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Old 23rd Jun 2012, 7:02 pm   #13
Lucien Nunes
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Join Date: Apr 2008
Location: London, UK.
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Default Re: Digital hard copy?

It is alarming to compare the densities and capacities of different storage media. Even different generations of ICs, as predicted by Moore's law, differ in capacity by ratios outside the realm of everyday experience. But when you start to compare optical or modern electronic storage media with historic technologies, the ratios can become laughable.

I have previously thought about the related question: How fast would you have to run 8-column paper tape to play back CD quality audio in real time?

The data rate encoded on a CD is actually 4,321,800 bits/sec. but we don't need as much data for paper tape storage. The 1,411,200 bits/sec of sampled data (44.1k X 2 chans x 16 bits) is subjected to CIRC (cross-interleaved Reed Solomon) error-correction, which increases the rate to 1,881,600 bits/sec. This is a useful feature to retain for paper tape as the high speed is likely to result in damage. You would be able to cut torn ends square and stick them together without interrupting the sound, just as a CD player can read past a small scratch.

Subcodes are then added, which we don't need, followed by eight-fourteen modulation. This is useful for the serial optical system as it makes the signal self-synchronising and reduces bandwidth (despite increasing the number of symbols stored). However we don't need it for paper tape as this has sync holes and stores at byte-width. Nor do we need the sync word added at the final stage.

So the data rate of 1,881,600 bits/sec is written to tape with 8 bits/byte and 10 bytes/inch. The necessary tape speed in MPH is therefore:
1,881,600 / 80 / 12 / 5280 * 3600 = 1336 MPH.
For a visualisation of this, consider a car driving along the motorway at 67 MPH with 20 tapes tied on to its rear bumper, all being read at once. 20 parallel tapes would be clumsy; you might consider one tape per channel, running at 668 MPH. This has the advantage of being slightly below the speed of sound.

An interesting point - the linear density of audio storage on tape is close to that of the air between speaker and listener. If you sit eight feet from the speaker, about seven feet of tape's sound capacity is in acoustic transit from driver to eardrum.

I leave as an exercise for the reader, the computation of the mass of stone tablets of ordinary construction required to store the contents of a 32GB memory stick.

Lucien
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