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# Lecture 5: System Response Using Fourier Transforms

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Schedule :: Fourier Series Formulas :: Nonperiodic Functions :: Useful Functions :: Simple Functions :: Fourier Transforms :: Properties :: System Analysis :: Signal Distortion :: Filters :: Parseval's Formulas

Let be the input to an LTIC system with transfer function and output . The response to the everlasting signal is . Thus . Now let the input be

By the definition of the FT, this is . By linearity, the output is

That is,

so we can say

In a sense, this is the whole point of Fourier analysis!
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 26). Lecture 5: System Response Using Fourier Transforms. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/5_5node5.html. This work is licensed under a Creative Commons License