Wind/Solar Electrics ???

Joel Kolstad wrote:

(I can't tell you how many times I've seen people stating something like,
'The Nyquist theorem requires sampling at at least twice the highest
frequency present in the signal," when of course it says no such thing.)

What do you think it means?

Nick

wrote in message
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Joel Kolstad wrote:
(I can't tell you how many times I've seen people stating something like,
'The Nyquist theorem requires sampling at at least twice the highest
frequency present in the signal," when of course it says no such thing.)

What do you think it means?

It means that perfect reconstruction of a signal requires sampling at at least
twice the _bandwidth_ of the signal present to insure that no aliasing occurs.

Two important points he

1) It's the bandwidth of the signal that matters, not the highest frequency
present (this is kind of the analog version of the digitial guys' "it's the
edge rate that matters, not the clock speed"). This fact is frequently used
to great advantage in radio receivers (and plenty of other designs, I'm sure).
2) The assumption that aliasing is inherently detrimental is not always true.
I've seen designs where well-defined bandpass filters were stuck in front of
an ADC and the aliasing was used _to advantage_ to let the ADC sample at much
closer to 2x then one could have obtained with more traditional filter design.
(Although I'd admit that this seems to have been more common when ADCs were
slower and you had to use all the tricks you could to get performance out of
them.)

---Joel

Joel Kolstad wrote:

1) It's the bandwidth of the signal that matters, not the highest frequency
present...

One might say "the highest frequency present" is the highest frequency
non-zero component of the power spectrum.

Nick

wrote in message
...
Joel Kolstad wrote:
1) It's the bandwidth of the signal that matters, not the highest frequency
present...
One might say "the highest frequency present" is the highest frequency
non-zero component of the power spectrum.

Sure, but the point is that you can sample a signal that's has all (of a good
approximation thereof, e.g., 99%) of its energy between 144-148MHz (this is
the 2m amateur radio band) at 10MSps and recover everything. I.e., the
bandwidth of the signal is only 4MHz, so you only have to sample at something
8MSps.

Joel Kolstad wrote:
wrote in message
...
Joel Kolstad wrote:
1) It's the bandwidth of the signal that matters, not the highest frequency
present...
One might say "the highest frequency present" is the highest frequency
non-zero component of the power spectrum.

Sure, but the point is that you can sample a signal that's has all (of a good
approximation thereof, e.g., 99%) of its energy between 144-148MHz (this is
the 2m amateur radio band) at 10MSps and recover everything. I.e., the
bandwidth of the signal is only 4MHz, so you only have to sample at something
8MSps.

IIUC that woudl demodulate the signal too?

NT

"Joel Kolstad" wrote in message
...
wrote in message
...
Joel Kolstad wrote:
1) It's the bandwidth of the signal that matters, not the highest
frequency
present...
One might say "the highest frequency present" is the highest frequency
non-zero component of the power spectrum.

Sure, but the point is that you can sample a signal that's has all (of a
good approximation thereof, e.g., 99%) of its energy between 144-148MHz
(this is the 2m amateur radio band) at 10MSps and recover everything.
I.e., the bandwidth of the signal is only 4MHz, so you only have to sample
at something
8MSps.


Only if you demodulate the signal first.

daestrom

Simple hetrodyne system will do that. No demodulating
required.

"daestrom" wrote in
message
...

"Joel Kolstad" wrote
in message
...

Sure, but the point is that you can sample a signal
that's has all (of a
good approximation thereof, e.g., 99%) of its
energy between 144-148MHz
(this is the 2m amateur radio band) at 10MSps and
recover everything.
I.e., the bandwidth of the signal is only 4MHz, so
you only have to sample
at something
8MSps.


Only if you demodulate the signal first.

daestrom

Joel Kolstad wrote:

Hey Joel, what are you doing over here. Are you a pilot too?

I've used this for subsampling, although you have to be very careful of
clock jitter when you sub-sample. a couple picoseconds of jitter on the
sampling of a 100 MHz signal is going to add substantial noise to the
signal.


(subsampling, for those here who haven't a clue what we are talking
about...this is an airplane owner's forum after all...is taking
advantage of the nyquist theorum to sample at less than the frequencyt
of the signal when the bandwidth of the signal is narrow. For example,
if you have a signal centered at 100 Mhz that only has a 10 MHz
bandwidth, you can sample it at something less than 100 MHz and still
recover all of the information. The more generally held belief is that
you would need to sample it at greater than 200 MHz in order to not lose
information).

"Ray Andraka" wrote in message
news:deZqf.31975$Mi5.3388@dukeread07...
Hey Joel, what are you doing over here. Are you a pilot too?

Hi Ray!

Hmmm... no, I'm not a pilot, I just got sucked in by the cross-posting
(starting from sci.electronics.design) and the topic has drifted considerably
since it started.

I've used this for subsampling, although you have to be very careful of
clock jitter when you sub-sample. a couple picoseconds of jitter on the
sampling of a 100 MHz signal is going to add substantial noise to the
signal.

Yes it is... I suspect that's why that projects such as GNURadio (which
sub-samples using something like 80 or 100MSps ADCs) tend not to be as
sensitive as more traditional analog receivers. (Someone made the comment
that the FM decoder in GNURadio doesn't really even work as well as a $5
transistor radio, which is true enough albeit perhaps missing the point of how
cool/fun it is to be able to write any modulator/demodulator you like if
you're not looking for the ultimate sensitivty.)

(For example, if you have a signal centered at 100 Mhz that only has a 10
MHz bandwidth, you can sample it at something less than 100 MHz and still
recover all of the information. The more generally held belief is that you
would need to sample it at greater than 200 MHz in order to not lose
information).

I believe that folks who think you need to sample at 200MHz (the intuitively
reaosnable answer) are those who were never made to /had the opportunity to
open up an undergraduate signals & systems book. :-) Thinking about things
like modulation are so much cleaner in the frequency domain once one gets the
whole "multiplication in one domain is convolution in the other" bit down.

---Joel

wrote in message
...
Joel Kolstad wrote:

(I can't tell you how many times I've seen people stating something like,
'The Nyquist theorem requires sampling at at least twice the highest
frequency present in the signal," when of course it says no such thing.)

What do you think it means?


Nyquist figured out that higher frequency components of the input signal
will 'alias' and you will lose the ability to tell them from lower frequency
components. In order to avoid 'losing information' and not being able to
tell whether a particular sample stream was from a low or high frequency
component, Nyquist's theorem states you must sample at least twice as fast
as the highest component present.
http://www.cs.cf.ac.uk/Dave/Multimedia/node149.html
http://www.efunda.com/designstandard...sp_nyquist.cfm

A lot of folks mistake it to think you need to sample at least twice as fast
as the 'signal of interest' also, and try to ignore high frequency
components of the input because they're 'not interested in that noise'. But
what Nyquist proved was that any frequency in the sampled signal that is
more than 1/2 the sample frequency will 'alias' and 'wrap around' and be
*indistinguisable* from a frequency component that is less than 1/2 the
sample frequency.

For example, if sampling at 1000 hz, and the sampled signal is a 900 hz
'pure sine wave', the sampled data would look *exactly* the same as if you
had sampled a 100 hz 'pure sine wave'. They would be 'indistinguisable'.
So if/when you try to convert the sampled data back to analog, how do you
know whether it should reconstruct a 100 hz wave, or 900 hz? You don't, so
you have a conundrum.

So, to avoid losing this 'information' of being able to tell if you had a
100 hz or 900 hz input, the standard thing to do is filter the input so that
there is *no* 900 hz input. Then, the resulting sample data must have come
from the 100 hz component. And if/when you want to reconstruct it, you
*know* it should form a 100 hz signal because no 900 hz signal could
possibly been present (you eliminated it before sampling).

And as Joel mentioned earlier, since most low-pass filters do not have
perfect 'cutoff' (IIRC, simple first-orders 'roll off' at something like 3
db/decade), it is more common to eliminate any frequency component that is
more than about 40% of the sampling frequency.

daestrom