d88pt@efd.lth.se (Peter Tomaszewski) (05/28/90)
Hi,
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?
Email : d88pt@efd.lth.se
thanks.........logajan@ns.network.com (John Logajan) (05/28/90)
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
jgk@demo.COM (Joe Keane) (05/31/90)
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.
harrison@sunwhere.DAB.GE.COM (Gregory Harrison) (05/31/90)
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
cdc@uafhcx.uucp (C. D. Covington) (06/01/90)
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
wilf@sce.carleton.ca (Wilf Leblanc) (06/02/90)
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.herman@marlin.NOSC.MIL (John W. Herman) (06/06/90)
-- 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
black@beno.CSS.GOV (Mike Black) (06/06/90)
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...
tldavis@athena.mit.edu (Timothy L. Davis) (06/07/90)
In article <48870@seismo.CSS.GOV> black@beno.CSS.GOV (Mike Black) writes: >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... I'm afraid you are, Mike. First of all, the Fourier transform is a linear operator: F[a x(t) + b y(t)] = a F[x(t)] + b F[y(t)]. Thus adding in the frequency domain has the same result as adding in the time domain. Linearity holds for continuous, discrete, and mixed versions of the Fourier transform and Fourier series. Second, two opposite-phase sinusoids SHOULD cancel each other. Have you ever played a wind instrument? While tuning, the rhythmic beating of the blended sound of two horns is the result of the sinusoids going in and out of phase. When the beating stops, you are in tune (same frequency). If you are more careful, you can play a long note to be both in tune and in phase with another player (w.r.t. a particular point in space), so that the volume of the summed sound waves of your two horns is near maximal. Of course, there are harmonics generated in the horn and the phase difference of the fundamental depends on the position of the instruments and the listener and the room acoustics, but my basic tenent remains that the sound pressure levels generated by each instrument can be algenraically summed to give the sound which would be produced by the instruments playing together. This brings up another question: How linear is the compression of air? Suppose you record each instrument in an orchestra individually from a microphone at some fixed location, say on the conductor's podium. You then add all the recordings thus made to produce a recording of the full orchestra. How does this compare to recording the orchestra all at one time, assuming a noise-free environment and a perfectly duplicated performance? If air compresses linearly, the two recordings should be the same. But I could imagine a "saturation" effect, for instance in the air around the piccolo section, which might cause a change in the frequency response for some instruments when played together. My guess is that this effect would require many atmospheres of sound pressure, since PV=nRT (the natural gas law) seems to work for any easily achievable pressure. Thus the volume would be far beyond the injury threshold for anyone nearby. But do I recall that at LOW pressures (as in the rarefaction waves that accompany compression waves) gases behave nonlinearly? Perhaps someone can enlighten me on the physical limits of sound production. Tim Davis tldavis@mit.edu
james@phred.UUCP (JAMES Taylor) (06/08/90)
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.
bdb@becker.UUCP (Bruce Becker) (06/09/90)
In article <1990Jun6.170458.25618@athena.mit.edu> tldavis@athena.mit.edu (Timothy L. Davis) writes: |In article <48870@seismo.CSS.GOV> black@beno.CSS.GOV (Mike Black) writes: |>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... | |I'm afraid you are, Mike. First of all, the Fourier transform is a linear |operator: F[a x(t) + b y(t)] = a F[x(t)] + b F[y(t)]. Thus adding in the |frequency domain has the same result as adding in the time domain. Linearity |holds for continuous, discrete, and mixed versions of the Fourier transform and |Fourier series. | |Second, two opposite-phase sinusoids SHOULD cancel each other. Have you |ever played a wind instrument? While tuning, the rhythmic beating of the |blended sound of two horns is the result of the sinusoids going in and out of |phase. When the beating stops, you are in tune (same frequency). If you are |more careful, you can play a long note to be both in tune and in phase with |another player (w.r.t. a particular point in space), so that the volume of |the summed sound waves of your two horns is near maximal. Of course, there |are harmonics generated in the horn and the phase difference of the fundamental |depends on the position of the instruments and the listener and the room |acoustics, but my basic tenent remains that the sound pressure levels |generated by each instrument can be algenraically summed to give the sound |which would be produced by the instruments playing together. In yet another instance of the interplay of art and technology, I recommend you investigate the work "Still and Moving Lines of Silence in Families of Hyperbolas", by Alvin Lucier. This piece, composed in 1983, is recorded on an album of the same name, on Lovely Records. A quote from the record jacket: "Still and Moving Lines of Silence in Families of Hyperbolas is based upon interference phenomena between two or moresound waves. When closely tuned musical tones are sounded, audible beats - bumps of loud sound produced as the sound waves coincide - occur at speeds determined by the difference between the pitches of the tones. The larger the difference, the faster the beating. At unison, bo beating occurs. Furthermore, if each tone originates from a separate source, the beats spin in elliptical patterns through space, from the higher source to the lower one." -- ,u, Bruce Becker Toronto, Ontario a /i/ Internet: bdb@becker.UUCP, bruce@gpu.utcs.toronto.edu `\o\-e UUCP: ...!uunet!mnetor!becker!bdb _< /_ "I still have my phil-os-o-phy" - Meredith Monk