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The Fourier Series — Part 1

A Fundamental and odd harmonics from 3 to 101

A Fundamental and odd harmonics from 3 to 101

Tonight’s post is about adding multiple sine waves to create another waveform. Each of the sine waves is an positive integer (whole number) multiple of the frequency of the base sine wave. These additional frequencies are called harmonics of the the base frequency.   The base frequency is called the fundamental frequency.,

The number of the harmonics may just be a few or it may be an infinite number of harmonics to produce a particular waveform.

The waveform in the first picture is approaching an ideal square wave.   The key word there is “approaching”   Obviously, it leaves a little bit to be desired because there is quite a bit of oscillation just before and just after the waveform does the swing from positive to negative and from negative to positive.   This wave was created using the odd harmonics from the 3rd to the 101st.   To make it better would require more harmonics and to make it ideal would require an infinite number.squarewave1-3   Obviously, I don’t have the computer power nor the time to calculate to infinity.    The picture to the right shows just the fundamental frequency and the third harmonic.

In the video I created, I promised to provide some links to some previous posts and videos about the graphing software and the programming software I used to create the data file.

squarewave1to13

The fundamental and odd harmonics through no. 13

The programming posts are based around my early attempts to do podcasts, but the post itself includes some very useful links.  The posts on the programming language, Python, can be found at:  Episode 44: Programming to learn logical thinking and Episode 45: More about programming and Python.

The posts about the graphing software, Veusz can be found at:  How I create all these graphs…. part 1 of 3; How I create all these graphs…. part 2 of 3;  and How I create all these graphs…. part 3 of 3.  Each of these last three posts has an embedded video, but there is additional links and information within the posts so I will only link the posts.

Should you desire the Veusz file and/or the Python file I used to create the data file, please e-mail me and I will send those to you.   Things are going to get interesting very soon.   🙂   The Video I created for this post is embedded below.

Gary

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“The Fourier Series — Part 1” by Create-and-Make.com is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.

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