Derivative Systems and Integrators

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Systems that perform calculus-like operations on their inputs can produce waveforms signifcantly different than present in the input. Derivative systems operate in a straightforward way: A first-derivative system would have the input-output relationship . Integral systems have the complication that the integral's limits must be defined. It is a signal theory convention that the elementary integral operation have a lower limit of −∞, and that the value of all signals at t = −∞ equals zero. A simple integrator would have input-output relation