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Complete Response

The complete response of a linear system consists of the superposition of (1) its response to the input signal $ \underline{u}(n)$ and (2) its response to initial conditions $ {\underline{x}}(0)$ :

$\displaystyle \underline{y}(n) = \underline{y}_u(n) + \underline{y}_x(n),
$

where $ \underline{y}_u(n)$ was defined in Eq.$ \,$ (G.3) and $ \underline{y}_x(n)$ was defined in Eq.$ \,$ (G.4) above.


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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
CCRMA