Decay Response, Initial Conditions Response

If a filter is in steady state and we switch off the input signal, we see its decay response. This response is identical (but for a time shift) to the filter's response to initial conditions. In other words, when the input signal is switched off (becomes zero), the future output signal is computed entirely from the filter's internal state, because the input signal remains zero.

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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.