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Issue 5.2


Experimenting with Fourier Series

A calculation-intensive graphics and benchmark application

Issue: 5.2 (January/February 2007)
Author: William H. Murray and Chris H. Pappas
Author Bio: Bill and Chris are department chairmen in Electrical Engineering Technology and Computer Studies, respectively, at Broome Community College in Binghamton, N.Y. Together they have written over 50 trade books on assembly language, Visual Basic, C, C++, C#, and more.
Article Description: No description available.
Article Length (in bytes): 10,077
Starting Page Number: 14
Article Number: 5208
Resource File(s):

Download Icon 5208.zip Updated: 2013-03-11 19:07:59

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Excerpt of article text...

Students embarking on a degree in electrical engineering or electrical engineering technology are sure to encounter the need to draw a sine wave sometime in their career. A professor once remarked in the 60's, that "the person that finds a way to draw a perfect sine wave will be famous."

Of course, when he made these remarks we were still in the earliest days of computers and we were a long way from Apple IIs and graphing calculators. With the advent of personal computers, the excitement of drawing a perfect sine wave has faded, but applications involving sine waves can, even now, be fascinating to study. Consider the work of Joseph Fourier.

Joseph Fourier was born in France in 1768. This was long before Nicola Tesla harnessed Niagara Falls and transmitted the first perfect sine waves over the earliest power grids. Fourier began experimenting with a mathematical series that today bears his name. Fundamentally, Fourier determined that any periodic waveform could be created by using the proper combinations of sine waves and their harmonics. By using calculus, equations can be derived for any such series. If you are interested in learning how to derive specific equations, electrical engineering and technology books, such as Advanced AC Electronics: Principles and Applications by J. Michael Jacob (published by Thompson, 2004; ISBN: 076682330-X) offer an excellent treatment of this subject.

For example, Jacob uses calculus to derive the Fourier series equation that will create a square wave when enough sine wave harmonics are added together. This equation is:

v(t) = A/2 + 2A/pi ((sin(wt) + (1/3) sin(3wt) + (1/5)sin (5wt) + (1/7)sin (7wt) ''''))

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