17.8 LAPLACE IMPULSE FUNCTIONS

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The convolution integral can be difficult to deal with because of the time shift. But, the Laplace transform for the convolution integral turns it into a simple multiplication.

Figure 17.34 The convolution integral in the Laplace s-domain

- the inverse Laplace transform provides the impulse response function.

- consider the example of a system. Note that the transfer function is the same as the output response for a unit impulse input.

- this is the most useful when trying to find the response to an arbitrary input.