Response from Initial Conditions Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search


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. (E.1),

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


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work] [Order a printed hardcopy]

``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (August 2006 Edition).
Copyright © 2007-02-02 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA  [Automatic-links disclaimer]