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Impulse response
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{{Short description|Output of a dynamic system when given a brief input}} [[File:Impulse.png|thumb|300px|right|The impulse response from a simple audio system. Showing, from top to bottom, the original impulse, the response after high frequency boosting, and the response after low frequency boosting.]] In [[signal processing]] and [[control theory]], the '''impulse response''', or '''impulse response function''' ('''IRF'''), of a [[dynamic system]] is its output when presented with a brief input signal, called an [[Dirac delta function|impulse]] ({{math|Ξ΄(''t'')}}). More generally, an impulse response is the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a [[Function (mathematics)|function]] of time (or possibly as a function of some other [[independent variable]] that parameterizes the dynamic behavior of the system). In all these cases, the dynamic system and its impulse response may be actual physical objects, or may be mathematical systems of equations describing such objects. Since the impulse function contains all frequencies (see [[Dirac delta function#Fourier transform|the Fourier transform of the Dirac delta function]], showing infinite frequency bandwidth that the Dirac delta function has), the impulse response defines the response of a [[linear time-invariant system]] for all frequencies.
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