Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



A Few FFTs Short of MPC
Posted:
Apr 15, 2012 11:20 AM


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 getmorebydoingless 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



