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Lecture 4: The Fourier Spectrum

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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 $f(t)$ having a compact trigonometric Fourier series, the set of amplitudes $\{C_n\}$ and the set of phases $\{ \theta_n\}$ 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 $\{C_n\}$ vs. the $\omega$ is the amplitude spectrum of the signal. A plot of the phase $\{ \theta_n\}$ vs. $\omega$ is the phase spectrum of the signal.

\begin{example}Show the magnitude and phase spectrum of the square wave from
the...
...rms are zero, so all
the information is conveyed in the $\{a_n\}$.
\end{example}


\begin{example}
\par
Find the Fourier series of the following signal, and plot i...
...splaymath}The magnitude and phase spectrum are:
\vspace*{3in}
\par
\end{example}

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . 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. This work is licensed under a Creative Commons License Creative Commons License