Chebyshev Window Design

Containing both code and data, libraries provide extended functionality to a programming environment. — Click for http://en.wikipedia.org/wiki/Library_(computer_science)

'GNU's Not Unix' (GNU) is the collection of free, open-source software that started the free, open-source software movement. Started by Richard Stallman as a collection of the main system tools in UNIX written in C, it has grown to become a primary component of Unix-compatible operating systems such as the Linux distributions. — Click for http://www.gnu.org/

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A filter in the audio signal processing context is any operation that accepts a signal as an input and produces a signal as an output. Most practical audio filters are linear and time invariant, in which case they can be characterized by their impulse response or their frequency response. — Click for https://ccrma.stanford.edu/~jos/filters/What_Filter.html

Linear programming refers to a class of computational optimization procedures. — Click for http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html

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Index: Spectral Audio Signal Processing

Spectral Audio Signal Processing

Optimal Window Design by linprog

LP Formulation of Chebyshev Window Design

Linear Programming (LP)

If we can get our filter or window design problems in the form

$\begin{displaymath}\begin{array}[t]{ll} \mathrm{minimize} & f^{T}x\\ \mathrm{subject}\, \mathrm{to} & \begin{array}[t]{l} \mathbf{A}_{eq}x=b_{eq}\\ \mathbf{A}x\le b\end{array}, \end{array}\end{displaymath}$

(4.60)

where $x,f\in\mathbb{R}^N$ , $b\in\mathbb{R}^M$ , is $M\times N$ , etc., then we are done.

The linprog function in Matlab Optimization Toolbox solves LP problems. In Octave, one can use glpk instead (from the GNU GLPK library).

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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

Linear Programming (LP)

``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

``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