Nyquist????

On Oct 28, 5:56&#4294967295;pm, jim <"sjedgingN0sp"@m...@mwt.net> wrote:
> Greg Berchin wrote:
>
> > On Mon, 27 Oct 2008 17:31:08 -0700 (PDT), robert bristow-johnson
> > <r...@audioimagination.com> wrote:
>
> > >the good guys say it's always 1/2 of the sampling rate,
>
> > The "good guys"?
>
> > I guess basing the Nyquist Frequency on characteristics of the signal
> > to be sampled must therefore be "elitist". &#4294967295;:-)
>
> Well if you are just in the planning stages of sampling a signal the definition
> of what may be the Nyquist Frequency might be a little murky.
>
> &#4294967295; &#4294967295; &#4294967295; &#4294967295; If you have a digital signal and you do a DFT and somebody comes along and
> observes that there is no energy in your signal at the Nyquist frequency - Is
> there any doubt as to what that means?
>

in my opinion, no.  Nyquist is what is in bin # N/2.  but this signal
is already sampled.  if it was DTFT and normalized radian frequency,
then Nyquist is unambiguously equal to pi.

IMO what is both the best and most prevalent semantic is that the
"Nyquist rate" is this property of a continuous-time signal that is
the open lower bound of acceptable sampling rates (which is twice the
frequency of the highest frequency component of non-zero amplitude in
the continuous-time signal) for that signal.  the "Nyquist frequency"
is this property of the sampling system which is the open upper bound
of frequency components that can be accurately represented with
sampling (which is half of the sampling rate).

i have heard of some few folks (and unfortunately O&S are among those)
saying that the Nyquist frequency is this property of a signal,
essentially half of the Nyquist rate or the frequency of the highest
non-zero frequency component.  i don't see that semantic as useful.
we already have baseband "bandwidth" or "band limit" for that
parameter.

r b-j

Greg Berchin wrote:
> On Tue, 28 Oct 2008 10:33:12 -0800, Glen Herrmannsfeldt
> <gah@ugcs.caltech.edu> wrote:
(snip)

> Then the only time that the concept of Nyquist Frequency has meaning
> is when, for example, one wants to sample a bandpass signal or an
> analytic signal WITHOUT shifting the spectrum to baseband in the
> process.  In such cases the Nyquist Frequency is equal to the highest
> (absolute value of) frequency of significant amplitude contained
> within the signal, and the Nyquist Rate is twice the Nyquist
> Frequency.

This brings in some complications.  The bandpass signal may not
be at a natural place for aliases of the baseband.

Consider a 20kHz sampling rate, sufficient for signals
band limited to less than 10kHz, say 8kHz as an example.

A signal band limited to between 101kHz and 109kHz could
easily be sampled at 20kHz.  A signal from 95kHz to 103kHz
would not be so easy to sample at 20kHz without mixing.

> Note that all of these entities are based upon characteristics of the
> signal to be sampled, not of the sampling itself.

I agree with this one.

-- glen