Chapter 22--Fourier Series: Fundamental Period, Frequency, and Angular Frequency

From Class Wiki
Revision as of 22:19, 5 January 2010 by Andrew.roth (talk | contribs)

Jump to: navigation, search

Under Construction

Please refrain from error checking until the 2 reviewers do their job. Thank you!

I can't figure out how to reference something. If someone knows how please let me know. Thanks!


Picture of a Sine Wave where f(x)=sin(x)

Long long ago, in a high school class called trigonometry, we leaned about periodic functions. A periodic function is a function that repeats itself over and over for infinity. The period of the function is the distance of one iteration that is infinitely repeating.

A signal f(t) is periodic if, for some T > 0 and all t,

f(t+T) = f(t)<ref>Textbook, 22.1</ref>

The picture to the right shows the plot of the standard sine function whose period is 2\pi. What the plot does not show is that the line keeps extending and repeating the bumps and valleys over the whole x axis, or (-\infty,\infty). But wait! Can't the period also be 4\pi or 6\pi? In fact it can. Because the graph of sin(x) repeats itself every 2\pi units, the period of the function is actually 2\pi n where n is any whole number from zero to \infty