# Lecture 4: The Fourier Spectrum

Schedule
::
Periodic Signals
::
Fourier Spectrum ::
Symmetry
::
Fundamental Frequency
::
Smoothness of the Function
::
Fourier
Series
::
Exponential Series
::
Spectra
::
Bandwidth
::
Energy
of Signals
::
Geometric Viewpoint

For a function having a compact trigonometric Fourier series, the set of amplitudes and the set of phases provide all the information necessary to represent the function. (This is interesting, if you think about it: a function which is defined at every point in a continuum can be represented with only a countable number of points.) A plot of the amplitudes vs. the is the

For a function having a compact trigonometric Fourier series, the set of amplitudes and the set of phases provide all the information necessary to represent the function. (This is interesting, if you think about it: a function which is defined at every point in a continuum can be represented with only a countable number of points.) A plot of the amplitudes vs. the is the

**amplitude spectrum**of the signal. A plot of the phase vs. is the**phase spectrum**of the signal.

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by the Contributing Authors.
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admin. (2006, May 23). Lecture 4: The Fourier Spectrum. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/4_2node2.html.
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