Pre-digital computer 'cranks out' Fourier Transforms

Video A group of American engineers have rescued and returned to operation a Fourier-Transform-calculating machine designed in the 19th century.

The machinery is an impressive reminder not only of what could be achieved in the pre-digital era, but also of the genius of its designer Albert Michelson, a name less-known to the general public than contemporaries like Albert Einstein.

Michelson's best-remembered achievements are contributions to setting a value to the velocity of light, and in collaboration with Edward Morley, constructing the famous Michaelson-Morley experiment which both disproved the theory of the aether and helped lay down the basis of interferometry.

Interferometry depends on the ability to identify the individual frequency-domain components of a complex light signal, using the Fourier Transform – and this is painfully laborious to do by hand.

The Harmonic Analyser. Image: Hammack, Kranz & Carpenter

As noted in the ebook accompanying the videos notes, Michelson wrote, anyone constructing a large number of sine waves by hand “has felt the need of some simple and fairly accurate machine” as a time-saver.

Hence the Harmonic Analyser: a piece of machinery that combines springs, cone gears, cylinder gears, rocker bars, a hand crank and a pen to both combine sine waves into complex functions, and in the other direction, perform a Fourier analysis to work out the frequencies that make up a waveform.

As “Engineer guy” Bill Hammack explains in the video below (third in his series), the machine operation is surprisingly simple: the user sets the wave they want analysed in the rocker bars of the machine and turns the crank. The pen outputs the coefficients - in other words, the sine waves (fundamental and harmonic) that make up the input function, and their relative amplitude.

Youtube Video

The machine Hammack and his collaborators demonstrate in their video series and e-book is a 20-spring unit.

That limits it to analysing a waveform with 20 samples. However, as they note in the book, Michelson also constructed an 80-sample machine.

The machine they used is held by the University of Illinois' Department of Mathematics, and was built by William Gaertner & Company. While the authors can't be certain of the age of the machine, they believe it was manufactured between 1901 and 1909. ®