# Pre-digital computer 'cranks out' Fourier Transforms

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 …

1. #### Limited to 20 samples

But they are analogue samples and so much purer

A real mathematician can hear the subtle details compared to this modern digital computer stuff

1. #### Re: Limited to 20 samples

Nice! I believe oxygen-free metals were used in the construction too! Calculation purity!

2. #### be careful about calling it Non- or Pre-Digital

Without a serious analysis of the mechanism, I will not commit to "Non-Digital". Since I see gears, it may work by counting gear teeth, which would qualify it as digital.

I will immediately accept mechanical, rather than electronic or electromechanical.

Calling it Analog, rather than Digital, would require use of continuous (such as differential pulleys, or turntables), rather than quantized (discrete gear teeth) mechanisms.

1. #### Re: be careful about calling it Non- or Pre-Digital

Bit early in the week to be pedantic, but have a pint on me.

2. #### Re: be careful about calling it Non- or Pre-Digital

A properly designed gear tooth will transfer torque continually

AFAIK this doesn't count teeth but uses gear cones as a variable transmission

3. #### Re: be careful about calling it Non- or Pre-Digital

There's always reading the PDF, it's free after all. The conic and cylindrical gear sets keep time for the sampling ratios. The amplitudes are determined by the position of bars placed along a set of rockers that are driven by the cylindrical gears. It's actually quite short and definitely worth the read. It was a rather long download but I don't know which end was the cause for the lack of speed.

4. #### Re: be careful about calling it Non- or Pre-Digital

Well the number of gears doesn't matter. It doesn't count steps you could also build it with rubber wheels. That part of the machine is only there to create gears running at n*x steps of speed.

5. #### Re: be careful about calling it Non- or Pre-Digital

Gear ratios are only used as frequency multipliers and output amplifiers. As far as I can tell, the actual mechanism that turns the crank rotation into cosines or Fourier series coefficients is analogue.

3. #### Also note

http://www.britannica.com/EBchecked/topic/22416/analog-computer#ref255067

4. #### Those often work by disk integrators

Not sure if this one in particular does, but the ones I've seen work by disk integrators. Essentially to do a Fourier analysis you need to calculate the integral of (x*sin(w*t)) with w being the frequency and t the time.

This can be done by disk (or sphere) integrators. They work like this:

You have a disk (let's assume it's horizontal) which can turn, for example it can follow your input signal. If you input signal goes up, it'll turn in one direction, if it goes down, it'll turn into the other direction, if it remains the same, the disk will stop.

On top of that disk, there's another, smaller disk mounted on an axle which can move to the left and right. The small disk pushes against the larger one in a way so the small disk turns with it.

Imagine the big disk revolves in one direction at one speed. If you move the small disk from left to right on it's axle, it'll turn in one direction on the left side, then gradually get slower as it approaches the center of the big disk where it will stop, before going on turning into the other direction at increasing speed. If you are a mechanic you can calculate that the speed of the small disk is proportional to the speed of the large disk multiplied by its position.

Do that twice for every frequency, once for the real part, once for the imaginary one, and you'll have a nice fourier analysis.

5. #### It's actually not normal Fourier transforms...

but discrete Fourier transforms, therefore that machine can work without integrators. Essentially what it does is to sum sinusoids. Must have been a nice tool for certain tasks.

6. #### MIT Radiation Labs WW2 harmonic analyzer used levers...

MIT Rad Lab vol.27 'Computing Mecanisms and Linkages' by Antonin Svodoba constructed costal tide harmonic analyzers using multiple pantographic arms and linkages to make 2 dimensional tide charts for an entire coastline by having each data point be a pantograph arm of a size equal to the shape of the point on the coastline where a table reading is needed (whew, couldn't simpifly this).

At least the entire WW2 Pacific Theater needed tide tables to do any troop landings... the US Coast and Geodesic Service did maps and Hydro readings (tide tables)...location and eq. facilities are still not public record...RS.

7. #### Spectrum analysis

Forgive my ignorance - but this topic raises the possibility of an answer to a question in this learned forum.

If you analyse the spectrum of a complex sound. Can you remove the in-band frequency components which are merely the heterodyne result of frequency mixing?

There is a famous Spanish song which is performed by a group of men. If they get their pitch and synchronisation exactly right then the listener also hears a phantom woman's voice singing.

1. #### Re: Spectrum analysis

Can you remover the heterodyne result? Not really as you are analysing the data - if you knew how it was produced and could do a full fourier transform then you could try to remove what you thought was generated but in this case it would be dangerous guesswork.

Any more info on this spanish song? I've heard a similar affect in some throat singing but that's real - in that the tones are there and not imagined in the receivers head.

1. #### Re: Spectrum analysis

I'll try and find the reference to this singing phenomenon. Unfortunately the wonderful new Yahoo Groups revamp has apparently lost the ability to search all historical posts in a group.

8. #### Wow

Some people are really fucking clever.

1. #### Re: Wow

No, we are pompous middle aged engineers being pedantic. You too can be one, just learn tech deeply (as in science), and wait 40 years for some sucker to ask your opinion.

9. Isn't this somewhat like the Doodson-Lege tidal-prediction engine?

[I have seen this particular machine in action. All things considered, it's surprisingly silent!]

1. Doodson-Lege tidal-prediction engine

Thanks for that. Never thought much about how tides were predicted. Excellent example of practicle application of mechanical analog engineering.

10. #### Fluid analogue Computer

Can we have an article on the Water sloshing Economics Analogue computer?

Wonderful boffinry.

I think this an Analogue Computer, but you can of course make Digital Computers with Cogwheels etc. Relays are easy if somewhat slow to build a digital computer (See Zuse Z1)

http://en.wikipedia.org/wiki/Z1_(computer)

1. #### Re: Fluid analogue Computer

Only if el Reg employs an Igor, and makes sure the thing is not *quite* accurate...

2. #### Re: Fluid analogue Computer

Actually the Z1 didn't use relays and it never was a full blown computer.

Mechanical calculators were quite common, they were still in use in specialists applications like cash registers well into the 1980s.

http://www.vintagecalculators.com/html/mechanical_calculators.html

Electronic analogue computers are also rather cool. They allow you to interact with differential equations.

You could, for example, patch in the differential equations for air flow over and under an airfoil. You could then set it up so it'll calculate a series of example air flows each one starting at a different height. You get a number of lines representing the air flow. If you have resources left you can make the computer even draw the shape of the air foil on the screen. This all is on an oscilloscope screen drawn dozens of times per second.

Now the clever thing is that it's calculated in real time, and you can build in some pots to be able to interactively work with your model. You can, for example, change the rotation of it or other parameters giving you a good idea of how it would behave in the real world. Of course even the best equipment won't get you more than 4 digits of accuracy, but it's a fast and quick way to solve differential equations.

11. #### Summing the inputs

The summing leaver at the top that takes the inputs from all twenty amplitude bars via some springs is just a fantastically simple bit of engineering.

I love it.

12. #### ww2 fire control computers

superb 40 minute intro to mechanical analog calculus

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