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Impulse response
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<p>In <a href="/facts/Signal_processing/Npaja6zb">signal processing</a> and <a href="/facts/Control_theory/aIuERpn6">control theory</a>, the impulse response, or impulse response function (IRF), of a <a href="/facts/Dynamic_system/782gREl5">dynamic system</a> is its output when presented with a brief input signal, called an <a href="/facts/Dirac_delta_function/V8PjRP8T">impulse</a> (δ(<i>t</i>)). 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 <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> of time (or possibly as a function of some other <a href="/facts/Independent_variable/dINfzIF2">independent variable</a> that parameterizes the dynamic behavior of the system). </p><p>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. </p><p>Since the impulse function contains all frequencies (see <a href="/facts/Dirac_delta_function/V8PjRP8T">the Fourier transform of the Dirac delta function</a>, showing infinite frequency bandwidth that the Dirac delta function has), the impulse response defines the response of a <a href="/facts/Linear_time-invariant_system/kEmj0QDC">linear time-invariant system</a> for all frequencies. </p>