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Embedded SystemsFPGAElectronics

Introduction to Digital Filters
    State Space Filters
       Complete Response

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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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Next: Transfer Function of a State Space Filter

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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