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d88pt@efd.lth.se (Peter Tomaszewski) writes:
>I would like to know how you combine two samples. If they are sampled at the
>same rate I suppose you can just add them together, but if I they different 
>rates? 

Interpolate.

-- 
- John Logajan @ Network Systems; 7600 Boone Ave; Brooklyn Park, MN 55428
- logajan@ns.network.com, john@logajan.mn.org, 612-424-4888, Fax 424-2853

In article <1990May28.112524.4264@lth.se> d88pt@efd.lth.se (Peter Tomaszewski) writes:
>I would like to know how you combine two samples. If they are sampled at the
>same rate I suppose you can just add them together, but if I they different 
>rates? 

If they are at the same rate, you just add or average them together.  If they
are at different rates, you have to convert one or both to the final rate.
Now, how to convert the sampling rate?  Basically, there are cheap ways to do
it, and there is the right way to do it.  This is a complicated topic, so i
won't get into it.

In article <1990May28.112524.4264@lth.se> d88pt@efd.lth.se (Peter Tomaszewski) writes:
>Hi,
>
>
>I would like to know how you combine two samples. If they are sampled at the
I suppose you could just interpolate one of the samples to have it's
datapoint be time-aligned with the other sample.  You could use the 
spline function in Matlab for instance, or just write a little
interpolator.  You would use time as the independant variable.

Greg Harrison 
GE

In article <4375@ge-dab.GE.COM>, harrison@sunwhere.DAB.GE.COM (Gregory Harrison) writes:
> In article <1990May28.112524.4264@lth.se> d88pt@efd.lth.se (Peter Tomaszewski) writes:
> >Hi,
> >
> >
> >I would like to know how you combine two samples. If they are sampled at the
> I suppose you could just interpolate one of the samples to have it's
> datapoint be time-aligned with the other sample.  You could use the 
> spline function in Matlab for instance, or just write a little
> interpolator.  You would use time as the independant variable.
> 
> Greg Harrison 
> GE

    I cannot tell if my previous posting went out yesterday.  We have had
disk full problems on our netnews server.  Interpolation is the correct
answer to get the inbetween samples.  The ideal interpolation pulse is
the sinc function  sin(pi*x)/(pi*x) as predicted by Nyquists sampling theorem
where the signal must be lowpass to avoid aliasing.  In fact the sinc pulse
is an ideal lowpass filter in the frequency domain - amazing.

    I did do an analysis of optimum truncated (time-limited) interpolation
functions and was led to the prolate spheroidal wave function set.  These
functions have optimum lowpass characteristics for a given time limitation.
If the time limitation is relaxed, we revert to the sinc pulse solution.

C. David Covington (WA5TGF)  cdc@uafhcx.uark.edu     (501) 575-6583
Asst Prof, Elec Eng          Univ of Arkansas        Fayetteville, AR 72701

The problem of combining samples is really a
problem of rate conversion (as was discussed
in previous articles).  A good reference
is:


    Ronald E. Crochiere, Rabiner, L. R., 
    "Multirate Digital Signal Processing," Prentice-Hall, 1983.
    ISBN 0-13-605162-6
 
A previous poster (Covington, I think), mentioned prolate
spheroidal wave functions.  Would any one have a good 
reference on this topic ??

---
<wilf@sce.carleton.ca>
W.P. LeBlanc             |     I don't think, therefore,
                         |     I am not.

--
One comment.  Even if two time series are sampled at the same rate,
interpolation will still be required if the samples are not taken at
the same time.
-- 
John Herman    ARPA:  herman@marlin.nosc.mil  Phome: (619)553-1466
Naval Ocean System Center Code 712
271 Catalina Blvd
San Diego, Ca. 92512-5000 

I always though combining two samples was not possible in the time domain.
If you add two opposite phase sine waves you'll get a null response.  It's
necessary to do a Fourier Transform to the frequency domain, add the 
amplitudes, and invert the transform.  This will give you twice the amplitude
of the original two sine waves (this would seem to be the desired effect).
Am I totally off-base in this rather long-held belief?
Mike...

In article <wilf.644264995@endor> wilf@sce.carleton.ca (Wilf Leblanc) writes:
>
>
>The problem of combining samples is really a
>problem of rate conversion (as was discussed
...  Would any one have a good 
>reference on this topic ??
>
>---
><wilf@sce.carleton.ca>
>W.P. LeBlanc             |     I don't think, therefore,
>                         |     I am not.


Perhaps one of the best references I've seen is a book (about to be published?)
by Dr Robert J. Marks II:

"Shannon Sampling and Interpolation Theory I: Foundations".

This book was written for a class in Shannon sampling at the University of Washington
Electrical Engineering department.  Try 
marks@blake.acs.washington.edu
for more information, although I don't know whether that email address remains good.
The book had been completed, and was in it's final rounds with the publisher last
fall, so it may now be available.