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WDF State Space Interpretation

Digital filters can be expressed in state-space form as

$\displaystyle \underline{x}(n+1) = A\, \underline{x}(n) + B\, \underline{u}(n)
$

by simply enumerating all delay elements as state variables $ \underline{x}^T(n)
= [x_1(n), x_2(n),\ldots, x_N(n)]$ , and finding the state transition matrix $ A$ by inspection. Any inputs are collected in $ \underline{u}(n)$ and determine the $ B$ matrix.


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``Wave Digital Filters'', by Stefan Bilbao and Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2017-06-05 by Stefan Bilbao and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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