Correlation error derivation?
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From: gct on 25 May 2010 11:36 Say I'm correlating a known signal against a received signal, obviously there's going to be some error in my peak location due to noise. I know you can formulate the error as a function of bandwidth, correlation time and SNR, but I've never seen it derived. Does anyone know of a good resource that derives this variance? (IEEE papers would be fine...)
From: Tim Wescott on 25 May 2010 12:07 On 05/25/2010 08:36 AM, gct wrote: > Say I'm correlating a known signal against a received signal, obviously > there's going to be some error in my peak location due to noise. I know > you can formulate the error as a function of bandwidth, correlation time > and SNR, but I've never seen it derived. Does anyone know of a good > resource that derives this variance? (IEEE papers would be fine...) The relevant set of literature to look for is "Detection and Estimation Theory". It's the basic stuff of which communications theory classes are made. Your problem in specific is very akin to radar (if it's not for real honest to gosh radar -- what are you trying to shoot down?). In the real world the return signal is often corrupted by more than additive noise -- one often sees multi path which we either want to resolve (in a radar), or reject (in a data communications application). It's one of the problem sets in Van Trees' "Detection, Estimation and Modulation Theory: the hardest book you'll ever get through" (Wiley, 1066 -- er, 1968). Including "radar" in your search terms may help. There's a lot of factors that come into play once you get beyond just simple additive Gaussian noise, so it may not be a problem that you can solve after reading just one paper. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
From: Rune Allnor on 25 May 2010 12:42 On 25 Mai, 18:07, Tim Wescott <t...(a)seemywebsite.now> wrote: > Including "radar" in your search terms may help. Adding "matched filter" might help, too. Rune
From: Tim Wescott on 25 May 2010 12:49
On 05/25/2010 09:42 AM, Rune Allnor wrote: > On 25 Mai, 18:07, Tim Wescott<t...(a)seemywebsite.now> wrote: > >> Including "radar" in your search terms may help. > > Adding "matched filter" might help, too. > > Rune D'oh. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com |