# Lecture 5: Some Useful Functions

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

Some interesting variations: Plot , , . Note that the

Plot. Also look at . Notice that the

Observe the following:

**The unit gate**or**unit pulse**is defined bySome 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 byPlot. 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:

- is even.
- is zero for .
- decays as .

**The signum function**is defined by
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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.
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