Drawn in by the Siren’s Song

When I say “siren” what do you think of? Ambulances? Air raids? Sigh. I was afraid you were going to say that. We’ve got work to do.

You see, the siren played an important role in physics and mathematics about 150 years ago. Through the first half of the 1900s, this fine apparatus was trivialized, used for its pure noise-making abilities. During the World Wars, the siren became associated with air raids and bomb shelters: a far cry from its romantic origins. In this article, we’re going to take the siren back for the Muses. I want you to see the siren in a new light: as a fundamental scientific experiment, a musical instrument, and in the end, as a great DIY project — this is Hackaday after all.

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Retrotechtacular: The Fourier Series

Here’s a really quick video which takes a different approach to understanding the Fourier Series than we’re used to. If you’re a regular reader we’re sure you’ve heard of the Fourier Series (often discussed as FFT or Fast Fourier Transform), but there’s a good chance you know little about it. The series allows you to break down complex signals (think audio waves) into combinations of simple sine or cosine equations which can be handled by a microcontroller.

We’ve had that base level of understanding for a long time. But when you start to dig deeper we find that it becomes a math exercise that isn’t all that intuitive. The video clip embedded after the break changes that. It starts off by showing a rotating vector. Mapping the tip of that vector horizontally will draw the waveform. The Fourier Series is then leveraged, adding spinning vectors for the harmonics to the tip of the last vector. The result of summing these harmonics produces the sine-based square wave approximation seen above.

That’s a mouthful, and we’re sure you’ll agree that the video demo is much easier to understand. But the three minute clip just scratches the surface. If you’re determined to master the Fourier Series give this mammoth Stanford lecture series on the topic a try.

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