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A Basic Aliasing Question

Started by Unknown August 23, 2004
"Richard Owlett" <rowlett@atlascomm.net> wrote in message
news:10ikcm0abkntoef@corp.supernews.com...
> Bhaskar Thiagarajan wrote: > >[SNIP] For designs where undersampling > > is used, it now becomes important to pick the right alias... > > Does this mean that in some cases you can sample at less than Nyquist > criterion? > [ If true, just point out some good keywords for Google search. ]
Yes, that's true (do read Jon's response where he clarifies the Nyquist criterion). Both 'bandpass sampling' and 'undersampling' should give you plenty of hits on Google. Cheers Bhaskar
Richard Owlett wrote:

> Bhaskar Thiagarajan wrote: > >> [SNIP] For designs where undersampling >> is used, it now becomes important to pick the right alias... > > > Does this mean that in some cases you can sample at less than Nyquist > criterion? > [ If true, just point out some good keywords for Google search. ]
I think it means not sampling fast enough to accomplish what's needed. Subsampling is something else, but I think it's what Bhaskar meant when he wrote undersampling. Rick Lyons's books have the best treatment of subsampling that I know of. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
"Jon Harris" <goldentully@hotmail.com> writes:

> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message > news:xxp3c2dsoig.fsf@usrts005.corpusers.net... >> Richard Owlett <rowlett@atlascomm.net> writes: >> >> > Bhaskar Thiagarajan wrote: >> > >[SNIP] For designs where undersampling >> > > is used, it now becomes important to pick the right alias... >> > >> > Does this mean that in some cases you can sample at less than Nyquist >> > criterion? >> >> Yes. > > I guess that depends on how you define the "Nyquist criterion". If you define > it to require sampling at more than twice the highest frequency component in the > original signal, then the answer is yes. But if you define the Nyquist > criterion to require sampling at more than twice the bandwidth of the original > signal, than no.
Yo', Jon, dude: chill. We all know everything depends on everything else, meaning depends on context, what "is" is is debatable, and the answer to the universal question is "39" (or was it 37?). -- % Randy Yates % "How's life on earth? %% Fuquay-Varina, NC % ... What is it worth?" %%% 919-577-9882 % 'Mission (A World Record)', %%%% <yates@ieee.org> % *A New World Record*, ELO http://home.earthlink.net/~yatescr
Randy Yates <randy.yates@sonyericsson.com> wrote in message news:<xxpsmaermef.fsf@usrts005.corpusers.net>...
> Here's something I don't remember about aliasing - someone please > verify whether or not this is correct. Assume the sample rate is > 2000 Hz for the sake of illustration. > > Conventional wisdom tells us that a 1200 Hz signal will look > like an 800 Hz signal due to aliasing. I say it may > look the same on a spectrum analyzer (i.e., its magnitude > spectrum may look the same), but it may actually be different > since the negative and positive frequency components of such > a wave are swapped. Hence if the original wave was a cosine > wave, the aliased wave will still be cosine (i.e., will look > identical to the original) since the positive and negative > frequency components are identical (cos x = (e^(i*x) + e^(-i*x))/2).
The "cosine" form is preserved, yes, but with an ambiguity, what the frequency is concerned.
> However, if the wave is any other type, it will look different.
Yes. A base-band continuous pulse would look different from a band-pass continuous pulse that produces the same discrete set of samples. But since both can be synthesized by sinusoidals, that doesn't help much, since the sinusoidals are ambiguous.
> Said perhaps more simply, xa(t) = -x(t). Since a cosine is > even-symmetric, xa(t) = -x(t) = x(t). Not true for a sine > wave or sinusoids of other phases.
This is the sine form, the cosine form you found in the correction you posted afterwards.
> Trivial, but something I'd never thought of before. Or > am I wrong?
You seem to be right in the two assertions (sampled sinusoidals being ambiguous wrt frequency, and the symmetry properties of sines/cosines) when viewing them individually. I don't see any connection between the ambiguity and the symmetry properties, though. I can't see how a cosine being even symmetrical around some time reference causes it to become ambiguous when sampled, if that's what you mean. Rune
Randy Yates wrote:
> We all know everything depends on everything > else, meaning depends on context, what "is" is is debatable, and > the answer to the universal question is "39" (or was it 37?).
It was 42. -- Jim Thomas Principal Applications Engineer Bittware, Inc jthomas@bittware.com http://www.bittware.com (703) 779-7770 To mess up a Linux box, you need to work at it; to mess up your Windows box, you just need to work on it. - Scott Granneman