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# Lecture 5: Some Useful Functions

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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

The unit gate or unit pulse is defined by

Some interesting variations: Plot , , . Note that the total width is and the function is centered around . The unit triangle function, also known as the hat function (or the chapeau function), is defined by

Plot. Also look at . Notice that the total width of the function is . The sinc function we have already met in the context of the F.S. of a square wave. To reiterate,

Observe the following:
1. is even.
2. is zero for .
3. decays as .
The signum function is defined by
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 26). Lecture 5: Some Useful Functions. 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_3node3.html. This work is licensed under a Creative Commons License