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From: jbuck@galileo.berkeley.edu (Joe Buck)
Newsgroups: comp.dsp,sci.math
Subject: Re: resampling problem
Message-ID: <11145@pasteur.Berkeley.EDU>
Date: 14 Feb 91 23:38:34 GMT
References: <1991Feb13.234510.22488@nuchat.sccsi.com>
Sender: news@pasteur.Berkeley.EDU
Reply-To: jbuck@galileo.berkeley.edu (Joe Buck)
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If you have available the exact x values where the samples are taken,
and your signal is band-limited, you can reconstruct exactly the
continuous-time signal.  Let x[n] be the space coordinate of the nth
sample; let y[n] be the measured value of the signal at that time.
First, consider a function that is zero for all x except at the
x[n] values, and has a Dirac delta function of height y[n] at
x = x[n].  Pass this signal through an ideal low-pass filter corresponding
to the band limit, and you have the continuous-time signal.  This
reconstruction works if the highest frequency in the data, f, is
less than 1/2T, where T is the maximum spacing between samples.
For this to work right at the boundary f = 1/2T you must have no
noise.  I think you could tolerate noise if you oversampled by a
good deal, so the LPF would take it out.

You can then resample the continuous-time signal at your desired
rate.

I recommend that you simulate this procedure before actually relying
on it.





--
Joe Buck
jbuck@galileo.berkeley.edu	 {uunet,ucbvax}!galileo.berkeley.edu!jbuck