Reply by glen herrmannsfeldt●November 2, 20082008-11-02

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

Reply by robert bristow-johnson●October 31, 20082008-10-31

On Oct 28, 5:56�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". �:-)
>
> 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.
>
> � � � � 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

Reply by Jerry Avins●October 29, 20082008-10-29

Greg Berchin wrote:

> On Tue, 28 Oct 2008 21:26:26 -0400, Jerry Avins <jya@ieee.org> wrote:
>
>> You don't need to know the center of the band with much precision. You
>> need only enough information to select the right image.
>
> Doesn't knowing which image is the right image imply that you know
> where the images were located, which in turn implies that you know the
> center of the band exactly?

You can figure it out exactly, but the exact center is quantized, so
choosing the correct image needs only an approximate value.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Reply by Greg Berchin●October 29, 20082008-10-29

On Tue, 28 Oct 2008 21:26:26 -0400, Jerry Avins <jya@ieee.org> wrote:

>You don't need to know the center of the band with much precision. You
>need only enough information to select the right image.

Doesn't knowing which image is the right image imply that you know
where the images were located, which in turn implies that you know the
center of the band exactly?

Reply by Jerry Avins●October 28, 20082008-10-28

Greg Berchin wrote:

> On Tue, 28 Oct 2008 22:24:31 +0000 (UTC), spope33@speedymail.org
> (Steve Pope) wrote:
>
>> I would think the Nyquist rate is necessary sample rate to
>> sample a signal without aliasing, and in the case of a bandpass
>> signal it is related to signal bandwidth and not absolute
>> frequencies in the signal.
>
> And that is exactly what I said in the first part of my post. But
> what happens if you have a strictly bandlimited bandpass signal that
> you want to sample without ambiguity? If you set your sampling
> frequency according to bandwidth alone (Nyquist Bandwidth = bandwidth;
> Nyquist Rate = Nyquist Bandwidth; sampling rate > Nyquist Rate), then
> you also need to know the center of the passband in order to
> reconstruct the signal. But if you set your sampling rate according
> to the highest |frequency| in the signal (Nyquist Frequency = |highest
> frequency|; sampling frequency > 2 x Nyquist Frequency), then you no
> longer need to know the center of the passband because it is
> constrained to be zero.

You don't need to know the center of the band with much precision. You
need only enough information to select the right image.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Reply by Greg Berchin●October 28, 20082008-10-28

On Tue, 28 Oct 2008 22:24:31 +0000 (UTC), spope33@speedymail.org
(Steve Pope) wrote:

>I would think the Nyquist rate is necessary sample rate to
>sample a signal without aliasing, and in the case of a bandpass
>signal it is related to signal bandwidth and not absolute
>frequencies in the signal.

And that is exactly what I said in the first part of my post. But
what happens if you have a strictly bandlimited bandpass signal that
you want to sample without ambiguity? If you set your sampling
frequency according to bandwidth alone (Nyquist Bandwidth = bandwidth;
Nyquist Rate = Nyquist Bandwidth; sampling rate > Nyquist Rate), then
you also need to know the center of the passband in order to
reconstruct the signal. But if you set your sampling rate according
to the highest |frequency| in the signal (Nyquist Frequency = |highest
frequency|; sampling frequency > 2 x Nyquist Frequency), then you no
longer need to know the center of the passband because it is
constrained to be zero.
-- Greg

>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.

I would think the Nyquist rate is necessary sample rate to
sample a signal without aliasing, and in the case of a bandpass
signal it is related to signal bandwidth and not absolute
frequencies in the signal.
Steve

Reply by Greg Berchin●October 28, 20082008-10-28

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

>In the case of an AM-DSB signal, it should be mixed down
>with the original carrier at DC. (Same for AM-DSB-SC)
>The Nyquist bandwidth is then half the signal bandwidth.

I would argue that the Nyquist Bandwidth equals the full
(double-sided, if baseband) signal bandwidth, because of the
generalization that I presented in my earlier post. When viewed that
way, the Nyquist Rate is always equal to the Nyquist Bandwidth,
whether the signal is baseband or modulated, real or complex.
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.
Note that all of these entities are based upon characteristics of the
signal to be sampled, not of the sampling itself.
-- Greg

Reply by jim●October 28, 20082008-10-28

Greg Berchin wrote:

>
> On Mon, 27 Oct 2008 17:31:08 -0700 (PDT), robert bristow-johnson
> <rbj@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". :-)

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.
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?
-jim
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Reply by robert bristow-johnson●October 28, 20082008-10-28

On Oct 28, 9:53�am, Rune Allnor <all...@tele.ntnu.no> wrote:

>
>
> 'Nyquist frequency' and 'Nyquist rate' are the same thing.

no they're not. i don't think there is a single textbook reference
that would support that, Rune. some people (like O&S) might say that
the Nyquist rate is always twice the Nyquist frequency (and i don't, i
believe the consensus convention is that the "Nyquist rate" is a
property of the signal to be sampled and the "Nyquist frequency" is a
property of the system doing the sampling), but i don't know of a
single reference that says they're the same.
it's just a convention of definition, but it's important for efficient
communication of ideas. i think that poor conventions die away due to
disuse and better conventions survive.
r b-j