Fourier Series - Square Wave Series

by Nathan Hoffman

Submitted : Spring 2012

The frequencies in a square wave and their incorporation into technology can reduce the bandwidth required to make a color television and explains why musical instruments sound differently. This paper discusses the square wave and how it is used in technology such as the television. The Fourier series reduces the square wave into its frequency components so it can be solved. After acquiring the series for a square wave, the sums of sine functions are graphed. As each sine graph is added, a square wave can be distinguished. The frequency is the inverse of the period of a sine wave so as “n” approaches infinity in the series, the frequency becomes greater. This paper supports the claim that all frequencies are needed to form a square wave. To illustrate this idea, I started with n=1 in the series to give the first function then after graphing the it, I gradually increased the term n from 1 to 4 then to 10, then graphed the functions. As each term of the series is added, the shape of the square wave can be further distinguished.

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