Hi Tim, Writing about the effects of "periodic sampling" is an interesting and educational thing to do.
My guess is that you'll have to address the controversial notion of "negative frequency", as well as why it is valid to show spectral replications (spaced Fs hertz apart) when we draw a freq-domain picture of the spectrum of a discrete (digital) signal.
One interesting aspect of periodic sampling is that it's easy to misinterpret the results of software modeling of the process of periodic sampling.
That's (I think) what happened when J. L. Smith wrote his "Breaking the Nyquist Barrier" in the July 1995 issue of the IEEE Sig. Processing magazine. I believe Smith misunderstood his software-generated plots when he wrote his embarrassing article. Smith claimed that he could violate the Nyquist Theorem and not lose any information (and avoid any ambiguous information) regarding some time domain signal. Smith's article resulted in a flurry of "Letters To the Editor" that debunked the article (See the Nov. 1995, Jan. 1996, and the May 1996 issues for examples of the letters.) How embarrassing that must have been for both Smith, and the Editors of the magazine who should have known better.
Another very "misguided" sampling article was "Apply Fundamentals To Avoid Surprises With Sampled Systems" written by Gerard Fonte and printed in the June 24th 1993 issue of EDN magazine. Fonte also claimed that you could violate Nyquist and not lose any information. Almost every paragraph of that article contains misconceptions and ambiguities regarding the Nyquist sampling theorem. It's truly a "ghastly" article --- and it also caused a deluge of "Letters To the Editor" pointing out all the errors in the article. (See page 25 of the Sept. 30th 1993 issue of the EDN magazine for example.)
I thought after all the criticism that Fonte received regarding his 1993 EDN that we'd heard the last from Mr. Fonte. Not so. He wrote another titled "Breaking Nyquist" in the October 1998 issue of the Circuit Cellar magazine. Again he claimed that the Nyquist sampling theorem is not valid and that it can be "broken" without causing "problems". Using vague, ambiguous, undefined terminology, Fonte again claimed that he can tell the difference between an Fo (F sub zero) discrete spectral component of an analog sinewave whose Fo frequency was less than Fs/2 and an Fo discrete spectral component of an aliased analog sinewave whose frequency was greater than Fs/2. In other words, he claims that "aliasing" (violating Nyquist) does NOT cause spectral ambiguity in the frequency domain. I can hardly wait for Fonte's next article.
(I'm not being hateful here...Fonte's probably a nice guy whom his family loves.)
My guess is, again, Fonte is using software to model the process of periodic sampling, and the signal he is "sampling" is a pure sinewave. Such modeling is very risky in my opinion because it's easy for a beginner in the field of DSP to misinterpret/misunderstand the results of such modeling.
Concerning sampling, Bonnie Baker wrote an article titled "Turning Nyquist Upside Down by Undersampling" in the May 12th 2005 issue of EDN magazine. The article discusses bandpass sampling. However, I think the article's title is unfortunate because bandpass sampling does NOT "turn Nyquist upside down"
---bandpass sampling is included in the Nyquist Sampling Theorem.
I tell the students in my DSP class that, "Periodic Sampling is one of the most misunderstood topics in DSP." I think I'm justified in making that claim.
Hey Tim, I think in any dissertation on "sampling" it would be a good idea to discuss bandpass sampling. Bandpass sampling is not only an interesting topic, but it's a very practical topic in these days of digital communications. (Just my two cents.)
See Ya', [-Rick-]