["Followup-To:" header set to sci.electronics.design.]
On Fri, 29 Sep 2006 22:35:46 GMT,
in Msg. said:
In the first sentence of your papere, you say that if the signal is band
limited to fo or less, then a sample frequency of 2fo or more is adequate to
contain completely all the information necessary to recreate the signal. My
understanding from water cooler conservation is that the signal bandwidth must
be strictly less than fo for a sample frequency of 2fo and that the signal
must be infinite in extent to allow perfect reconstruction.
I see it that way as well. A pure sine signal of exactly f_0, sampled at
exactly 2f_0, might come out as all-zero, or as a pulse train with
alternating polarity and an amplitude of anything between 0 and V_p.
There is not enough information to reconstruct the signal in this case.
However, if you sample the same signal at 2f_0+f_e (f_e being very
small, think epsilon), it will come out as a pulse train with
alternating polarity and the amplitude modulated by a beat frequency
f_e. This would seem to be not enough information to reconstruct the
signal, but in fact that's not true: A f_0 sine is the only possible
input signal because the modulated pulse train contains frequency
components greater than f_0 which couldn't have been in the input signal
(which, as a prerequsitite to Nyquist, is brick-walled at f_0).
So, the way I see it is that the sampling frequency must be strictly
greater than the highest frequency in the input.