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Derivative Systems and Integrators

18 March, 2015 - 16:28

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 y(t)=\frac{d}{dt}x(t). 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

y(t)=\int_{-\infty }^{t}x(\alpha)d\alpha