![]() The Laplace transform comes in two varieties: The transfer function generalizes the frequency response characterization of an LTI system’s input-output behavior and offers new insights into system characteristics. Hence, the output of an LT system is obtained by multiplying the Laplace transform of the input by the Laplace transform of the impulse response, which is defined as the transfer function of the system. ![]() As with complex sinusoids, one consequence of this property is that the convolution of time signals becomes multiplication of the associated Laplace transforms. For example, we shall see that continuous-time complex exponentials are eigenfunctions of LTI systems. Many of these properties parallel those of the Fourier Transform. ![]() The Laplace transform possesses a distinct set of properties for analyzing signals LTI systems.
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