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Response from Initial Conditions

The response of a state-space model to initial conditions, i.e., its initial state $ {\underline{x}}(0)$ is given by, again using Eq.$ \,$ (G.1),

$\displaystyle \underline{y}_x(n) = C A^{n-1}{\underline{x}}(0), \quad n=0,1,2,\ldots\,. \protect$ (G.4)


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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