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**Topic under **Control Mode

**Source:** www-control.eng.cam.ac.uk

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Tue Mar 13, 2018 01:06:59 PM

__Short Desciption__:

Impulse responses, step responses and transfer functions.Summary
The
impulse response,
step response and
transfer function
of a Linear, Time Invariant and causal (LTI) system each completely characterize the inputoutput properties of that system.
Given the input to an LTI system, the output can be deterermined:
In the time domain: as the convolution of the impulse response and the input.
In the Laplace domain: as the multiplication of the transfer function and the Laplace transform of the input.
They are related as follows:
The step response is the integral of the impulse response.
The transfer function is the Laplace transform of the impulse response.

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