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Topic: Approximating GCF
Replies: 6   Last Post: Aug 1, 2014 8:05 AM

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James Waldby

Posts: 365
Registered: 1/27/11
Re: Approximating GCF
Posted: Jul 17, 2014 9:22 PM
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On Fri, 18 Jul 2014 00:47:58 +0000, James Waldby wrote:...
> Let's say you are given n values y_1 ... y_n. By knowledge about some
> process, you know that each y_i is some random noise d_i plus r * x_i,
> where r, x_i, and d_i are unknowns except that all the x_i are integers.
> You want to compute r.
>
> There may be a way of writing the problem as a mixed integer linear
> programming problem, or it might be analyzed as a clustering problem,
> and there might be a continued-fractions method. A Fourier analysis
> might have a spike at frequency 1/r or a multiple.


Ignore the bit about Fourier analysis.

> Also consider the following brute force approach:
[snipped]
The snipped approach is like using a matched filter with r = u/j.
See <http://en.wikipedia.org/wiki/Matched_filter> re matched filters.

--
jiw



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