Fourier...? An introduction

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The english translation is currently under construction. Additionally, there might be some potential for optimization necessary at some points.

After reading this article, you should have an overview of the Fourier-Transform and the algorithm of the Fast-Fourier-Transform. The main focus is that no assumptions are made, but that an understanding is built on the foundation of school physics/mathematics.

It is important for you to think about the content yourself and learn actively by using your intuition to understand the content. Because of this there will be small questions to think about, which look like this:

What is $\sin(0)$ ?

$\pi$

It is ok, if you can't answer some questions, but you should always try to fully understand the correct answer.

Notes

Additionally at times there will be some notes:

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These notes are mathmatical additions which could be helpful.

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These notes reference more in-depth material for further reading, but they are not essential for understanding the article.

Appendix

The contents in the appendix are also recommended. They are essential for understanding some of the article. Especially the parts about complex numbers and complex exponentials are very recommended.

1. Complex Numbers