🚀 go-pugleaf

In article <Abj8CR200WBN04RPUr@andrew.cmu.edu>, kr0u+@andrew.cmu.edu (Kevin William Ryan) writes:
> F0O@psuvm.psu.edu
> >     I was reading an article that states the Nyquist theorm as:
> >     "The sample frequency must be at least twice the highest frequency
> >component within the analog signal for an accurate representation of the
> >analog signal".

I think this should be "GREATER than twice the highest frequency
component".

> >     i.e. If you have a 60HZ sine wave, and you sample at 120HZ, you're
> >only going to get two points per cycle.

If you sample ABOVE 120Hz, you will have enough information to
reconstruct your original signal as described.
If you sample at precisely 120 Hz, you will be unable to reconstruct
accurately.

Without loss of generality, consider samples at t = kT, where k is an
integer, and T is (1/120)s:
    x(t) = cos(120*pi*t)
is indistinguishable from
    y(t) = 2 * cos(120*pi*t + (pi/3))
when comparing the sampled data.  Therefore, there is a reconstruction
ambiguity.

>     No, it applies to all signals, as the _minimum_ possible sampling
> rate that will without error give you the signal back. Sampling a sine
> wave at the Nyquist rate will give you, in the best case:
> 
>     | | | | | | | | |
>     -----------------
>      | | | | | | | |
> 
> where alternate samples hit the plus and minus peaks of the sine wave.
> Practically, to ensure that you aren't just hitting the nodes rather
> than the peaks of the waves, it's best to sample much faster. However,
> it is possible to reconstruct it accurately with Nyquist rate sampling,
> and impossible to reconstruct it accurately if sampled any slower. The
> Nyquist criterion gives the minimum rate at which you can sample and
> retain information. 

I believe this is misleading... One must sample ABOVE the Nyquist rate
(not AT the Nyquist rate) for reconstruction to be possible.
I think this is a fairly common misconception, though.

Sorry kwr -- I don't mean to be impolite.

Best regards,
ruck
-- 
John R Ruckstuhl, Jr	ruck%sphere@cis.ufl.edu, sphere!ruck
University of Florida 	ruck@cis.ufl.edu, uflorida!ruck