# Difference between revisions of "Chapter 22--Fourier Series: Fundamental Period, Frequency, and Angular Frequency"

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==Period, Frequency, and Angular Frequency== |
==Period, Frequency, and Angular Frequency== |
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− | [[Image:Sinewave.png| |
+ | [[Image:Sinewave.png|450px|thumb|right|Picture of a Sine Wave where f(x)=sin(x)<ref>http://en.wikipedia.org/wiki/File:Sine.svg</ref>]] |

===Period=== |
===Period=== |
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<center>A signal <math>f(t)</math> is periodic if, for some <math>T > 0</math> and all ''t'',</center> |
<center>A signal <math>f(t)</math> is periodic if, for some <math>T > 0</math> and all ''t'',</center> |
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− | <center><math>f(t+T) = f(t)</math><ref> |
+ | <center><math>f(t+T) = f(t)</math><ref>DeCarlo/Lin, Linear Circuit Analysis--Time Domain, Phasor, and Laplace Transform Approaches, Second Edition. Figure 22.1</ref></center> |

Where T is the period |
Where T is the period |
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The '''fundamental angular frequency''' is defined as <math>\omega_0 = 2\pi f_0 = \frac{2\pi}{T_0}</math>. |
The '''fundamental angular frequency''' is defined as <math>\omega_0 = 2\pi f_0 = \frac{2\pi}{T_0}</math>. |
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==Author== |
==Author== |
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==Reviewers== |
==Reviewers== |
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+ | Brandon Vazquez |
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+ | Ben Blackley |
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==Readers== |
==Readers== |
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+ | Thomas Wooley |
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+ | Jaymin Joseph |
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+ | John Hawkins |

## Latest revision as of 03:30, 20 January 2010

22 lines (currently)

1 reference

1 figure

123 points

## Contents

## Period, Frequency, and Angular Frequency

### Period

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.

*t*,

Where T is the period

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

### Frequency and Angular Frequency

The **Frequency** is the number of periods per second and is defined mathematically as

The standard unit of measurement for frequency is Hz (Hertz). 1 Hz = 1 cycle/second

The **Angular Frequency** is defined as

The standard unit of measurement for angular frequency is in radians/second.

### Fundamental Period, Frequency, and Angular Frequency

The **fundamental period** is the smallest positive real number for which the periodic equation holds true.

The **fundamental frequency** is defined as .

The **fundamental angular frequency** is defined as .

## References

<references />

## Author

Andrew Roth

## Reviewers

Brandon Vazquez

Ben Blackley

## Readers

Thomas Wooley

Jaymin Joseph

John Hawkins