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Re: A Few FFTs Short of MPC
Posted:
Apr 16, 2012 1:01 AM
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What has been and is being called "matched filtering" might better be
called "a few steps short of complete match filtering" [which has the
often desirable effect of _adding_ in some low pass filtering].
Noise is often at higher frequencies so no one is going to complain
too much about this fortuitous get-more-by-doing-less situation.
North didn't have time to be mathematically politically correct
during
a war, certainly not before machines costing less than a few days pay
could calculate a dozen 1024 FFTs in seconds.
Mathematicians, however, aren't satisfied with "well it woOOorks"
jerry rigs. Since there isn't any major war going on recovering the
original signal can now be considered, if only as a matter of form.
This is easy to do in the frequency domain. Just take the square
root
of the product of signal X template. Excel makes this operation on
complex numbers easy with IMSQRT.
Now you can see the results of the frequency & phase angle matching
without the seemingly inherent low pass filtering effects obscuring
the match.
Engineers like to get lucky with Fortuna but they also like dedicated
operations. Do the _complete_ matched filter. After the original
signal is recovered _then_ you add in whatever additional filtering
you think is necessary.
Even for signal detection recovering the original signal will often
be
a better route. What would be easier to detect? A triangle or a
square wave?
Bret Cahill
"The mind invents things more easily than words. That's why so many
bad terms come into existence."
-- Tocqueville
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