On Sat, 18 Oct 2008 12:50:57 -0700, Tim Wescott wrote (in article ):
You state in your own paper that sampling at the Nyquist rate is meaningless without phase (and how can you have phase if you sample at the Nyquist rate?). So I respectfully submit that your premise is incorrect. In theory, you need to sample at least greater than twice the highest frequency component.
Just change your into from
"The Nyquist theorem states that if you have a signal that is perfectly band limited to a bandwidth of f0 then you can collect all the information there is in that signal by sampling, as long as your sample rate is 2f0 or more."
to ---sample rate > 2f0 or more.
The form of the theorem you are using is for analytical functions of infinite extent. Thus the misconception. If you can not sample for an infinite length of time (and who has the time for that?), you must exclude the equality.
Your intro should say function instead of signal and remove the other references to bandwidth and signals, then relate it to the Fourier Transform to define bandlimiting. Note the FT is also from -infinity to infinity.
Or you can just say >2f0.
-- Charlie Springer