Re: Need to calculate Nyquist frequency from data
- To: mathgroup at smc.vnet.net
- Subject: [mg41251] Re: Need to calculate Nyquist frequency from data
- From: Sseziwa Mukasa <mukasa at jeol.com>
- Date: Sat, 10 May 2003 04:01:34 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Friday, May 9, 2003, at 03:20 AM, Bob Buchanan wrote: > Hello, > > I have a time series of real numbers which I can treat as representing > a signal. How do I estimate the Nyquist frequency from the time > series? If the previous question does not make sense, is it the case > that the Nyquist frequency can only be estimated if one has a > continuous function of time to work with? > Once you sample information is lost. In particular, any signal energy at frequencies higher than half the sample rate will be aliased into sampled bandwidth. Without a model of the original signal it is impossible to exactly reconstruct the original signal. That said you still have a few options for estimating the original spectrum. You can attempt to fit a model function to your time series or interpolate and resample at a higher rate. Another approach is to try some kind of harmonic inversion approach like Maximum Entropy (as described in Skilling, J. & Bryan, R.K., (1984), Mon. Not. R. astr. Soc., 211, 111-124 not the method ascribed to Burg found in Numerical Recipes) or some kind of Bayesian approach. You can find descriptions of the latter methods by searching for the term MaxEnt and following the links. If after doing this you have some reason to believe your spectral estimate is accurate you can search for the largest nonzero frequency component and call it half the Nyquist frequency. Note that for any nonstationary signal (ie. one whose frequency components change with time) or a signal which is finite in duration there is no Nyquist frequency; the signal is by definition not bandwidth limited. If you're lucky the spectrum decays in intensity as frequency goes to infinity and you can cut off at some value and still have a reasonable approximation of the continuous spectrum in the sense that the discrete power spectrum will have large values near the extrema of the continuous power spectrum. Note that regardless of aliasing, the discrete spectrum is not exactly equivalent to the continuous spectrum, but for bandwidth limited signals there is a precise relationship between the two. Regards, Ssezi
- Follow-Ups:
- Re: Re: Need to calculate Nyquist frequency from data
- From: Stepan Yakovenko <yakovenko@ngs.ru>
- Re: Re: Need to calculate Nyquist frequency from data