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Ian
  • Member for 14 years, 11 months
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Applications of the Chinese remainder theorem
(cont'd from above) The solution is to send out a few different types of pulses (say, with different wavelengths of light), with each type of pulse having it's own pulse interval, and making those intervals coprime. Then you can use the CRT to calculate range mod some very large distance (where you know, practically speaking, that you won't be registering any reflections from such large distances).
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Applications of the Chinese remainder theorem
To elaborate on this, because it's more applied than the rest: Many radar systems work by sending EM pulses out at regular intervals, waiting in between pulses to look for reflections from objects. You want to calculate an object's distance from the time it takes to see a reflection. If time between pulses is very long, this works, but if you're observing something dynamic you want fast updates, so you need shorter time between pulses. But then you don't know which pulse's reflection you're seeing, so object range is only known modulo (speed of light)*(pulse interval). (cont'd)
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non-abelian groups of prescribed order
@Qiaochu: You're right, I didn't read your reply carefully enough. Sorry!
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non-abelian groups of prescribed order
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