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| Re: Canarsie CBTC (100320) | |||
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Re: Canarsie CBTC |
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Posted by Stephen Bauman on Sat Jun 18 10:51:16 2005, in response to Re: Canarsie CBTC, posted by AlM on Sat Jun 18 08:54:29 2005. Still, I SUSPECT it's not possible to measure velocity accurately enough, based on anecdotal evidence, but certainly can't prove it.While there are many numerical integration techniques, there are very few for numerical differentiation. Here's one of the problems. Consider Fourier transforms (moment generating functions for those used to statistics) and the operation for differentiation in the time domain with what happens in the frequency domain. Time domain differentiation is equivalent to multiplying the Fourier transform by the frequency. So, if there is a small additive high frequency noise component it's going to swamp the derivative. The reverse is true for integration; the transform is divided by the frequency. That means that high frequency noise will have very little effect. This indicates that whatever numerical differentian technique is chosen, it must incorporate some form of band limiting to be immune to noise. Band limiting introduces delays into the result. So, if one wants to derive velocity from position measurements, one has the choice of making the computed velocity either timely or accurate but not both. I don't propose that this is a proof, but it should point you in the proper direction. |
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