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The purpose of this article is to show you step-by-step examples of how to use the Fourier transform algorithm to multiply two numbers. The primary advantage of using fourier transforms to multiply numbers is that you can use the asymptotically much faster 'Fast Fourier Transform algorithm', to achieve better performance than one would get with the classical grade school multiplication algorithm. This article is actually just a more specific illustration of the ideas shown in overlap add and overlap save , which contains even more details than are provided here. Therefore, if you find that details are missing in this article, they are likely to be found in the previous one.