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No, Christine, that is not how it works...

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real_jj

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In Reply to: Re: No, Christine, it is not. posted by Christine Tham on June 21, 2006 at 19:26:45:

The theorem depends on two things.
1) The applicability of Fourier Analysis to real (meaning actual,physical, not real vs. imaginary or complex) signals. This has long ago been proven. (well, perhaps not for some relativistic or quantum issues, but those are not an issue here)
2) The applicability of the convolution theorem. This is also long-since established.
That's it. End of discussion.
You didn't answer serveral questions. 1) Have you tried this. 2) Did you dither your quantizer. 3) Did you ensure that any modulation of any test signal did not push it over fs/2?

Follow Ups:

Your are falling into a hole ... - Christine Tham 20:10:17 06/21/06 (1)
Your two points has no bearing on the fact that a necessary precondition for the theorem is not being fulfilled. If a theorem says "A is true provided B and C are true" and if C is not true then A is undefined. That's it. End of discussion.
And you never posed any of the questions that you are now belatedly asking. But the answers are:
1. Yes, including some theoretical modelling and some empirical observations
2. No, and if i did the results would have been worse, at least from a theoretical perspective
3. Yes, and in fact reconstruction errors can be observed as low as fs/4
- Actually, my post is conclusive... - real_jj 22:08:19 06/21/06 (0)
  The conditions under which the sampling theorem is valid are simply not under debate.
  I have no idea where you came up with this idea, but that's how it is.
  And there are no reconstruction errors at all as low as fs/4. I've done this, over and over.
  If your claim was correct, your cell phone (if you have one) would not work. Both its speech coder and its modem would fail.
  That, by itself, is conclusive evidence that your assertion is wrong.
  I have a strange feeling that you forgot to include your reconstruction filter all of a sudden. Could that be it?
  Are you confusing the "beating" due to out-of-band aliases, perhaps? I've certainly heard THAT before.

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