Xref: utzoo comp.dsp:1304 sci.math:15429 Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!sun-barr!lll-winken!elroy.jpl.nasa.gov!usc!jarthur!nntp-server.caltech.edu!gah From: gah@hood.hood.caltech.edu (Glen Herrmannsfeldt) Newsgroups: comp.dsp,sci.math Subject: Re: resampling problem Message-ID: Date: 27 Feb 91 22:57:46 GMT References: <1991Feb13.234510.22488@nuchat.sccsi.com> <25328@netcom.COM> Sender: news@nntp-server.caltech.edu Organization: California Institute of Technology, Pasadena Lines: 16 The Nyquist theorem does not require equal spaced points. Equal spacing is convenient, and good in terms of S/N ratio. If your samples are infinitely narrow (points in time), then, theory says that if you multiply each point by a dirac delta function centered at that time, and filter it through the appropriate band limiting filter, you will get the same result as the original signal through such band limiting filter. If the points are not equally spaced, then errors in the position of those points are magnified in the final result. If you have velocity or acceleration, you use first or second derivative of the dirac delta function, I believe. (I have never actually tried this.) As a side thought, if you know all the derivatives of a function at a single point in time, you can find the value of the function for all times. The problem is you have to know them exactly.