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In this article "Sampling: What Nyquist Didn't Say, and What to Do About It" from Wescott, the author shows in Figure 6, the plot of the frequency spectrum of a signal which goes through a LPF before sampling and its aliased component. He says: You can see that this is not going to give good performance. In fact, if you take all the aliased energy into account the ratio between the correct signal and the aliased signal is exactly 1:1

Figure 6

The Figure 6,to which he refers, is attached in this message.

From my understading, the only components that are relevant are those shown up to 4000 Hz, and the actual signal (in black) has a bigger area than the aliased component (in dotted blue). Why does he say is is a 1:1 energy ratio? What am I not getting from this?

Thank you

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    $\begingroup$ @timwescott is an active member here, I’ll let him answer this for you and if he doesn’t I will ;) $\endgroup$
    – Jdip
    Nov 9, 2023 at 16:55
  • $\begingroup$ I dunno what Tim wrote, but, if you know what your reconstruction filter looks like, computing the ratio of the energy of all of the images to the energy of the original baseband, that's a solved problem I think. It's the images that can possibly fold back into your baseband that become aliases. $\endgroup$ Nov 11, 2023 at 8:07

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@Link Coquin. When there’s confusion, or a disagreement, about some signal processing operation I follow the advice given to me years ago by DSP practitioner Randy Yates. Randy said, “Go back to the definitions. Never forget the definitions!”

In Wescott’s paper regarding his Figure 6 spectra he wrote “if you take all the aliased energy into account the ratio between the correct signal and the aliased signal is exactly 1:1!” The question is, What did he mean by “ratio”, ratio of what? If he meant the ratio of the total energy of the solid spectral curve (the area under the solid curve over the frequency range of zero –to- 4000 Hz) over the total energy of the dashed curve (the area under the dashed curve over the frequency range of zero –to- 4000 Hz), then clearly that ratio is greater than one.

Link Coquin, you wrote, “What am I not getting from this?” Your question is super valid. Perhaps Tim Wescott will respond and help answer your question.

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