Complete Response

In general, the so-called complete response of a linear, time-invariant filter is given by the superposition of its

• zero-state response and
• initial-condition response.

``Zero-state response'' simply means the response of the filter to an input signal when the initial state of the filter (all its memory cells) are zeroed to begin with. The initial-condition response is of course the response of the filter to its own initial state, with the input signal being zero. This clean superposition of the zero-state and initial-condition responses only holds in general for linear filters. In §G.3, this superposition will be considered for state-space filter representations.

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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.