Fourier Analysis With A 100-year-old Mechanical Computer

‘Engineer Guy’ Bill Hammack is the professor you wish you had. He’s a member of the faculty at the University of Illinois and the creator of a series of videos that explain technology.

This set of videos take a look at Albert Michelson’s Harmonic Analyzer – a nineteenth century mechanical computer that performed Fourier analysis by using gears, springs and levers to calculate with sines and cosines—an astonishing feat in an age before electronic computers.

Fourier analysis is the study of how complex functions can be broken down into simple ones. In the area of sound and synthesis, Fourier analysis can be used to break down any periodic sound into component sine (and cosine) waves. And, going in the opposite direction, sine waves can be combined to create complex sounds.

This is now done with computers, but 100 years ago, it was done with machines. 

In the first video, above, Hammack introduces the Harmonic Analyzer. In the second video, he looks at how the machine can be used to synthesize complex waves:

in the third video, Hammack looks at using the machine to do analysis:

The last video dives into the technical details of how the Harmonic Analyzer is configured:

As noted in the videos, Hammack has published a book that explores the Harmonic Analyzer. It’s available at Amazon and it’s also available as a free PDF download.

8 thoughts on “Fourier Analysis With A 100-year-old Mechanical Computer

  1. That’s genius. I remember doing my O-Level Physics project on waveform creation by commendeering all the sine wave generators in the lab to create sawtooth, triangle and square waves using overtones. This is like a steampunk version.

  2. Yes but seeing Math (of which I’m very bad at) at such a visual and mechanical level, makes it so much easier to comprehend whats going on.

  3. This made my day, great break from news about the latest and greatest in gadgetry. Did anyone else wish they could sample the sound when he bumps the springs in the first video?

  4. Just watch, Deadmou5 is going to have several of these built so he can use them to generate new OSC shapes for Xfer Serum.

    … seriously though, this is an incredibly cool machine. Stuff like this reminds us all how whiny we are that our current super cool space-tech can’t get the right sound we want (because we have yet to put in enough effort!).

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