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  Duhamel's integral

y(t): system's response
x(t): signal input
h(
t-t): weighting term for time dependent response


(1)

Duhamel's convolution integral describes the dependence of a system's output signal from its input with respect to the input signal's amplitude and its time course. As described in eqn. (1) the reaction of the transfer element is corresponding to the sum of the previous input signals during infinitesimally short periods multiplied with a weighting term that is specific for the transfer system. The weighting term gives for each point of time the strength, with wich the respective input signal influences the system's output.

 

 


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