🚀 go-pugleaf

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