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[mathcad] Re: DSP method
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Author: Oakley, Philip SELEX UK
Posted: Tue, 17 Jan 2006 11:19:28 +0000
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The potential accuracy can only be determined from your knowledge of the signal (and its digitisation).
Basically you need to know that it is band-limited in some way such that there is a particular part of the band that has no confounding alias components. For a regularly sampled data stream, any frequency f(w.t) is confused with f([s+/-w].t) where s=sampling frequency (which may include jitter). [this is for Real data, rather than I-Q sampled Complex data where only the + out of the +/- applies]
As long as you can identify a suitable spot where you no aliases then you can get quite fine sub-resolution.
The sub resolution depends on the number of sample point. This is obvious when n=1 sample [all you get is 'before' or 'after' for time resolution!!]
Philip
From: Mark Smith "mailto:mark.smith"
Sent: 17 January 2006 10:51
To: Mathcad Discussion List
Cc: ''
Subject: [mathcad] Re: DSP method
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Hi Chris
You wrote... "The Nyquist frequency doesn't limit the accuracy of the phase
measurement.
This is determined more by the total length of the data, and how sharp the
correlation is. You can interpolate to find the peak of the correlation,
but this is only one sample from a distribution. If the same experiment
were repeated multiple times, one would expect to find a scatter on this
position. Depending on the quality of the data this scatter could more or
less than the time step."
Thanks for this it is as I had a feeling that this was the case but is there
a way to determine what the theoretical accuracy is from the data. I want to
only have to sample at a rate sufficient for the accuracy I need given the
level of noise present, slow A2D's are cheeper than fast ones.
I can improve accuracy by averaging many sets of data to reduce scatter but
again I'd like to keep this to a minimum.
cheers
mark
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